word formation hypothesis

Inflection and Derivation

Dr. will styler - lign 120, today’s plan.

Inflection, Derivation, and Split Morphology

Lexical Families

Inflectional Paradigms

How are words constructed when making language?

We’ve been thinking mostly about the surface result.

“What’s present at the end of the process”

… but there’s a process involved!

What is the nature of word formation in actual linguistic practice?

The Split-Morphology Hypothesis

Why might we want Morphology to be split?

• Many argue there are two stages of word construction!

Two ‘types’ of word formation

Deriving or creating ‘new words’

By Derivation (e.g. read -> readable, reader, unread)

Or by Compounding (e.g. readthrough, sight read, proofread)

These form lexical families of derivationally-related lexemes

Inflecting words to make the gramatically necessary forms during language use

Read -> reads, read, is read, has read

These form paradigms of inflectionally-related word forms

Inflection vs. Derivation Intuitions

What ‘belongs in the dictionary’?

Reader? Reading? Reads? Proofread?

Nerd? Nerdy? Nerds? Nerding? Nerd out?

What forms are missing?

Can you think of a noun which can’t take a plural?

Can you think of an adjective which can’t take un-?

What affixes change the lexical category of the base?

What affixes leave the word ‘meaning the same thing’?

So, how do we split morphology?

These represent two very different worlds

Not just for morphology!

We’re not going to take a strong stand on which one is correct

We’ll focus on the consequences of either of these perspectives for Language

But we will treat the inflection vs. derivation distinction as useful and meaningful

Paradigms and Inflection

Inflectional Morphology

The addition of morphemes which change the meaning of a lexeme in a given linguistic or grammatical context

Certain grammatical contexts demand certain forms

*“I see three cat yesterday”

• I saw three cats yesterday

*“John walk to work and see Jane dog”

• John walked to work and saw Jane’s dog

*“Walk in nature make me feel more alive”

• Walking in nature makes me feel more alive

These forms are very predictable

A given grammatical (e.g. 3sg) or situational (e.g. plural, past) context requires certain morphemes

We do not need to memorize (most of) them

These new word forms are generated ‘on the fly’

Inflectional Forms form Paradigms

A set of word-forms which belong to a single lexeme

Noun paradigms are often called declension classes

Verb paradigms are often called verb conjugations

Russian Case Marking Paradigm

Turkish possessive paradigm.

Spanish Verb Conjugations

Word Families and Derivation

How are words created.

A single unit of form and meaning, which may have many word-forms

Sometimes, lexemes are just made up

These words are roots , and are not analyzable

These words were not created from an existing word!

Often, new word-forms are created from existing lexemes

burn -> ‘burner’

left -> ‘lefty’

boy, soy -> ‘soyboy’

pad, phone, OS -> iPad, iPhone, iOS

beauty -> ‘beautiful’

tender -> ‘tenderness’

These words are analyzable, and multi-morphemic!

Derivational Morphology

Adding affixes or other morphological units to a lexeme to create a new word forms

This process creates ‘families’ of words

A list of word-forms which are all derivationally related to a single lexeme

Pretty, Prettily, Prettyish, Non-Pretty, Anti-Pretty, Prettify?

Tight, tighten, overtighten, tightener, tight-ish, anti-tighten?

Rock, rocklike, Rocky, De-rock, derocker, non-rock, Rockify/Rocken?

What about these?

Hook, Unhook, Rehook, Hooky, Hookup, Right Hook, Fish-hook

Rock, rocker, rock out, anti-rock, rock-esque

These are not considered word families

1) They introduce new concepts

2) The lexical category of the bases are different

3) The meanings are unpredictable (e.g. rocker, hooker)

… but this is still derivational morphology!

Word families can be treated like paradigms

… but they’re often incomplete.

Not all derivational affixes can apply to all lexemes

There’s less contrast in ‘sweeten’ vs ‘sweetify’, ‘unhappy’ vs. ‘non-happy’

• Compare ‘cat’ vs. ‘cats’, ‘walk’ vs. ‘walked’

The process is less predictable

You don’t know whether an affix ‘works’ without language knowledge

The meanings aren’t clear, necessarily

So, we have derivation and inflection

One builds paradigms, and changes words ‘online’ according to situational or grammatical context

One builds lexical families, and seems to produce new words which belong in the dictionary

What’s the problem?

Distinguishing Derivation and Inflection

How can you tell these apart.

“Am I looking at two members of a lexical family, or two forms in the same paradigm?”

“Where, in a split-morphology point of view, was this word formed?”

The ‘-ful’ in ‘bountiful’ is an example of…

The ‘-en’ in ‘darken’ is an example of…

The ‘-er’ in ‘computer’ is an example of…

The ‘-less’ in ‘tactless’ is an example of…

The ‘un’ in ‘unimpressed’ is an example of…

The ‘re’ in ‘re-adjust’ is an example of…

This can be trickier than it seems!

Sometimes, it’s tricky.

In Spanish, the diminutive is ‘-it@’

• Gato -> Gatito
• Señora -> Señorita
• Libro -> Librito
• Ardilla -> Ardillita

… but both ‘gatos’ and ‘gatitos’ can be pluralized

Is the Spanish diminutive inflection or derivation?

Many linguists consider this a continuum

Your textbook gives you a list of properties

… but even those point to gradience!

It’s complicated!

Luckily, we don’t need to make hard-and-fast decisions

We can think about the theoretical issues

… and talk about the things that are classically considered inflectional or derivational

Wrapping Up

There’s theoretical debate about the nature of morphology in the mind

Some morphology feels inflectional, some feels derivational

Inflectional seems like it builds new word forms on-line in paradigms

Derivational morphology seems to create new word form families in the lexicon

The line is blurry, but that’s OK!

For Next Time

• We’ll dive into inflection a bit more!

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How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk,  "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

Hypothesis Types

Hypotheses examples.

• Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on your research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

The Importance of Operational Definitions

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type suggests a relationship between three or more variables, such as two independent and dependent variables.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative population sample and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."
• "Children who receive a new reading intervention will have higher reading scores than students who do not receive the intervention."

Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

• "There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
• "There is no difference in scores on a memory recall task between children and adults."
• "There is no difference in aggression levels between children who play first-person shooter games and those who do not."

Examples of an alternative hypothesis:

• "People who take St. John's wort supplements will have less anxiety than those who do not."
• "Adults will perform better on a memory task than children."
• "Children who play first-person shooter games will show higher levels of aggression than children who do not." 

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when  conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a  correlational study  can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Thompson WH, Skau S. On the scope of scientific hypotheses .  R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:].  Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ?  PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies .  Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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3 Theoretical Issues in Word Formation

Rochelle Lieber is Professor of Linguistics at the University of New Hampshire. Her interests include morphological theory, especially derivation and compounding, lexical semantics, and the morphology-syntax interface. She is the author of several books: On the Organization of the Lexicon (IULC, 1981), An Integrated Theory of Autosegmental Processes (State University of New York Press, 1987), Deconstructing Morphology (University of Chicago Press, 1992), Morphology and Lexical Semantics (Cambridge University Press, 2004), and Introducing Morphology (Cambridge University Press, 2010). She is the co-author, with Laurie Bauer and Ingo Plag of the Oxford Reference Guide to English Morphology (Oxford University Press, 2013). Together with Pavol Štekauer she has edited two handbooks, the Handbook of Word Formation (Springer, 2005) and the Oxford Handbook of Compounding (Oxford University Press, 2009).

• Published: 08 January 2019
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This chapter surveys a number of frameworks and theoretical issues in the analysis of derivation and compounding that have occupied morphologists over the last six decades, and begins to assess what has been achieved over this period. Topics include the formal nature of word formation, the relevant units of analysis, the form of morphological rules and processes, the relationship of morphological theory to syntax and phonology, and the theoretical treatment of lexical semantics. The chapter also explores a variety of narrower issues such as bracketing paradoxes, headedness, the question of affix ordering, and the nature of derivational paradigms.

3.1 Introduction: what is the goal of a theory of word formation?

It makes sense to begin an overview chapter such as this with a ‘big picture’ question: what should a theory of word formation do, and how far has morphological theory gone in the past towards fulfilling that goal? For the most part, this chapter is intended to review a variety of frameworks and specific theoretical concerns that have occupied morphologists over the last six or so decades, but it also seems important to take the opportunity to assess what we have achieved over this period. Not all readers will agree with my assessment, but to the extent that it stimulates discussion about goals, the results can nevertheless be positive.

First, to be clear about my subject matter, I take word formation to refer to derivation and compounding, in other words to those processes that give rise to new lexemes and the semantic categories which those new lexemes instantiate, as opposed to inflection. Derivation can be effected by such formal operations as affixation, conversion, internal stem changes, and various sorts of non-concatenative processes, including reduplication, root and pattern, and subtractive processes. 1 The formal processes involved in derivation may of course figure in inflection as well, so it is important to delineate at least some functions and/or semantic categories that are typical of word formation: transposition (that is, change of category such as noun to verb, adjective to noun, and so on with little or no semantic addition beyond what results from the change of category 2 ), creation of agent, patient, and other participant forms, formation of evaluatives and terms denoting collectives, abstracts, negatives and privatives, spatial, relational and temporal forms, various aspectual categories of verbs, and so on. As ten Hacken ( 2014 ) shows, it is not always clear where to draw the line between inflection and derivation, and indeed, in the eyes of some theorists, whether to draw such a line at all. Nevertheless, we will proceed on the assumption that the division makes sense.

What then should be the overarching goal of a theory of word formation? From the perspective of a generativist like myself, the obvious answer would be to characterize the workings of the mental lexicon, by which I mean something fairly wide-ranging. 3 In the early days of generative morphology, the salient question for the theorist would have been “What are the mechanisms available to a native speaker of a language that allow her to produce and understand a potentially infinite number of new lexemes in that language?” But that characterization has a number of limitations. First, it puts the emphasis on the formal means of creating new lexemes and obscures questions of semantics. More seriously, it implies that the important questions in morphological theory are parallel to those in syntactic theory, namely the generation of forms, without considering whether the parallel is apt. I would argue that it is not, at least not entirely. We now know that there is an important difference between syntax and morphology: whereas storage plays at most a small role in syntactic theory, the question of storage is of serious importance in morphological theory, especially with regard to word formation. When we talk about the workings of the mental lexicon, we must consider not only the generation of forms but also their storage. And with storage, in turn, come issues of lexical access, of frequency effects, and of local analogy that do not arise in syntactic theory.

In § 3.2 I will begin by reviewing issues concerning the formal nature of word formation: the relevant units of analysis, the form of morphological rules and processes, the treatment of non-concatenative word formation. Section 3.3 takes up issues concerning the relationship of morphological theory to syntax and phonology. In § 3.4 , I will raise the issue of the relationship between theoretical treatments of word formation and accounts of lexical semantics. In § 3.5 , I will survey a variety of narrower issues that have been prominent in the theory of word formation over the years: bracketing paradoxes, headedness, the question of affix ordering, and derivational paradigms.

3.2 Theory and structure

One of the most basic issues with which the theory of word formation is concerned is the nature of the units that the theory manipulates. If we begin by looking at a complex word such as operationalize in English, a linguistically naïve but literate speaker of English might be inclined to divide this word into several pieces:

The separated parts of the word are meaningful units and illustrate examples of what linguists call morphemes , units that are traditionally defined as the smallest meaningful units of which words are composed. Morphological theories that accept the notion of the morpheme as a unit generally also assume that morphemes must be assembled or put together by rules of some sort that create complex forms with hierarchical structure. Such theories have come to be called, following Hockett ( 1954 ), Item-and-Arrangement (IA) theories. The IA paradigm lends itself to looking at word formation as a species of syntactic operation. IA theories of word formation were prominent in generative theory in the 1980s and 1990s, including the work of Lieber ( 1980 , 1992 ), Selkirk ( 1982 ), and Di Sciullo and Williams ( 1987 ), among others. Although these theories differ in detail, they share the basic assumption that morphemes are stored in the mental lexicon and assembled by a set of rules modeled on the phrase structure rules of generative grammar, as illustrated by the rules and structure in (2):

Pretheoretically, the notion of ‘morpheme’ seems relatively straightforward, especially in view of the simple example in (1), but discussions of the concept going back to the 1940s in the work of Bloch ( 1947 ), Hockett ( 1954 ), Nida ( 1948 ), and Harris ( 1942 ), as well as much subsequent work, including Anderson ( 1982 , 1992 ), Beard ( 1995 ), Aronoff ( 1994 ), among many others, have shown that it is not. The IA paradigm is easily applied to strictly agglutinative word formation like that exemplified in (1), but rapidly becomes problematic when we look at derivation that involves internal stem change (3a), reduplication (3b), subtraction (3c), or root and pattern relationships (3d):

In examples like those in (3), there are no obvious ‘pieces’ or ‘things’ that can be isolated to which we could assign a meaning like ‘pluractional’, ‘plural’, ‘nominalizer’, ‘intensive’, or ‘reciprocal’.

Even in a language like English that overall lends itself to an IA treatment, there are a number of aspects of word formation that challenge the classic definition of the ‘morpheme’. For example, English is rife with words of Latinate origin like report , deport , import , export , purport , transport , or report , remit , receive , regress , resist , refer which many native speakers perceive to be complex. That is, many speakers can segment them into two pieces (that is, re + port , de + port , etc.), although it is clear that the pieces exhibit no apparent constant meaning (see also operate in (2), which could be analyzed by some as oper-ate ). Similarly, in English we often find what Bauer, Lieber, and Plag ( 2013 : ch. 9 ) call ‘extenders’, by which they mean meaningless elements that appear under various circumstances between a base and an affix, for example, the ‑n- in Plato-n-ic or tobacco-n-ist . These too pose problems for the classic definition of morpheme.

One possible alternative to postulating morphemes as the minimal meaningful units of which words are constituted is to view complex words as indivisible, but related to each other and to their bases via formal operations which are more akin to phonological than to syntactic rules. This general framework has been called an Item-and-Process (IP) approach (Hockett 1954 ), 5 and has figured prominently in the work of Aronoff ( 1976 ) and Anderson ( 1982 , 1992 ), among many others. Returning to our initial example, a form like operationalize would be constructed by a sequence of operations of the following sort:

In their strictest forms IP theories claim that derived words have no internal structure, so that operation , operational , and operationalize are internally no more complex than operate , a point to which we will return below.

IP theories have the advantage that they are more easily able to account for the sorts of word formation illustrated in (3). Whereas it is prima facie difficult to isolate anything like morphemes in cases of internal stem change, reduplication, root and pattern word formation, and subtraction, all of these can be easily modeled as processes. For example, the pluractional stem formation rule in Anywa illustrated in (3a) can be stated as in (5):

Rules in IP frameworks can manipulate distinctive features for internal changes, and repeat or delete segments in cases of reduplication, root and pattern, or subtractive morphology.

However, this is not to say that IA frameworks are in principle incapable of accounting for so-called non-concatenative processes such as those illustrated in (3). Indeed, a prominent line of research beginning with the work of McCarthy ( 1979 , 1981 ) has developed the idea that morphemes can be units consisting of elements both above and below the level of the individual phonological segment. In cases of internal vowel or consonant change, morphemes can consist of individual distinctive features that get associated with a base. Lieber ( 1984 , 1987 , 1992 ) treats both consonant mutation and umlaut in such terms. For reduplication, morphemes can consist of timing units (C and V stripped of other distinctive features) (Marantz 1982 ) or prosodic constituents (McCarthy 1982 ) that are then associated with segmental material from the base, and subtractive morphology can consist of association of the segmental material of a base to a prosodic constituent smaller than that of the original (see, e.g., Lappe 2007 , on hypocoristics in English). In other words, this line of research argues that the units involved in so-called non-concatenative word formation may not look like classic morphemes, but that they can nevertheless be characterized as minimal meaningful units.

The interesting thing about this long-standing theoretical debate is that in the end IA and IP treatments of word formation (at least these early ones) do not end up too far from each other. IP claims to treat both concatenative and non-concatenative word formation in the same way are matched by IA claims that the same can be true in a framework that embraces the notion of the morpheme, as long as the morpheme can be composed of both sub-segmental units such as distinctive features and supra-segmental units such as timing units, syllables, or other prosodic constituents. One of the very clear differences between IP and IA theories was, however, alluded to above, namely that derived words in IP frameworks explicitly lack internal structure. The prediction is that rules of word formation should never have to refer to the internal structure of their bases. This claim has been disputed, however, in the work of Carstairs-McCarthy ( 1992 ) and Booij ( 2009b , 2010a , 2012 ). Bauer, Lieber, and Plag ( 2013 ) also point out facts from English that call the prediction into question, namely that there are affixes in English (‑ ancy/‑ency , ‑ine , ‑en V , ‑let , ‑ster ) that never attach to complex bases, and that therefore must have some way of ‘seeing’ whether a word is simple or complex. The preceding characterization of theories of word formation is somewhat simplistic, however. In assessing theories of inflection, Stump ( 2001 : 1–3) outlines a taxonomy that involves two intersecting axes that together define four sorts of theory (see also Stump, Chapter 4 this volume). With respect to one axis, frameworks can be either lexical or inferential . Lexical theories assume that inflections like English plural ‑ s are morphemes that have their own entries in the mental lexicon, just as lexemes do, whereas in inferential models inflections are introduced by rules and have no lexical entries of their own. This is essentially the distinction I outlined above between IA and IP theories. Orthogonal to this distinction is Stump’s distinction between incremental and realizational frameworks. In the former “words acquire morphosyntactic properties only as a concomitant of acquiring the inflectional exponents of those properties” (2001: 2); in other words, the rule or morpheme that introduces ‑ s also introduces the morphosyntactic feature [+plural]. In the latter, a base is associated with a set of morphosyntactic properties, in this case [+plural], and this in turn allows the association of that base with a formal exponent of those morphosyntactic properties, in English typically the exponent ‑ s , but in certain cases ‑ en , ‑ren , etc. Stump’s insight is that the lexical/inferential and incremental/realizational distinctions allow us to characterize four separate types of framework, each of which is instantiated in specific theories of inflection:

What is of interest to us here is not the way that these combinations play out in the realm of inflection—Stump argues that inflection is best served by theories that are inferential and realizational—but how (or if) they play out in terms of theoretical models of word formation. The IA versus IP discussion in essence focuses on the first of these axes (Lexical versus Inferential). Interestingly, there has been somewhat less explicit discussion in the literature of how the Incremental versus Realizational distinction plays out in terms of theories of derivation. It is to this point that I turn now.

Let us take as our starting point a highly productive English affix like the ‑ er that occurs in forms like writer , freighter , computer , villager . In an Incremental theory, we would either have an affix with an entry in the lexicon or a rule that introduces Xer . Either would also indicate both the category of the base and the categorial and semantic result of adding to the specified base. Both classical IA and IP frameworks are incremental in this sense, the Lexical version characterizing IA, the Inferential version characterizing IP. In the Realizational models, the ‑ er affix would again either have a lexical entry or be introduced by a rule of some sort, but what would differ is the information available in the entry or rule; specifically, the entry or rule would lack the derivational equivalent of ‘morphosyntactic’ properties. Rather, such properties would be a function of either the tree into which the affix is inserted in the Lexical version (for example in the framework of Distributed Morphology (Siddiqi, Chapter 8 this volume)) or the rule that effects the creation of specific word forms in the Inferential version (e.g. Lexeme Morpheme Base Morphology).

There are two issues that arise in realizational treatments of word formation that do not arise in incremental treatments. The first is how (or whether) to determine which of a number of potential affixes gets inserted into the tree or added by the word formation rule. Whereas for any given base, there is generally a single exponent for any given morphosyntactic constellation of features in inflectional paradigms, there are often a number of competing exponents in derivational categories. For example, alongside ‑ er , English has at least ‑ ant and ‑ ist as well. Bases are generally conventionalized with one or another of these affixes, but need not be. 6 A realizational model must have a plausible story about what determines the insertion of any given exponent into a particular tree.

Perhaps more vexing, however, is the question of what the derivational equivalent of ‘morphosyntactic’ features would be, that is, what kind of semantic representation the lexical affix is associated with in the tree or rule. Realizational theories of word formation by definition adhere to what Beard ( 1995 ) has called the Separation Hypothesis, where morphosyntactic or semantic properties of words are introduced separately from their phonological exponents. But adherence to the Separation Hypothesis makes it imperative that we be able to characterize what those morphosyntactic or semantic properties are. There is some consensus about what basic morphosyntactic features are of relevance to inflection (features of number, tense, aspect, person, etc.), but to date there is little systematic discussion of what range of distinctions are relevant in word formation and how they are to be represented. In Lexeme Morpheme Base Morphology, Beard ( 1995 : ch. 9 ) assumes that the same set of morphosyntactic features that figure in case-marking would also be available for characterizing derivation, so that one morphological rule in English would introduce a feature like AGENT which would eventually be matched for any given base with ‑ er or ‑ ant . But Beard does not discuss the full range of derivational possibilities such as derived verbs and adjectives of various sorts, evaluative morphology, or quantitative or relational affixation, for example. Therefore the actual execution of such a featural system for derivation is left to the imagination (see Stump, Chapter 14 this volume).

Distributed Morphology (henceforth DM) also does not fare particularly well in this regard, first because there is relatively little discussion of derivation in DM in the literature, but more importantly as there is almost no explicit development of the semantic or ‘morphosyntactic’ properties of derivational word formation. Where derivation is discussed at all, affixes are inserted under functional projections of various sorts or “flavors”, as Harley ( 2009 : 132) puts it. She points out in passing that functional heads that come to dominate affixes will have to be specified for semantic information, but characterizes this information only informally: verbal functional heads, for example, can come in varieties like CAUSE, BECOME, and DO, and adjectival functional heads in varieties like ‘characterized by’, ‘able to’, or ‘like’. The nature of the functional projections that would be needed to characterize the breadth of the derivational system of any language has yet to be discussed systematically. As Baeskow ( 2010a , 2010b ) points out, where derivational morphology is discussed at all (e.g. Volpe 2005 ; Siddiqi 2010 ), the subject tends to be transpositional morphology in which the semantic contribution of the affix (beyond the category change) is arguably small; as she points out, DM fares less well when faced with semantically robust category-changing affixes like English ‑ er , and even worse with non-category-changing affixes like English ‑ dom , ‑ hood , and ‑ ship .

Where does this leave us? One conclusion that might be drawn is that both lexical and inferential approaches to word formation have their strengths. Although lexical analyses are more easily applied to concatenative and especially agglutinative word formation and inferential analyses to non-concatenative processes, either approach can be adapted to either sort of formal process. The choice between incremental and realizational approaches, however, hinges on a subject that has received fairly little attention in the literature, namely, the semantic side of word formation. Indeed, one of the few attempts to provide a sustained and thorough account of the lexical semantics of word formation is found in the work of Lieber ( 2004 , 2006 ). I will return in § 3.4 to the place of lexical semantics in the study of word formation. The issue of how a semantic analysis of word formation is to be paired with the formal analysis has yet to be broached systematically, although see Lieber ( 2014a ) for a preliminary discussion of the problem.

3.3 Components: the place of word formation in the grammar

Theoretical issues that confront the study of word formation of course go beyond the nature of the units and the formal means by which complex words are to be generated. Morphology cannot be studied apart from other aspects of language like syntax, phonology, semantics, and pragmatics. Discussion of the interface of morphology with these components has largely centered on syntax and phonology, so these are the ones I will focus on here.

3.3.1 The interface with syntax

The historical development of morphology as a distinct field within generative grammar is a subject that has been well covered in the literature (see, e.g., Spencer 1991 ; Štekauer 2000a ; Scalise and Guevara 2005 ; Lieber and Scalise 2006 ; Anderson, Chapter 2 this volume; ten Hacken, Chapter 6 this volume; Montermini, Chapter 7 this volume), so I will not review it in detail here. Rather, I offer a brief synopsis in order to draw out the central issues that are at stake in this debate.

Most theorists would agree that the critical moment in this history was the publication of Chomsky’s ( 1970 ) ‘Remarks on Nominalization’. Before this watershed article, to the extent that morphology was studied at all among generativists, it was treated as a sub-field of syntax with what we would now recognize as matters of word formation—nominalizations, compounding—analyzed as the end result of transformational rules: Lees’ ( 1960 ) The Grammar of English Nominalizations is a prime example of such work, but Zimmer ( 1964 ) and Brekle ( 1970 ) might also be mentioned as examples of work in this vein. Whether or not Chomsky intended it this way, ‘Remarks’ was in effect taken as a manifesto for linguists to pay attention to morphology on its own terms. One way of doing this was to propose a distinct component for morphology apart from syntax; in the theoretical terms of the day, morphologists sought to claim their own turf. The formal secession of morphology from syntax was codified in various principles that can be grouped together under the rubric of the Lexical Integrity Hypothesis: among these are the Generalized Lexicalist Hypothesis (Lapointe 1980 ); the Word Structure Autonomy Condition (Selkirk 1982 ); the Atomicity Thesis (Di Sciullo and Williams 1987 ), all of which differ in detail, but not in spirit.

The essential issue in the lexicalist debate was the extent to which rules of morphology and rules of syntax can interact with each other. In frameworks that adhere to the strictest form of the Lexical Integrity Hypothesis, rules of morphology cannot manipulate or ‘see’ elements of structure above the level of the word and rules of syntax cannot manipulate or ‘see’ elements below the level of the word. In weaker versions of the Lexical Integrity Hypothesis, word formation is treated as the domain of the lexicon, separated from the syntactic component, although inflection is treated as a part of syntax (Anderson 1982 ).

Adherence to any form of the Lexical Integrity Hypothesis, of course, does not prevent us from postulating morphological rules that mimic or look like syntactic rules, as long as they are not syntactic rules per se. Theoretical frameworks like those of Lieber ( 1980 ) or Selkirk ( 1982 ), or treatments of compounding like those found in Roeper and Siegel ( 1978 ), are Lexicalist in the sense that syntactic rules and morphological rules do not interact, but in terms of the formal nature of morphological rules themselves they all take their cue from the syntactic theories of their day. Lieber ( 1980 ) and Selkirk ( 1982 ) propose various versions of phrase structure-like rules to form complex words, and Roeper and Siegel ( 1978 ) propose a lexical transformation to account for synthetic compounds.

By the mid 1980s, however, it was already quite apparent that there were types of data that called into question even the weaker versions of the Lexical Integrity Hypothesis. That is, attention began to be drawn to phenomena like so-called phrasal compounds (7), phrasal affixation (8), or affixal conjunction (9) that at least prima facie suggest some interaction of syntax and morphology:

Phenomena such as these are not unique to English of course: Savini ( 1983 ), Toman ( 1983 ), Hoeksema ( 1988 ), Lieber ( 1988 , 1992 ), and Lieber and Scalise ( 2006 ) offer similar examples from Afrikaans, Dutch, German, Italian, Spanish, and Japanese.

Three sorts of responses have arisen to such empirical challenges to the Lexical Integrity Hypothesis. The first involves arguments to the effect that phrasal compounding and phrasal affixation are only an apparent challenge to the Lexical Integrity Hypothesis because the empirical evidence is unconvincing. Analyses like those in Bresnan and Mchombo ( 1995 ) and Wiese ( 1996 ) try to argue that the phrasal element in such formations is strictly limited to lexicalized units or quotative contexts, and therefore that real access to syntactic operations is not necessary for morphological processes; to the extent that phrasal material appears in complex words, the phrases involved can be assumed to have some representation in the lexicon. But the corpus data in (7) and (8) suggest that this cannot be correct. The choice of phrasal element in such forms is apparently quite free. For those who accept that the data pose a real challenge, two responses are possible. On the one hand are theoretical frameworks that return to the pre-‘Remarks on Nominalization’ assumption that word formation is syntax: among these are Lieber ( 1992 ), Halle and Marantz ( 1993 ) and DM in general, and most recently Borer ( 2013 ). On the other hand are frameworks that allow for limited interaction between morphology and syntax, among them Lieber and Scalise ( 2006 ) and Booij ( 2010a ).

The question that we need to consider is once again what is really at stake in this debate. Early on, the Lexical Integrity Hypothesis amounted largely to a claim to legitimacy for the study of word formation within generative grammar. But the issue of legitimacy is no longer in question. In syntax-only theories, the appeal has always been to theoretical elegance: why postulate different sets of rules when one system might work for both morphology and syntax? But there is more at stake in the debate now than theoretical elegance: the real question is the extent to which words behave differently from phrases and sentences. 8 We should ask whether the distinction between words on the one hand and phrases and sentences on the other is categorical, gradient, or non-existent. The sort of data in (7)–(9) suggest that there is no strict categorical distinction, but I will argue that the choice between the latter two options cannot be based entirely on formal grounds or theoretical elegance, but might rather hinge on psycholinguistic issues such as the relative balance of rules and storage, the effects of frequency and analogy, and so on. We will return to these issues in §§ 3.5 and 3.6 below.

3.3.2 The interface with phonology

At about the same time that morphology was establishing itself as a legitimate subject for study in its own right, a separate thread of theoretical development began to explore the relationship between morphology and phonology. Arising from the treatment of phonological and morphological boundaries in Chomsky and Halle ( 1968 ), the framework of Lexical Phonology and Morphology looked at the interaction of rules of phonology and morphology. Again, the history of this development is available in such works as Spencer ( 1991 ), Kaisse and Hargus ( 1993 ), Giegerich ( 1999 ), Kaisse ( 2005 ), among others, so I will only briefly outline the main issues here.

Chomsky and Halle ( 1968 ) note that different derivational affixes in English exhibit different phonological behavior. Some affixes are associated with changing the stress pattern or segmental makeup of the bases to which they attach (or both), while others have no effect on either the stress pattern or segmental makeup of their bases; the former are associated with a + boundary in the theory of Chomsky and Halle ( 1968 ) and the latter with a # boundary. The boundary distinction of Chomsky and Halle ( 1968 ) is, however, not particularly explanatory: the real issues are why these affixes display different behavior, how this behavior is to be modeled in the grammar, and what sorts of predictions can be derived from the model.

The framework of Lexical Phonology and Morphology, developed in the work of Siegel ( 1974 ), Allen ( 1978 ), Kiparsky ( 1982b , 1985 ), Selkirk ( 1982 ), Rubach ( 1984 ), Halle and Mohanan ( 1985 ), Mohanan ( 1986 ), among many others, is an effort to answer these questions. Details differ from one theorist to the next, but the overarching idea behind the framework is largely the same, namely that rules of morphology are to be divided into levels or strata with each level associated with a specific block of phonological rules. Within each level we normally expect to find cyclic application of affixes and phonological rules where their environments are met, but once we leave a particular level we are in principle unable to revisit it. In English, Level 1 morphology and phonology contains roughly the + boundary affixes of Chomsky and Halle ( 1968 ) as well as irregularly inflected forms and phonological rules that assign stress and make segmental changes of various sorts to bases. Level 2 contains the # boundary affixes and other phonological rules, but crucially not the phonological rules of Level 1, so that stress, once fixed at the earlier level, cannot be affected by further affixation at the later level. The placement of compounding and regular inflection differs from one model to the next, as does the number of levels proposed for any given language, but in general compounding and regular inflection follow derivational affixation.

The theory of Lexical Phonology and Morphology makes clear predictions that Level n morphology in any given language should not be found outside Level n+1 morphology, and generally that derivational affixation should not be found outside compounds. Similarly, regular inflection should not be found inside either derived words or compounds. These predictions turn out to be problematic for a number of reasons, however. Gussmann ( 1988 ), for example, points to the cases where Level n affixes indeed do appear outside Level n+1 affixes, and as a result to the necessity for allowing loops between levels. He also points out that Lexical Phonology and Morphology has no explanation for the observation that even within a single layer there can be restrictions on the ordering of various affixes with respect to one another. Most tellingly, he identifies the general problem that treatments of Lexical Phonology and Morphology tend to weigh in far more heavily on the discussion of phonology than on the discussion of morphology. With regard to English, only a small subset of morphological phenomena is ever treated in any given work, and where specific affixes are explicitly assigned to Level 1 or Level 2, which affixes are assigned to which level seems to differ from one work to the next (compare Selkirk 1982 ; Kiparsky 1982b ; and Spencer 1991 , e.g.); no work in this tradition gives a systematic or comprehensive overview of morphology. What does emerge from the tradition of Lexical Phonology and Morphology, however, is the need to look more carefully at the issue of affix ordering, a subject to which we will return in § 3.5.3 .

Interestingly, while the issue of what governs the ordering of affixes has continued as an important matter of theoretical discussion since the heyday of Lexical Phonology and Morphology, it has largely been separated from the issue of the ways in which morphology can trigger phonological rules of various sorts. This line has received somewhat less attention, although it has been pursued in the work of Inkelas ( 1998 ) and Inkelas and Orgun ( 1998 ). They argue for what Inkelas and Orgun ( 1998 : 365) call ‘Co-Phonologies’, namely “the phonological mapping associated with a given morphological construction”. More recently, Bauer, Lieber, and Plag ( 2013 : ch. 9 ), in a detailed treatment of the morphology of English, come to the conclusion that “each derivational category comes with its own set of phonological restrictions and properties, and that the stratal division of the lexicon is at best a gradient in psycholinguistic or statistical terms (Hay 2001 ; Plag and Baayen 2009 ) and at worst non‑existent in structural terms…” (Bauer, Lieber, and Plag 2013 : 164). Indeed, they give extensive support to the idea that each affix in a language can potentially be subject to a different array of phonological behaviors. 9

3.4 Morphological theory and lexical semantics

While issues of the formal nature of rules and the relationship between morphology and other components of grammar have received extensive attention over the last three decades, issues pertaining to the semantics of word formation have been given far less attention. In this section I will outline some of the theoretical issues that arise in the study of the semantics of word formation, looking first at the semantics of derivational affixes and then at compounds.

3.4.1 Derivation

Until relatively recently, little attention has been paid to the systematic modeling of the semantics of derivation, and what has been done has concentrated on the semantics of affixation. There is no doubt much to be said about the semantics of non-concatenative processes, but I will make the assumption here that the semantic properties of such formal processes are not in principle different from those of concatenative processes, and therefore will confine the discussion to the semantics of affixation.

Lieber ( 2004 ) suggests that there are a number of theoretical issues that must be addressed in a theory of the semantics of affixation. First and foremost is the need to have a system of representation that is broadly cross-categorial, in the sense that it can account equally well for the semantic properties of nouns, verbs, adjectives, and adverbs, in other words, all open lexical categories. Second, it must be able to characterize the semantics not only of category-changing derivation but also non-category-changing derivation. And finally, it must account for two important properties that appear frequently in derivation. First, affixes are often polysemous, in the sense that a given affix can display a number of more or less related meanings: the classic example is that of English ‑ er which can form not only agent and instrument nouns ( driver , computer ), but also stimulus ( thriller ), location ( diner ), quantity ( fiver ), means ( stroller ), and even patient ( loaner ) nouns. Second, languages frequently have several affixes that display the same meaning, and indeed the same range of polysemy (e.g. ‑ ize and ‑ ify in English). The relationship between form and meaning in affixation is often not one-to-one. The question, then, is how to characterize the meanings that can be conveyed by affixes or other word formation processes such that they explain these properties.

It has been common in the literature on morphology to assume that the meaning of lexical items is divided between a relatively more formal part that is relevant to syntax, variously called event structure (Rappaport Hovav and Levin 1996 , 1998 ), grammatical semantic structure (Mohanan and Mohanan 1999 ), argument structure (Pustejovsky 1995 ; Baeskow 2010a ), or the semantic skeleton (Lieber 2004 ), and a less formal part that contains those encyclopedic elements of meaning that are of no syntactic relevance. These aspects of meaning have been called the constant (Rappaport Hovav and Levin), the encyclopedia (Harley and Noyer 2000 ), or the semantic body (Lieber 2004 ). Most theorists construct the formal part of the lexical semantic representation as a hierarchically arranged system of functions and their arguments. Where theoretical treatments differ is in the explicitness with which the functions themselves are articulated. Lieber ( 2004 ) provides the most detail in this regard, proposing a number of binary and privative features that can characterize lexical semantic skeletons as well as a principle of coindexation by which the arguments of affixal skeletons can be integrated with those of their bases. Affixal polysemy arises in this system by virtue of the relatively underspecified semantics of affixal skeletons as well as from their general lack of encyclopedic content. The existence of multiple affixes with the same function follows from the small semantic space circumscribed by the featural system. Baeskow ( 2010a , 2010b ) begins to develop a similar system, but makes use of a somewhat different set of features in her formal representations of affixal meanings; she adds as well the notion of prototypes and of qualia structure (Barsalou 1992 ; Pustejovsky 1995 ) to account for affixal polysemy.

A somewhat different tack is taken in what Baeskow ( 2010a , 2010b ) refers to as Neo-Constructionist models, by which she means both DM and Borer’s ( 2005a , 2005b ) Exo-skeletal model of derivation. In Neo-Constructionist models the formal aspects of meaning are presumably represented by the functional projections of the syntactic tree, with encyclopedic elements of meaning being relegated to so-called Vocabulary Items. As mentioned in § 3.3.1 above, this is an aspect of DM that has been left largely underdeveloped, however, so it is as yet unclear to what extent DM will be capable of treating the semantics of word formation adequately. Borer’s ( 2013 ) analysis of argument structure versus referential nominalizations includes explicit discussion of the functional projections that determine the interpretion of those nominalizations, but does not yet offer an overall account of the functional projections that would be necessary to characterize a wider range of derivational affixes.

3.4.2 Compounding

Any treatment of compound semantics needs to account for a number of generalizations:

Headedness: compounds are frequently (although apparently not always) headed in the sense that one of the compound constituents determines both the syntactic category and the semantic type of the resulting compound.

Some compounds receive interpretations in which one constituent is construed as an argument of the other. In the tradition of English morphology, these are typically referred to as synthetic compounds, but as this term is not entirely applicable cross-linguistically, I will use the term argumental compounds instead (see also Bauer, Lieber, and Plag 2013 ).

In non-argumental compounds the semantic relationship between the first and second compound constituent is largely unpredictable.

It would be impossible in the small space of this section to do justice to the extensive literature on the interpretation of compounds, so I will focus here on two issues that have occupied the attention of theorists in the last several decades. An excellent general overview of the topic can be found in ten Hacken ( 2009 ).

The first issue is the extent to which the relationship between the head and non-head constituents of non-argumental compounds is determinate and therefore a matter to be modeled in our grammar. In early treatments of compounding, for example Lees ( 1960 ) and Levi ( 1978 ), the attempt was made to treat the semantics of non-argumental compounds as fully determinate, and specifically to characterize compound meaning using a fixed list of semantic functions like made of, used for, similar to, used by , and so on. There are several problems with such treatments. First, it is impossible to arrive at a constrained, finite list of functions, as a potentially infinite number of relationships between compound constituents can be found. Second, for novel compounds at least, it is impossible to determine in advance which of a number of potential interpretations will be associated with the compound; that is, we have no way of knowing whether the function involved in the derivation of the compound rabbit blanket would be ‘used by’ or ‘made of’ or any other plausible predicate. Finally, in analyses in which the semantic function determining the relationship between compound constituents is deleted by transformation, the rules involved must be unappealingly powerful.

The majority of theorists have therefore taken the position that there is no grammatical or semantic rule that generates compound interpretation in non-argumental compounds. An exception in this regard is Jackendoff ( 2009a ), which is a relatively recent attempt to treat compound semantics as a result of a number of semantic schemas; Jackendoff’s Parallel Architecture account is far more successful than early attempts at modeling the semantics of non-argumental compounds, however, in that his theory allows for the free generation of new schemas. Another approach is that of Štekauer ( 2005b ), who examines in an experimental study the probability with which speakers associate a novel compound with one meaning or another.

The second matter that has received repeated attention over the years is the mechanism by which the non-head of an argumental compound receives its interpretation. The claim is typically made that the non-head constituent in argumental compounds is generally to be interpreted as the internal argument of the verb from which the head constituent is derived (e.g. truck driver ), or possibly as an adjunct ( pan frying ), but never as an external argument (i.e. child eating is only possible if it involves cannibalism). The earliest accounts of argumental compounds are purely syntactic (Lees 1960 ). Roeper and Siegel ( 1978 ) provide the first treatment in the lexicalist tradition, proposing a so-called lexical transformation adhering to what they name the First Sister Principle, their way of encoding the restriction on the interpretation of the non-head constituent of argumental compounds to non-external arguments. Selkirk’s ( 1982 ) First Order Projection Condition and Lieber’s ( 1983 ) Argument Linking Principle do largely the same work in frameworks that do not allow lexical transformations. A return to purely syntactic analyses of argumental compounds can be found in the neo-transformational analyses of Roeper ( 1988 ) and Lieber ( 1992 ), following the work of Baker ( 1988 ) on noun incorporation, as well as more recently in the DM account of Harley ( 2009 ).

Interestingly, over this period, although the dispute over the formal mechanism that gives rise to the interpretation of non-argumental compounds has been vigorous, the range of facts on which these analyses have been based has largely remained the same. It is only with the corpus-based work of recent years that a wider range of facts has been noted that potentially calls these treatments into question. That is, it appears that, contrary to received wisdom, quite a few argumental compounds permit a reading in which the non-head can be interpreted as the external argument of the verbal base of the head. Lieber ( 2004 , 2009a , 2010 ) points out the existence of compounds like city employee in which the first constituent by necessity must be interpreted as the external argument of employ , but the existence of compounds like court desegregation , census enumeration , community exploration , or eyewitness misidentification in which context makes it clear that the first constituent is to be interpreted as external argument suggests that the analysis of argumental compounds faces challenges that have yet to be met. 10

3.5 Other theoretical issues

In the sections above we have looked at what might be considered ‘big picture’ issues that have been prominent in the theoretical modeling of word formation processes over the last four decades. Here we will look at a variety of issues that arise independently of the formal mechanisms embraced by a theory or the positioning of those mechanisms relative to other components of the grammar. I include here such issues as the applicability of the notion of ‘headedness’ to word formation, the characterization of productivity and blocking, the mechanisms that determine the ordering of affixes, so-called ‘bracketing paradoxes’, and the applicability of the notion of ‘paradigm’ to word formation.

3.5.1 Headedness

The notion of ‘head’ is a familiar one in syntactic theory: the head is typically defined as the item that determines the category and distribution of the phrase as a whole. Zwicky ( 1985c ), however, points out that in syntactic phrases there are a number of characteristics that contribute to the definition of head, among them that the head is the element that subcategorizes for or governs other items in the phrase, the element that determines agreement or concord, and the element that determines the semantic type of the whole. Starting with Williams ( 1981 ), the notion of head has been applied within morphology as well, although its utility has been the subject of substantial controversy (Zwicky 1985c ; Hudson 1987 ; Scalise 1988 ; Bauer 1990 ; Haspelmath 1992 ; Štekauer 2000b ; Scalise and Fábregas 2010 ). Williams ( 1981 : 245) defines the head as the element that “has the same properties” as the word as a whole. Among those properties that he mentions explicitly are category, inflectional class (which we will not be concerned with here), and lexical features, among which he counts features like [+latinate]. 11

The chief difficulty with applying the notion of head in complex words is that it only corresponds in part with the notion as it is used in syntax. As Zwicky ( 1985c ) points out, with respect to compounds one element (the righthand one in English) determines both the category, morphosyntactic features and semantic type of the complex word, although the element that is head in that sense cannot be said in any meaningful way to select for or subcategorize the non-head element of the compound. On the other hand some affixes do seem to select their bases, as well as determine the category and morphosyntactic features of the complex word, but cannot be said to determine semantic type, at least not in the same way we understand this with regard to phrases or compounds. Closer scrutiny complicates the picture with respect to affixation in that subcategorization or selection can be a two-way matter, with affixes selecting specific sorts of bases, but also bases selecting specific affixes (Bauer 1990 ; Giegerich 1999 ). Further, the existence of exocentricity in compounding—that is, compounds that either have no clear head (e.g. argumental compounds like pickpocket or coordinate compounds like parent–teacher in a parent–teacher conference ) or possibly two heads (e.g. coordinate compounds like blue-green )—strengthens the conclusion that the concept of head in word formation, whatever its utility, cannot be the same as it is in syntax.

Again, it is worth asking what is at stake in this debate. In terms of the morphological theory of the 1980s and 1990s, what was at stake was the legitimacy of modeling word formation rules on analogy to syntactic rules: if ‘head’ is an important notion in syntax, of necessity it must be in morphology, and more particularly, we would expect the notions to coincide. Insofar as some current theories of morphology continue in this tradition (see § 3.3.1 ), the problem of determining what we mean by the head of a complex word still remains. But in other frameworks, it is not clear that much is at issue, in the sense that ‘head’ may be defined independently for morphology and syntax, or dispensed with altogether in morphology. For example, in a recent assessment of the notion of headedness in the framework of Construction Morphology, Arcodia ( 2011 ) notes that headedness in word formation is not a phenomenon per se, but something that emerges more or less strongly as a higher-level generalization across schemas. Indeed nothing would be missed in the theory if the notion of head were dispensed with altogether.

3.5.2 Productivity and blocking

Another issue that is largely independent of and orthogonal to major theoretical debates concerns two interlocking concepts: productivity and blocking. Productivity is concerned with the ease with which new words can be formed using various word formation processes. Blocking is concerned with the purported tendency of an existing word with one meaning or function to preclude the coining of another word with the same meaning or function. While the definition of productivity has not been hugely controversial, how to measure productivity has been more so, and especially perplexing has been the question of what blocking is, or even whether it exists at all.

Discussions of productivity often start with inflection, as inflection typically presents a relatively clear pattern. Inflectional processes tend to be highly productive in the sense that every noun will have some sort of plural and every verb some sort of past tense in a language which inflects for those distinctions. Further, the existence of one inflected form, say, an irregular plural like mice or feet , will typically preclude the existence of a regular form (* mouses , * foots ). In contrast, derivation presents a much less neat picture and indeed necessitates a closer look at these concepts. Unlike inflection, derivational processes can differ widely in their productivity. Although some processes may be every bit as productive as inflectional processes (e.g. suffixation of ‑ ness in English), others may show only moderate productivity (e.g. ‑ ity or ‑ ment ), and others might be entirely unproductive (e.g. ‑ th ). Bauer ( 2001 ), following Corbin ( 1987 ), teases apart two strands in the notion of productivity. First, we can treat word formation processes in a binary fashion as being either available or unavailable. Then, for those that are available, we can focus on the degree to which they can be used, so that word formation processes may be more or less profitable. In other words, word formation processes either give rise to new words or they don’t ( availability ) and if they do, may do so to a greater or lesser extent ( profitability ).

How to measure productivity in more than an impressionistic way is a dicier matter. The productivity of a word formation process cannot be assessed simply by counting types in a dictionary, for example, as the point of measuring productivity is not to see how many words there already are with a particular affix, but how many words in principle there could be. Further, word formation processes frequently have restrictions of various sorts. Some affixes may attach only to bases of specific syntactic and semantic categories or to bases that have a particular segmental or prosodic shape. One might think that the more restrictions that accrue to a process, the less productive it is likely to be. But as Aronoff ( 1976 ) points out, perhaps what we should be concerned about in assessing productivity is not how restricted the pool of bases is for a given affix, but the extent to which an affix is found to attach to those bases that meet the relevant restrictions.

Another way of looking at the productivity of an affix is to observe frequency patterns of derivatives with that affix in a corpus. As Baayen ( 1989 , 1992 ) suggests, the more productive a process the higher the proportion of low frequency formations we expect to find formed by that process, in a corpus; he argues that the proportion of hapaxes (defined as items with a frequency of one) in a corpus formed with a particular affix to the overall number of tokens formed with that affix can give a rough measure of productivity in this sense. Further, the higher the proportion of low frequency items, the likelier we are to find a process semantically transparent. In other words, there is an inverse correlation between semantic compositionality and frequency: the more high frequency items are to be found with an affix, the higher the level of lexicalization they display.

Intimately intertwined with the notion of productivity is the notion of blocking. Aronoff ( 1976 : 43) defines blocking as “the nonoccurrence of one form due to the simple existence of another”. The example he gives is that simplex forms like glory or fury seem to block forms like gloriosity and furiosity . 12 The assumption that seems to lie behind blocking is that for items that are listed (as opposed to coined on line), there is only one semantic slot to fill in the mental lexicon. Once a slot is filled, another form cannot be coined to fill that slot; so furiosity is blocked by fury , but furiousness can be formed, as long as we assume that the output of highly productive word formation processes is not stored (an assumption that has been called into question in the psycholinguistic literature; see, e.g., de Vaan, Schreuder, and Baayen 2007 ). Much of the discussion of blocking (e.g. Kiparsky 1983 ; van Marle 1985 ; Rainer 1988 ; Plag 1999 ; Giegerich 2001 ) is devoted to discussing the precise mechanisms that account for the phenomenon, trying to make blocking follow from other aspects of the grammar—say stratification or the Elsewhere Condition—or from functional principles like the avoidance of synonymy. But such theorizing presupposes that speakers actually do avoid synonymy and therefore that blocking actually is a phenomenon in need of explanation. I would argue that it is not.

Bauer, Lieber, and Plag ( 2013 : 568) note that there are two sorts of problems with the idea of blocking. First, in this age of massive corpora it is impossible in principle to make clear-cut judgments on the occurrence or non-occurrence of particular forms; it is dangerous to rely on our intuition for such judgments, as words that might seem implausible or downright bad can often be found attested in a large enough corpus, and indeed can seem entirely unremarkable in context. Second, if the function of blocking is to avoid synonymy, we need to be clear on what we mean by synonymy if the concept is to be useful. If items cannot be deemed synonymous unless they are identical not only in denotation, connotation, and register, but also must be used by all members of a speech community (according to gender, socioeconomic status, and so on) at a specific moment in time, we would have a hard time proving any pair of words ever to be synonymous. If we stick to denotation, connotation, and register alone, however, the concept of blocking turns out to be chimerical.

A prime example might be the cases of English ‑ ity and ‑ ness . Riddle ( 1985 ) has argued that although doublets occur with these affixes, there is always a subtle difference in meaning between the items in the pair. She points to examples like hyperactivity , which is a medical condition, as opposed to hyperactiveness , which is merely a property that can be attributed to an individual without implying a diagnosis. More generally, she suggests that if doublets appear with these two suffixes, the ‑ ity form will always denote something that is more specialized or reified than the ‑ ness form. But as Bauer, Lieber, and Plag ( 2013 : 257–8) point out, it is not difficult to find pairs like purity and pureness , exclusivity and exclusiveness , passivity and passiveness that are attested in COCA in contexts that reveal no semantic distinction. Similar examples can be found in affixes that derive adjectives from nouns (‑ al , ‑ic , ‑esque , ‑y ) and even among negative prefixes ( in- , un- , de- , dis- , a- ) or affixes that form event/result nouns from verbs (‑ ation , ‑al , ‑ment , ‑ure , etc.). Indeed what we find is that derivational doublets abound, some of which reveal distinctions in meaning, but many of which do not. Data such as these point to the conclusion that blocking per se does not exist, and that our intuitions to the contrary must be the result of ease of lexical access in the mental lexicon, which in turn is linked to frequency effects.

3.5.3 Affix ordering

Another issue that is in principle independent of the choice of theoretical frameworks is that of accounting for the restrictions that can be observed on the ordering of affixes. To the extent to which the matter has been studied cross-linguistically several generalizations are agreed upon. First, it is normally the case that inflectional affixation occurs outside derivational affixation. Second, within derivation, it seems most often to be the case that the number of combinations of affixes that are attested is far smaller than would be predicted if just categorial selection were at stake; that is, if affix a attaches to adjectives and affixes b, c, and d form adjectives, we might expect a to be found on bases ending in any of b, c, or d. But this is rarely what we find. The question, then, is how to explain the restrictions that we do find.

The earliest extended treatments of affix ordering phenomena in the generative tradition are in the framework of Lexical Phonology and Morphology, discussed in § 3.3.2 above. Theoretically, any affix at Level 2 should attach to the output of both Level 1 and Level 2, assuming that the c-selectional properties of that affix are met. But as Fabb ( 1988 ) points out, this is not at all the case. In English, far fewer combinations are attested, and Fabb argues that other principles must be at stake. His solution is to assume that ordering restrictions follow entirely from selectional properties of individual affixes. Aronoff and Fuhrhop ( 2002 : 61–5) argue that there can also be language-specific constraints on affix ordering: they suggest that German, for example, has a class of closing suffixes including ‑ heit/‑keit , ‑in , ‑isch , among others, by which they mean suffixes that must be the last affix in a word, unless some sort of linking element is added outside them to facilitate further affixation (so schönheitslos ‘beautyless’ is possible, but not schönheitlos ). For English they propose the constraint that only one Germanic suffix is possible in any derived word. 13

Hay ( 2002 , 2003 ) argues that affix ordering is largely driven by principles that are less formal and more psycholinguistic in nature, an approach that has been called by Plag ( 2002 : 528) “Complexity Based Ordering”. According to this principle, the ordering of affixes is a matter of their parseability, that is, the extent to which they can be easily separated from their bases, as well as the extent to which their effects are semantically transparent. More parseable affixes will occur outside less parseable ones. Crucially, parseability may differ for a given affix from one form to the next, so that, for example, the suffix ‑ ment is less parseable in a word like government than in one like amusement . Work along these lines is pursued in Plag ( 2002 ), Hay and Plag ( 2004 ), Baayen and Plag ( 2009 ), Manova ( 2010 ), and Zirkel ( 2010 ), among others. For a much more complete overview of the subject of affix ordering, the reader is referred to Saarinen and Hay ( 2014 ).

3.5.4 Bracketing paradoxes

The term ‘bracketing paradox’ is used to refer to several different kinds of structural mismatches that can be found in complex words; it is not a unitary phenomenon. On the one hand, we find cases where the arrangement of morphemes that is dictated by phonological restrictions on affixation is different from that implied by the semantic interpretation of the complex word: so, for example, the form unhappier must be structured as [un [[happy]er]] on the grounds that comparative -er in English does not typically attach to trisyllabic bases, but as [[un[happy]] er] on the basis of its meaning ‘more unhappy’. On the other, we find cases like ungrammaticality which are given the structure [un [[grammatical] ity]] in order to conform to the level-ordering of Lexical Phonology and Morphology, but where the semantic interpretation would dictate the structure [[un [grammatical]] ity]. Similar to the ungrammaticality cases are cases like transformational grammarian or nuclear physicist (Spencer 1988 ) in which semantics dictates that the compound be internal to the derivational affix, whereas derivation is typically assumed to be internal to compounding.

What is important to note is that the two cases can be treated quite differently. Whether cases like ungrammaticality or transformational grammarian constitute bracketing paradoxes is a theory-internal matter. In theories that are not based on level-ordering, there is nothing that forces the structure in which un - is external to ‑ ity . Similarly, if one’s theory allows affixation to apply to compounds, as the data in Bauer, Lieber, and Plag ( 2013 ) suggest is necessary, only one structure is necessary for the transformational grammarian cases, namely the one that coincides with the semantic interpretation. Cases like unhappier are not so easily dismissed, however.

As nicely summarized in Spencer ( 1991 : ch. 10 ), there have been a number of approaches to bracketing paradoxes in the literature, including principles of lexical relatedness (Williams 1981 ; Masini and Audring, Chapter 18 this volume), mapping (Sproat 1985 ), and movement (Pesetsky 1985 ). However, if we must only account for the unhappier class of cases, a simpler solution is available. If we assume that words have both prosodic structure and morphological structure, as seems likely on independent grounds, and that the two structures need not be isomorphic, we can adopt an approach in which so-called bracketing paradoxes are simply words that have non-isomorphic prosodic and structural analyses. Both Aronoff and Sridhar ( 1983 , 1987) and Booij and Lieber ( 1993 ) approach bracketing paradoxes in these terms.

3.5.5 Derivational paradigms

I briefly take up one final theoretical issue here which has not been prominent in the literature, but which perhaps should be more so, that is, the question of whether the notion of ‘paradigm’ is of relevance with respect to word formation, as opposed to inflection. For a recent general overview of the topic, see Štekauer ( 2014 ). What we mean by ‘paradigm’ is a bit different with regard to derivation than with regard to inflection. In the latter case, we can think of a paradigm as the set of word forms that realize all relevant inflectional properties for a given lexeme (Bauer 2004a : 80–1). For derivation we are dealing by definition with sets of different lexemes, so what we mean by derivational paradigms are sets of derived forms that share the same base. These are sometimes referred to as morphological families.

We might ask whether there is any need for the derivational paradigm as a construct within a theory of word formation. Certainly the concept of morphological family has been shown to be a useful one in the psycholinguistic literature (Schreuder and Baayen 1997 ; Plag and Baayen 2009 ) in explaining results of reaction time experiments concerning derived forms. But even in purely theoretical terms the argument might be made for its utility as a theoretical construct. For example, there are pockets of derivation in English whose behavior is hard to explain in terms of independent rules because the primary relationship exhibited is not between the derived form and its base, but between two or more derived forms. Van Marle ( 1985 ) notes that there are semantic relationships that obtain between derived words sharing a base that cannot be explained simply by reference to the shared base. For example, Bauer, Plag, and Lieber ( 2013 , ch. 23 ) observe that for every noun in ‑ ism , there are potential derived forms in ‑ ist and ‑ istic . Interestingly, the ‑ istic adjectives frequently are more closely related semantically to the ‑ ism nouns than to the ‑ ist nouns; so communistic is typically interpreted as meaning ‘pertaining to communism’ rather than as ‘pertaining to communists’.

Another point of utility for the derivational paradigm is as a mechanism for explaining certain back formations. As Bauer ( 1997 ) and Štekauer ( 2014 ) point out, given a derivational paradigm like aggressive, aggressor, aggression …alongside active , actor , action , act , we are led to backform the verb aggress . In other words, the derivational paradigm supplies a frame in which local analogy can be said to operate.

A third area of interest involves so called ‘splinters’, that is, pieces of words that do not constitute morphemes in any classic sense, but which nevertheless give rise to new forms. For example, in English items such as - holic ( sexaholic , workaholic , chocoholic , yogaholic ) or - rific ( cheeserific , moisturific , Twitterific , splatterific ) cannot be said to constitute bona fide affixes, but they nevertheless allow creation of new forms on analogy to established forms like alcoholic or terrific . It might be argued that items of this sort are too marginal for a theory of word formation to owe them any formal treatment, but we dismiss them at our peril. Each one of these may give rise to only a handful of new forms, but there are a lot of such splinters and until we analyze them we do not really know what they have to tell us about word formation.

3.6 Conclusion

What can we conclude from this overview about the theory of word formation? First, I would argue that the nature of the formalism we use for modeling rules of word formation is perhaps not as critical as we once thought. Second, regardless of what we think about the formal nature of rules of morphology, the semantic characterization of morphemes (or morphological rules or functional projections that host morphemes) deserves much more attention than it has hitherto received. Most importantly, I suggest that we still have a lot to learn about the data that a theory of word formation should be responsible to. It goes without saying that theorists want to make the strongest possible claims that are consistent with the data, but we still have much to learn about what those data are, even for well-studied languages like English, Dutch, or Italian. Finally, attention to what might seem like small matters—whether or not blocking is a real phenomenon, the analysis of affix order, the nature of derivational paradigms and apparent local analogy as a mechanism for word formation—all point to a significant difference between morphology and other components. It is overwhelmingly clear that word formation involves computation of some sort—that is, the generation of new forms. But it is also apparent that because already coined words may be stored, some of the patterns we find may be attributed to the effects of frequency and the concomitant vagaries of lexical access. This suggests that although word formation may be analogous to syntax or phonology in some ways, it is nevertheless a unique domain that must be studied on its own terms.

What counts as non-concatenative is, of course, in part a theory-internal matter. In the work of McCarthy ( 1979 , 1981 ) and Marantz ( 1982 ), reduplication and root and pattern processes are non-concatenative.

Generally, the semantic effects of transposition have not been extensively studied, but see Spencer ( 2010 ) for some attention to the issue.

This is, of course, not the only possible answer to this question. For example, from the point of view of the onomasiological tradition, the overarching goal driving the theory of word formation is the characterization of the naming process, that is, the delineation of how concepts come to be instantiated in word forms. See Štekauer ( 2005a ) for an explanation of this perspective.

Root and pattern word formation is alternatively referred to as ‘templatic’ word formation, a term which I avoid here as it invites confusion with a sort of word formation found in highly polysynthetic languages in which affixes are ordered according to a series of slots or ‘templates’. See for example, Vajda ( 2014 ) for a treatment of the Yenisean language Ket in terms of templates in this sense.

Hockett ( 1954 ) outlines a third framework called Word and Paradigm (WP) which I will not discuss here, as it is more pertinent to theories of inflection than to theories of word formation; this model is especially prominent in the work of Matthews (1972) and Anderson ( 1992 ). See also Blevins, Ackerman, and Malouf (Chapter 13 this volume) and Stump (Chapter 14 this volume).

At least this is the commonsense understanding. We will return to this issue in § 3.5.2 on Blocking below.

COCA is the Corpus of Contemporary American English (corpus.byu.edu/coca).

Borer ( 2013 : 307) also appeals to theoretical rigor as an advantage of syntax-only accounts, although without comparing them to any specific lexicalist analysis.

Bauer, Lieber, and Plag ( 2013 ) prefer to characterize this behavior in terms of output conditions on affixed words rather than on the linear application of phonological rules.

All examples from the Corpus of Contemporary American English (COCA).

Williams also proposes what he calls the Righthand Head Rule (RHR), which determines the rightmost element in a complex word to be the head. I will not discuss the RHR here, as it is clear that from a cross-linguistic perspective it cannot be correct.

Rainer ( 1988 ) distinguishes between what he calls token blocking, also called synonymy blocking elsewhere in the literature (Giegerich 2001 ), and type blocking. The former is the sort of blocking that Aronoff defines. The latter involves cases where affixes that have the same function (say the suffixes ‑ al and ‑ ment , both of which form nouns from verbs) preclude each other. Plag ( 1999 ) argues that this should not be treated as blocking, but rather is a matter of competition between rival affixes, which is frequently governed by complementary selectional properties of those affixes.

As Bauer, Lieber, and Plag ( 2013 ) show, however, data from corpora like COCA suggest that it is not unusual to find more than one Germanic suffix in complex words in English.

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• How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2: Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

Step 5: Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

Step 6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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How to Develop a Good Research Hypothesis

The story of a research study begins by asking a question. Researchers all around the globe are asking curious questions and formulating research hypothesis. However, whether the research study provides an effective conclusion depends on how well one develops a good research hypothesis. Research hypothesis examples could help researchers get an idea as to how to write a good research hypothesis.

This blog will help you understand what is a research hypothesis, its characteristics and, how to formulate a research hypothesis

Table of Contents

What is Hypothesis?

Hypothesis is an assumption or an idea proposed for the sake of argument so that it can be tested. It is a precise, testable statement of what the researchers predict will be outcome of the study.  Hypothesis usually involves proposing a relationship between two variables: the independent variable (what the researchers change) and the dependent variable (what the research measures).

What is a Research Hypothesis?

Research hypothesis is a statement that introduces a research question and proposes an expected result. It is an integral part of the scientific method that forms the basis of scientific experiments. Therefore, you need to be careful and thorough when building your research hypothesis. A minor flaw in the construction of your hypothesis could have an adverse effect on your experiment. In research, there is a convention that the hypothesis is written in two forms, the null hypothesis, and the alternative hypothesis (called the experimental hypothesis when the method of investigation is an experiment).

Characteristics of a Good Research Hypothesis

As the hypothesis is specific, there is a testable prediction about what you expect to happen in a study. You may consider drawing hypothesis from previously published research based on the theory.

A good research hypothesis involves more effort than just a guess. In particular, your hypothesis may begin with a question that could be further explored through background research.

To help you formulate a promising research hypothesis, you should ask yourself the following questions:

• Is the language clear and focused?
• What is the relationship between your hypothesis and your research topic?
• Is your hypothesis testable? If yes, then how?
• What are the possible explanations that you might want to explore?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate your variables without hampering the ethical standards?
• Does your research predict the relationship and outcome?
• Is your research simple and concise (avoids wordiness)?
• Is it clear with no ambiguity or assumptions about the readers’ knowledge
• Is your research observable and testable results?
• Is it relevant and specific to the research question or problem?

The questions listed above can be used as a checklist to make sure your hypothesis is based on a solid foundation. Furthermore, it can help you identify weaknesses in your hypothesis and revise it if necessary.

Source: Educational Hub

How to formulate a research hypothesis.

A testable hypothesis is not a simple statement. It is rather an intricate statement that needs to offer a clear introduction to a scientific experiment, its intentions, and the possible outcomes. However, there are some important things to consider when building a compelling hypothesis.

1. State the problem that you are trying to solve.

Make sure that the hypothesis clearly defines the topic and the focus of the experiment.

2. Try to write the hypothesis as an if-then statement.

Follow this template: If a specific action is taken, then a certain outcome is expected.

3. Define the variables

Independent variables are the ones that are manipulated, controlled, or changed. Independent variables are isolated from other factors of the study.

Dependent variables , as the name suggests are dependent on other factors of the study. They are influenced by the change in independent variable.

4. Scrutinize the hypothesis

Evaluate assumptions, predictions, and evidence rigorously to refine your understanding.

Types of Research Hypothesis

The types of research hypothesis are stated below:

1. Simple Hypothesis

It predicts the relationship between a single dependent variable and a single independent variable.

2. Complex Hypothesis

It predicts the relationship between two or more independent and dependent variables.

3. Directional Hypothesis

It specifies the expected direction to be followed to determine the relationship between variables and is derived from theory. Furthermore, it implies the researcher’s intellectual commitment to a particular outcome.

4. Non-directional Hypothesis

It does not predict the exact direction or nature of the relationship between the two variables. The non-directional hypothesis is used when there is no theory involved or when findings contradict previous research.

5. Associative and Causal Hypothesis

The associative hypothesis defines interdependency between variables. A change in one variable results in the change of the other variable. On the other hand, the causal hypothesis proposes an effect on the dependent due to manipulation of the independent variable.

6. Null Hypothesis

Null hypothesis states a negative statement to support the researcher’s findings that there is no relationship between two variables. There will be no changes in the dependent variable due the manipulation of the independent variable. Furthermore, it states results are due to chance and are not significant in terms of supporting the idea being investigated.

7. Alternative Hypothesis

It states that there is a relationship between the two variables of the study and that the results are significant to the research topic. An experimental hypothesis predicts what changes will take place in the dependent variable when the independent variable is manipulated. Also, it states that the results are not due to chance and that they are significant in terms of supporting the theory being investigated.

Research Hypothesis Examples of Independent and Dependent Variables

Research Hypothesis Example 1 The greater number of coal plants in a region (independent variable) increases water pollution (dependent variable). If you change the independent variable (building more coal factories), it will change the dependent variable (amount of water pollution).

Research Hypothesis Example 2 What is the effect of diet or regular soda (independent variable) on blood sugar levels (dependent variable)? If you change the independent variable (the type of soda you consume), it will change the dependent variable (blood sugar levels)

You should not ignore the importance of the above steps. The validity of your experiment and its results rely on a robust testable hypothesis. Developing a strong testable hypothesis has few advantages, it compels us to think intensely and specifically about the outcomes of a study. Consequently, it enables us to understand the implication of the question and the different variables involved in the study. Furthermore, it helps us to make precise predictions based on prior research. Hence, forming a hypothesis would be of great value to the research. Here are some good examples of testable hypotheses.

More importantly, you need to build a robust testable research hypothesis for your scientific experiments. A testable hypothesis is a hypothesis that can be proved or disproved as a result of experimentation.

Importance of a Testable Hypothesis

To devise and perform an experiment using scientific method, you need to make sure that your hypothesis is testable. To be considered testable, some essential criteria must be met:

• There must be a possibility to prove that the hypothesis is true.
• There must be a possibility to prove that the hypothesis is false.
• The results of the hypothesis must be reproducible.

Without these criteria, the hypothesis and the results will be vague. As a result, the experiment will not prove or disprove anything significant.

What are your experiences with building hypotheses for scientific experiments? What challenges did you face? How did you overcome these challenges? Please share your thoughts with us in the comments section.

Frequently Asked Questions

The steps to write a research hypothesis are: 1. Stating the problem: Ensure that the hypothesis defines the research problem 2. Writing a hypothesis as an 'if-then' statement: Include the action and the expected outcome of your study by following a ‘if-then’ structure. 3. Defining the variables: Define the variables as Dependent or Independent based on their dependency to other factors. 4. Scrutinizing the hypothesis: Identify the type of your hypothesis

Hypothesis testing is a statistical tool which is used to make inferences about a population data to draw conclusions for a particular hypothesis.

Hypothesis in statistics is a formal statement about the nature of a population within a structured framework of a statistical model. It is used to test an existing hypothesis by studying a population.

Research hypothesis is a statement that introduces a research question and proposes an expected result. It forms the basis of scientific experiments.

The different types of hypothesis in research are: • Null hypothesis: Null hypothesis is a negative statement to support the researcher’s findings that there is no relationship between two variables. • Alternate hypothesis: Alternate hypothesis predicts the relationship between the two variables of the study. • Directional hypothesis: Directional hypothesis specifies the expected direction to be followed to determine the relationship between variables. • Non-directional hypothesis: Non-directional hypothesis does not predict the exact direction or nature of the relationship between the two variables. • Simple hypothesis: Simple hypothesis predicts the relationship between a single dependent variable and a single independent variable. • Complex hypothesis: Complex hypothesis predicts the relationship between two or more independent and dependent variables. • Associative and casual hypothesis: Associative and casual hypothesis predicts the relationship between two or more independent and dependent variables. • Empirical hypothesis: Empirical hypothesis can be tested via experiments and observation. • Statistical hypothesis: A statistical hypothesis utilizes statistical models to draw conclusions about broader populations.

Wow! You really simplified your explanation that even dummies would find it easy to comprehend. Thank you so much.

Thanks a lot for your valuable guidance.

I enjoy reading the post. Hypotheses are actually an intrinsic part in a study. It bridges the research question and the methodology of the study.

Useful piece!

This is awesome.Wow.

It very interesting to read the topic, can you guide me any specific example of hypothesis process establish throw the Demand and supply of the specific product in market

Nicely explained

It is really a useful for me Kindly give some examples of hypothesis

It was a well explained content ,can you please give me an example with the null and alternative hypothesis illustrated

clear and concise. thanks.

So Good so Amazing

Good to learn

Thanks a lot for explaining to my level of understanding

Explained well and in simple terms. Quick read! Thank you

It awesome. It has really positioned me in my research project

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Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

• Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
• Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
• Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
• Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
• Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
• Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

• Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
• Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
• Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
• Education : “Implementing a new teaching method will result in higher student achievement scores.”
• Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
• Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
• Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

• In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
• In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
• I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

• Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
• Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
• Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
• Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
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• Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

• Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
• Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
• Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
• Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
• Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
• Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

• Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
• May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
• May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
• Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
• Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
• May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

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According to Chomsky (1970), raising to subject and raising to object may not take place inside nominalizations. This claim has largely been accepted as fact ever since. For instance, Newmeyer (2009) repeats the claim as crucial evidence for the Lexicalist Hypothesis, the view that word formation takes place in a component of the grammar separate from the phrasal syntax. This paper shows with attested examples and survey data that the claim is false: raising to subject and raising to object are both grammatical inside nominalizations. This argues for a purely syntactic model of word formation, and against Lexicalist accounts. Additionally, the paper shows that one argument against syntactic accounts of nominalization, that from coordination, does not go through, clearing the way for the most parsimonious type of theory: one with only one combinatorial component, not two distinct ones for phrases versus words.

syntactic word formation, raising, nominalization, the Lexicalist Hypothesis, experimental syntax

How to Cite

Bruening, B., (2018) “Word formation is syntactic: Raising in nominalizations”, Glossa: a journal of general linguistics 3(1): 102. doi: https://doi.org/10.5334/gjgl.470

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1 Introduction

The literature includes two broad approaches to word formation. On the Lexicalist approach, the atoms of syntax are words, and word formation therefore requires a component of grammar separate from the phrasal syntax. In this type of theory, there are two distinct combinatorial systems in the grammar, the phrasal syntax and some word formation component. 1 According to the other view, there is only one component of grammar, a system of syntax. This system is responsible for putting all complex elements together, whether those things are words or phrases. The atoms of syntax in this approach are something smaller than words, something like morphemes. 2

This paper argues for the latter view and a model of grammar with only one combinatorial system. It does so by contesting the longstanding claim from Chomsky ( 1970 ) that raising to subject and raising to object do not take place in nominalizations. They actually do, as attested examples and an acceptability survey show. This, I argue, requires a syntactic account of nominalization, where the phonological word that pronounces a nominalization is put together by the syntax. Lexical analyses of nominalization cannot account for the attested patterns without additional stipulations. Additionally, some of the Lexicalist literature has argued against purely syntactic accounts of nominalization on the basis of coordination. I also address this argument, and show that it is without force. There is no issue from coordination for any syntactic account of nominalization, and the syntactic analysis is best at accounting for raising in nominalizations.

Section 2 begins by presenting new data regarding raising inside nominalizations. Section 3 proposes a syntactic account of nominalization and argues that Lexicalist accounts are inadequate. Finally, section 4 shows that the argument against syntactic accounts from coordination does not go through.

2 Raising is grammatical inside nominalizations

As stated above, Chomsky ( 1970 ) claimed that nominalizations may not include raising to subject or raising to object:

This claim was contested by Postal ( 1974: Chapter 10 ), but Chomsky ( 1977: note 47 ) and Kayne ( 1984: 142–143 ) dismissed Postal’s counterexamples. 3 The claim seems to have been accepted since. For instance, Jacobson ( 1990 ) uses the putative ungrammaticality of raising in nominalizations as an argument for her analysis of raising. Newmeyer ( 2009 ) cites such examples as crucial evidence for the Lexicalist Hypothesis, the hypothesis that (at least some) word formation is accomplished in a lexical component of grammar separate from the phrasal syntax.

According to Chomsky and Newmeyer, the Lexicalist Hypothesis rules out raising to subject and raising to object in the input to nominalization, because they are rules of the phrasal syntax. The output of lexical rules like nominalization feeds the phrasal syntax, and not vice versa. (See section 3 for discussion of Lexicalist models where raising is lexical rather than syntactic.)

In this section, I contest the claim that examples like (1b) and ones similar to (2b) are ungrammatical. I for one as a native speaker of English have always found (1b) perfectly acceptable. This is borne out by attested examples from corpora and an acceptability survey using Amazon Mechanical Turk. As for raising to object as in (2b), many speakers do not accept it with this particular word ( belief ), but examples of raising to object with nominalizations of other verbs are attested and accepted.

2.1 Attested examples

Numerous examples of raising to subject can be found with likelihood and certainty . I have found many examples on the web which I and others polled informally find perfectly acceptable:

Note that at least one of these comes from a published book.

Examples of clear raising to subject with likelihood can also be found in the Corpus of Contemporary American English ( http://corpus.byu.edu/coca/ ). Here are a few examples:

I found no clear examples of raising to subject in COCA with certainty , however.

As for raising to object, it too is attested in nominalizations, though at a much lower rate (and speakers judge them to be less acceptable in the survey reported below). I was unable to find any examples in COCA, but the following are some examples from the web:

Native speakers polled informally find at least some such examples to be acceptable, although they typically report that they are less acceptable than raising to subject. Many people do not accept raising to object with proof or belief (but numerous examples of proof appear on the web), but raising to object does seem to be acceptable with nominalizations of some other verbs (see the acceptability survey below).

These attested examples contradict the judgments reported in the literature by Chomsky ( 1970 ), Kayne ( 1984 ), Newmeyer ( 2009 ), and others. 4

2.2 Acceptability survey

I also conducted a survey using Amazon Mechanical Turk. For this purpose I made use of the free tools described in Gibson et al. ( 2011 ) and available at http://tedlab.mit.edu/software/ , modified for the purposes of this experiment.

The experiment used a 2 × 2 design with factors raising to subject (“Subj”) versus raising to object (“Obj”) and nominalization (“Nom”) versus clause (“Clause”) . Experimental items were constructed in sets of four on the following pattern:

Raising to subject predicates were only be certain and be likely and their corresponding nominalizations certainty and likelihood . The raising to object verbs used were acknowledge, pronounce, recognize, estimate, calculate, observe, presume , and calculate ( calculate was accidentally used twice). All of these have nominalizations with either -tion or -ment . The complete list of items appears in the appendix.

Eight sets of four were constructed and divided into four lists, so that each subject saw only one item from each set. Each subject rated two exemplars of each condition. Subjects rated each sentence on a scale of 1 to 5, as follows: 1: Extremely unnatural, 2: Somewhat unnatural; 3: Possible, 4: Somewhat natural, 5: Extremely natural. 5 Each sentence was also accompanied by a comprehension question to make sure that the subjects were not just answering randomly without reading the sentence. For the set above, the question was, Was that radical group eager to start a civil war? Questions were always answered yes or no and always had a right answer (an obvious one). Subjects were discarded from the analysis if they answered more than 25% of the questions incorrectly.

In addition to the 8 experimental items that each subject judged, each also rated 22 fillers. Six of these were items for an unrelated experiment. Two of these were judged by the experimenters ahead of time to be acceptable, while the other four were unacceptable (but survey participants actually judged 5 of the 6 to be unacceptable). The other 16 were control sentences that were created by modifying examples taken from the web, typically on-line newspaper articles. Each of the sixteen was manipulated to create an ungrammatical match, where the manipulation was changing the word order of S, O, or V, or a P and its object. A couple of examples follow (the ungrammatical sentences were not presented with the star):

As stated, there were 16 pairs of controls, and once again each subject saw only one member of each pair. Subjects therefore rated a total of 30 sentences (8 experimental items + 6 fillers from another experiment + 16 control items). A different list was created for each subject with the presentation order randomized.

120 participants (“workers,” in Amazon Mechanical Turk parlance) were recruited from within the USA. Ten subjects were excluded for reporting a language other than English as their first language, for getting less than 75% correct on the comprehension questions, or for leaving more than 20% of the questions unanswered. This left 110 subjects whose data entered into the analysis.

Median ratings and mean ratings and standard deviations are shown below (again, the scale is 1–5, 1: Extremely unnatural, 2: Somewhat unnatural; 3: Possible, 4: Somewhat natural, 5: Extremely natural):

For comparison, median and mean ratings on the grammatical and ungrammatical controls are shown below:

Various statistical tests indicate that there are significant differences between the four conditions. For instance, a two-way ANOVA shows a main effect of subject versus object (F(1,876) = 15.4038, p < 0.0001) and a main effect of clause versus nominalization (F(1,876) = 7.8591, p = 0.0052), as well as an interaction (F(1,876) = 12.9237, p = 0.0003). 6 Post-hoc pairwise t-tests show that Subj_Clause and Subj_Nom do not differ from each other (p = 0.9439), but Obj_Clause and Obj_Nom do (p < 0.0001). Subj_Nom and Obj_Nom also differ (p < 0.0001), but Obj_Clause and Subj_Clause do not (p = 0.9955), nor do Obj_Clause and Subj_ Nom (p = 0.8577). In other words, Obj_Nom differs from the other three conditions, which do not differ from each other.

These results indicate that native speakers of English do not consider raising to subject in nominalizations degraded in any way compared to raising to subject in clauses. In fact, the mean rating was actually higher for nominalizations than it was for clauses, although this difference is not significant. I conclude that Chomsky ( 1970 ) was simply wrong to claim that raising to subject does not take place in nominalizations. It does.

As for raising to object, it is rated lower in nominalizations relative to the other three conditions, which do not differ from each other. This indicates that it is not as acceptable as raising in clauses or raising to subject in nominalizations. On the other hand, the mean (and median) rating for the Obj_Nom condition is still quite high, much higher than the ungrammatical control sentences. It should also be noted that there is little evidence of a dialect split: only seven out of 110 subjects rated both Obj_Nom sentences that they saw 2 or 1. All eight of the Obj_Nom items were also rated quite high (a similar range for each), so it is not the case that one or two items were responsible for the slightly lower mean rating. It appears that overall, raising to object is simply slightly less acceptable in nominalizations than raising in clauses or raising to subject in nominalizations.

The question is what we are to make of this result. It is not possible to decide that below a given mean rating (say, 2.5) sentences are ungrammatical, and above that they are grammatical. For one thing, the judgments reported by subjects are judgments of acceptability, not grammaticality, and judgments of acceptability are affected by numerous non-grammatical factors (such as length, complexity, and familiarity). Such factors can both lower subjects’ ratings for sentences that we must consider grammatical, and raise subjects’ ratings for sentences that we must view as ungrammatical within a well-motivated model of grammar.

This means that we have two options. The first option is that we can decide that raising to object is not grammatical in nominalizations, but other factors lead subjects to rate such examples surprisingly high in acceptability. The second option is that we can decide that raising to object is grammatical in nominalizations, but other factors lead subjects to assign examples of it somewhat lower ratings of acceptability.

I believe that several considerations favor the second view. First, the median and mean ratings of the Obj_Nom condition are quite high, close to 4 on a 5-point scale (the median rating is 4). This is much higher than we would expect for truly ungrammatical sentences, at least without some kind of “illusion” of the type discussed in Phillips et al. ( 2011 ). No such grammaticality illusion seems to be at work here, however. In cases of grammaticality illusions, native speakers will initially accept the examples, but then, given more time, agree that the examples are actually unacceptable. This does not seem to be the case with the examples of raising to object in nominalizations. Typically, native speakers that I have consulted either do not revise their initial judgments at all, or they revise them positively given more exposure to such examples.

Second, we have now concluded that raising to subject is grammatical in nominalizations. Given that, we should have every reason to expect that raising of all kinds would be possible, since in most models of grammar raising to subject and raising to object are very similar, parallel operations. That is, within a motivated model of grammar, there is no reason to expect that raising to object would be ungrammatical in nominalizations, if we accept that raising to subject is. Third, there may be an independent reason that raising to object is judged slightly less acceptable than raising to subject. Consider first that Chomsky ( 1970 ) contrasted raising to subject in nominalizations, which he judged to be ungrammatical, with raising to subject in gerunds, which is acceptable:

According to Chomsky ( 1970 ), (at least some types of) gerunds are formed syntactically and can include any relation or operation that is part of the phrasal syntax. However, gerunds are not very acceptable with raising to object when the object is marked with of :

One could claim that all nominals with of , including gerunds, are lexically derived and so do not permit syntactic operations. However, gerunds with of do permit particles and they do not permit the logical object to appear as a prenominal possessor, in contrast with other nominalizations ( Abney 1987 ). These sorts of facts led Abney ( 1987 ) and others to propose syntactic accounts of gerunds with of . An alternative explanation is that there are restrictions on what can appear with of in a nominalized form of a verb. The first object of a double object construction never can, for instance ( Kayne 1984 ; Pesetsky 1995 ), see (14), and various verbs that take direct objects also do not allow those with of (15):

It appears that there are some (poorly understood) restrictions on what can appear with of , 7 and this is what leads subjects to view raising to object with nominalizations as less than fully acceptable, since the raised object in a nominalization must appear with of . This is not about the grammaticality of combining raising to object and nominalization, however, it is something about the acceptability of different kinds of objects with of . It is probably not the case that this is a hard grammatical constraint, since subjects do rate NPs raised to object and marked with of as fairly acceptable in context (see the examples in the appendix). Postal ( 1974 ) also presented examples like the following, which also seem to involve raising to object:

It is therefore possible in principle for a non-thematic object of a verb to appear marked with of in a nominalization derived from that verb. However, there seem to be some restrictions which make this less acceptable than raising to subject, although I cannot at this point say exactly what those restrictions are. One suggestion I will tentatively offer is that internal arguments marked with of in a nominalization are somewhat less acceptable if they are not canonical patients of the nominalized verb stem. 8

To sum up, several considerations favor the view that raising to object is grammatical but somewhat degraded in acceptability in a nominalization. I know of no considerations that would favor the opposite view according to which raising to object is ungrammatical in nominalizations, but something leads subjects to rate examples surprisingly high in acceptability. I conclude that both raising to subject and raising to object are grammatical within nominalizations. Raising to subject is not any less acceptable in nominalizations than it is in clauses. Raising to object is slightly degraded in nominalizations as compared to clauses, but this seems to be due to poorly understood factors governing the acceptability of NPs marked with of in nominalized forms of verbs. In principle, raising to object is grammatical in nominalizations, and any model of grammar should be able to capture this.

3 Discussion and analysis

Attested examples and the acceptability survey described in the previous section indicate that both raising to subject and raising to object do take place in nominalizations. In this section, I discuss the consequences of this finding and propose a purely syntactic account of nominalizations, adopting existing proposals from the literature.

3.1 Discussion: Lexical versus syntactic models

The first important point is that the facts of raising cannot be taken as an argument in favor of the Lexicalist Hypothesis, as Chomsky ( 1970 ) and Newmeyer ( 2009 ) presented them. Contrary to their assertions, raising to subject and raising to object do feed nominalization. In the kind of feed-forward view advocated by Chomsky ( 1970 ), nominalization could not be a lexical process if raising is syntactic. In this view, lexical processes strictly precede the syntax, and it is not possible for a syntactic process to feed a lexical one.

Can we then use the existence of raising in nominalizations to argue against the Lexicalist model, and for a purely syntactic theory with no separate lexical component? Not yet, because there are theories where raising is also accomplished lexically, for instance LFG and HPSG (e.g., Bresnan 1982a ; Pollard & Sag 1994 ; Müller 2006 ; Müller & Wechsler 2014 ). In this type of account, there is no syntactic raising at all. Rather, lexical entries for raising verbs simply specify that a certain syntactic argument is not a semantic argument of the verb but is instead interpreted as the subject of a non-finite complement of the same verb. For, instance, declare as a raising to object verb says that it takes an NP complement and a non-finite clause as another complement. The NP receives no interpretation with respect to the predicate declare , it is instead interpreted as the subject of the non-finite complement. So, in declare those acts to be wrong, those acts is syntactically but not semantically the object of the verb declare ; it receives its semantic interpretation solely from the lower clause. In this analysis, there is no syntactic raising, although we get the semantic effect of the object NP functioning as the logical subject of the non-finite clause. It receives no interpretation qua object. The analysis of control is almost identical, except that the object (or subject, in the case of subject control) is assigned two semantic roles, one as the missing subject of the infinitive and one as the object of the higher verb (see especially Pollard & Sag 1994: 132–145 ).

The raising to object stem, declare in our example, as a verb stem can undergo lexical rules that can affect verb stems. For instance, it can undergo a lexical rule of nominalization. This will relate the stem to a nominal declaration , which will inherit the argument structure of the raising to object stem. That is, it too will take an NP object and a non-finite clause, and the NP object will be interpreted as the semantic subject of the non-finite clause. This will be the raising to object declaration . (Presumably the declaration that takes a finite CP complement instead is related to a verb stem declare that also takes a finite CP complement; if one wanted to relate this form to raising-to-object declare , then another lexical rule would accomplish that.)

This type of lexical account is compatible with the facts as we have seen them here. However, there is an argument against this type of analysis, and for a purely syntactic account. This argument comes from Williams ( 2015: 312 ). In the opposing syntactic account, a verb stem takes a non-finite complement clause, out of which the subject raises to become the object of the verb stem. This entire syntactic construct forms the input to nominalization in an example like the following:

That is, the nominalization God’s declaration of them to be wrong can only be formed from the full phrase [ declare them to be wrong ], where the NP has undergone raising (see below for an analysis).

The difference between the two accounts is that in the lexical analysis, the nominalization is only a nominalization of a verb stem, not a phrase. The nominalization takes the arguments of the stem it is formed from, but they will not necessarily be present in the syntax. In contrast, in the syntactic account, raising to object is purely syntactic, and there can be no such thing as raising to object in the absence of a full phrase structure to support it (that is, raising will not be possible unless there is a clause for the NP to raise out of).

The argument against the lexical account comes from the fact that arguments of nominalizations are never obligatory. Now, they have sometimes been claimed to be, so it is important to establish that they are not. For instance, Grimshaw ( 1990 ) claimed that certain types of nominalizations (her “complex event nominals”) require that their internal arguments be realized. However, this was shown by Reuland ( 2011 ) to be false. Here are a couple of his examples, which show that as long as there is a supporting context, complex event nominals do not require their internal argument ( Reuland 2011: 1294 ):

In these examples, the internal argument of the verb is obligatory, but it can be left out in the corresponding nominalization (even with the definite determiner, which Grimshaw claims is not possible). A few more examples of my own follow:

See also Lieber ( 2016 ), who cites several attested examples of complex event nominals without their internal arguments.

The question arises, of course, of why arguments of nominalizations, complex event nominals in particular, have been thought to be obligatory in the past. Adger ( 2013 ) suggests that there is a pragmatic requirement of identifiability on the arguments of such nominals. If there is no context that can identify the argument, then it will appear to be obligatory, but if there is a context, then it is not. I note that in this respect, nominalizations are behaving just like verbs that idiosyncratically permit their arguments to drop, but where those dropped arguments are interpreted as definites. For instance, win and notice permit their internal arguments to be missing, but only if what is won or what is noticed is pragmatically identifiable ( Fodor & Fodor 1981 ; Dowty 1981 ; Fillmore 1986 ):

It therefore appears that verbs idiosyncratically choose whether their arguments are obligatory or optional, and they furthermore choose whether any missing argument is interpreted as a definite or an indefinite (the optional arguments of eat and steal are indefinite, for instance, and do not need to be identifiable at all; see Williams 2015: Chapter 5 for discussion and references). Nominalizations as a class, in contrast, have optional internal arguments that are interpreted as definites. They can therefore only be dropped when the context provides a unique, identifiable referent for the missing argument. This is something that the analysis of nominalization will have to specify (see below), but all that is important here is the conclusion that arguments of nominalizations are never obligatory in the syntax. Provided a suitable context, the arguments of nominalizations can always be dropped, just like the internal arguments of win and notice .

A more recent claim that there are nominalizations with obligatory arguments comes from Müller ( 2018 ). Müller cites German examples like Bartträger , ‘bearded man’ (lit. ‘beard-bearer’) and Spassmacher , ‘jester’ (lit. ‘fun-maker’). English examples of this sort might include babysitter and treehugger . According to Müller, such nominalizations may not have the meaning they do without the internal argument. These examples are of a very different type, however. All of Müller’s examples involve a particular verb stem with a particular object which, just when combined, have a conventionalized meaning. It is not that träger , ‘bearer’, requires an object, rather, the meaning of ‘bearded man’ only resides in the particular combination Bart-träger . 9 Similarly, treehugger is only a pejorative term for an environmental activist with that particular object. A planthugger or pandahugger does not have that meaning. Moreover, whether the logical object can be dropped or not is idiosyncratic. As an example, sitter can be used by itself, for instance, We won’t be able to go out tonight if we can’t get a sitter could be uttered by either a parent or a dog owner, but a bulldozer operator could not complain about the huggers lying down in front of his machine. In contrast, as I will show below, the facts involving raising are systematic . They should not be handled on a case-by-case basis, simply listing requirements of individual lexical items (as Müller 2018 appears to advocate), but demand a systematic, grammatical account.

Having established that arguments of nominals are never obligatory, we can turn back to the argument against the lexical account. To illustrate optionality of arguments with the kinds of nominalizations under discussion, it is possible to talk about a declaration , with no syntactic realization of a complement clause or NP. We should then expect that the arguments of the nominalization formed from raising-to-object declare are also optional. Moreover, since this declaration takes two objects, an NP and a non-finite clause, they should be independent of one another (compare placement of the stones on the path, placement of the stones, placement on the path ). We should be able to drop the complement clause while keeping the NP, and preserve the raising to object interpretation. This is not possible, however. A raising to object interpretation is only ever possible in the presence of the complete phrase structure for it. God’s declaration (to him) is grammatical by itself but implies a proposition, but God’s declaration of those acts is nonsensical, and certainly does not imply a predicate that takes those acts as its subject. The same is true of all such examples: any NP after of can only be taken as the thematic direct object of the verb used as a simple transitive, and never as the subject of an implied predicate:

This is true even when a supportive context of the type illustrated in (18–19) is provided:

Since, in the lexical account, the NP object and the non-finite clausal object are independent, that account also expects that it should be possible to drop the NP object while keeping the non-finite clause. However, that is not possible, either:

The generalization is that nominalizations may only have a raising interpretation when they actually occur with overt raising of a phrase out of a phrase. 10 This in turn means that the nominalization must be a nominalization of phrasal syntax. Treating raising and nominalization lexically makes the wrong predictions. Compare control verbs, which can nominalize and drop the non-finite clause argument:

In the lexical account, control verbs and raising verbs are treated in an almost identical fashion, as mentioned above (and see more below). There is no way to distinguish the two for this purpose.

Of course, the lexical account could stipulate that when a nominalization is related to a raising to object stem, the arguments of the stem are obligatory in the nominalization. This would be nothing but a stipulation, however, and would contradict the general pattern where arguments of nominalizations are not obligatory (as we just saw with control verbs, for instance). In contrast, the syntactic view predicts that raising could never be possible in the absence of the phrase structure that is necessary for its existence.

This argument can be extended from the nominal to the clausal domain. In the lexical account, there is no literal raising to object or raising to subject, even in clauses. As described above, the lexical entry for a raising verb says that the verb takes an NP and a non-finite clause as arguments, and specifies that the NP is interpreted as the subject of the non-finite clause. The NP is not the syntactic subject of the non-finite clause it is the semantic subject of. Raising in this account is treated exactly like control, with the only difference being that a control verb also assigns a thematic interpretation to the NP (so the NP plays two thematic roles; see Pollard & Sag 1994 for extensive discussion). However, observe that control verbs often permit their clausal argument to drop, while the NP argument remains:

This is never possible with raising ( Jacobson 1990 ). A raising to subject or raising to object interpretation is simply not available in the absence of the clause the NP raised out of. The only possibility is VP ellipsis within the clause, not dropping the entire clause:

If raising were really a verb taking two syntactically independent arguments, an NP and a clause of some type, we would not expect this dependency between them. We do not observe it in control. A purely syntactic theory of raising, in contrast, does expect this dependency: raising requires the presence of a clause for the NP to raise out of. If there is no clause, there can be no raising.

Pollard & Sag ( 1994 ) claim that the above facts follow in the lexical theory from a principle that they call the Raising Principle:

According to Pollard & Sag ( 1994 ), this principle ensures that subjects not assigned a semantic role by the predicate they are a syntactic argument of can only appear when an unsaturated phrase is also present (as a co-argument of the predicate). But note that this principle is a pure stipulation, stating by brute force what follows as a consequence from the syntactic theory. The Raising Principle could not follow from some kind of general semantic recoverability condition, for instance. The semantic content of missing arguments is clearly recoverable and applicable to pronounced arguments. Consider the following question-answer pair:

The semantic content of the missing non-finite clause in the answer is obviously recoverable and applicable, for if it were not, the answer would be nonsensical and there would be no basis for the judgment that a plural NP is a felicitous answer to the question and a singular is not. The answer has no overt representation of the item that requires a plural (the reciprocal). This means that a missing argument can be recovered and interpreted semantically, and, in particular, an overt NP can be interpreted with respect to the missing argument. Since this is possible with control, it should be possible with raising, too, and there is no justification for the Raising Principle. Similarly, we already noted that raising is possible in the presence of VP ellipsis, where the lexical item that assigns the raised NP its thematic role is not actually present (34a). Other kinds of elliptical processes are also fine with raising, for instance sluicing (34b), fragment answers (34c), and bare argument ellipsis (34d):

There is no general requirement that the predicate that assigns the raised NP its semantic role be present overtly. The Raising Principle, then, cannot follow from anything, and is nothing but a stipulation. 11

I conclude from these facts that we need a syntactic account of raising, not a lexical one. Raising is only ever possible with the full syntactic structure that the syntactic account requires. This is true in both clauses and nominalizations, and so we need a syntactic account of both.

3.2 A syntactic analysis

For the purposes of this paper I will try to make the minimal assumptions necessary for a syntactic account of raising in clauses and in nominalizations. In clauses, I will assume that a verb or adjective takes a non-finite TP as its complement. In raising to object, the subject of this non-finite TP raises to an object position in the main clause, which I will take to be Spec-VP. There is a head Voice above VP which projects the external argument ( Kratzer 1996 ). This external argument typically moves to Spec-TP (not shown in the tree below). The verb V moves to Voice to produce the correct word order (strikethrough indicates lower copies of moved elements):

An adverb can adjoin to the intermediate projection of V, giving the word order God declared them so forcefully to be wrong .

I suggest that the motivation for the movement of the subject of the non-finite embedded clause is related to but is not case. A long tradition holds that subjects of non-finite clauses do not receive case within the non-finite clause, and have to receive case from elsewhere. Following Kratzer ( 1996 ), active Voice (one that projects a thematic specifier) is what assigns accusative case to a syntactic object. I propose that case assignment is strictly local, so that Voice can only assign case to an NP that is the specifier or complement of its sister. In the tree above, the sister of Voice is VP, so case assignment is only possible to Spec-VP or to the complement of V. Voice cannot assign case to the subject of the non-finite clause. However, V can optionally be endowed with an EPP feature ( Chomsky 2000 ) that attracts an NP from within its complement to its specifier. This causes the embedded subject to move to Spec-VP. When Voice is active, this NP will be assigned accusative case there. (If no EPP feature is given to V, the NP will not move and the derivation will crash, because the NP will not be assigned case.)

Raising to subject will be similar, except that Voice will not project any external argument (it is non-active). It therefore also does not assign accusative case. The only case assigner is the matrix T, which assigns nominative case. Given the locality condition on case assignment, T can only assign case to either Spec-VoiceP or the complement of Voice, so this time the lower subject will have to move to Spec-VoiceP. I assume that heads can freely be given EPP features, so Voice can be endowed with an EPP feature which attracts the embedded subject. In Spec-VoiceP, the embedded subject can be assigned nominative case by the matrix T. Of course, English also requires an NP in Spec-TP, which I formalize as T also having an EPP feature, only on T it is obligatory. This will cause the NP to move further, to Spec-TP:

Turning to nominalizations, numerous syntactic accounts have been proposed for deriving nominalizations from phrases (e.g., VPs). These include, among others, Marantz ( 1997 ); Alexiadou ( 2001 ); Borer ( 2003 ); Roeper ( 2005 ); Bruening ( 2013 ). I will adopt the account in Bruening ( 2013 ), where a nominalizing head N takes an unsaturated projection of Voice as its complement (a VoiceP that has not projected its thematic specifier). N may project an NP in its own specifier:

The NP in Spec-NP may be, but does not have to be, interpreted as the unsaturated argument role of Voice. Alternatively, a by-phrase can adjoin to Voice and fulfill the same function (see Bruening 2013 for details). Importantly, Voice is not active, since it does not project a thematic specifier. This means that it does not assign accusative case. However, the head N can assign case, I propose. Ns assign genitive case rather than accusative case.

I will adopt the view that of is the spellout of genitive case, assigned to the syntactic object by the nominalizing head N. As mentioned above, Voice in a nominalization is non-active and so does not assign accusative case. The N head is able to assign case, but the case that Ns assign is genitive. Once again, case assignment is local, so in (37) above the complement of the V stem will have to move to Spec-VoiceP. Once again this is accomplished by giving Voice an [EPP] feature. At the same time, the V stem moves through Voice to N, where the complex V-Voice-N is pronounced relocation :

The tree in (38) spells out the internal structure of the NP complement of V in the higher position. I assume that NPs can have a K(ase) head merged with them. In English, this head is only spelled out on non-pronominal NPs when the case that is assigned to the NP is genitive. In that case, K is spelled out as of . In Spec-VoiceP, the NP is sufficiently local to N for N to assign genitive case, and K is accordingly spelled out as of . 12

Turning to a raising to object example, in (39), everything is exactly the same, except that the NP that moves and gets assigned genitive case starts as the specifier of the lower TP, rather than the complement of the V:

Once again, the subject of the non-finite clause is not close enough to the case assigner, so it has to move. The case assigner, N, takes Voice as its complement, so the embedded subject has to move to Spec-VoiceP, as indicated. Voice again needs to be given an [EPP] feature. As for the heads involved, the V moves through Voice to N, where V-Voice-N are pronounced as declaration . As with relocation , the NP that is assigned genitive case has a K merged with it, which is pronounced of when assigned genitive case. 13

As mentioned above, outside of raising the internal arguments of nominalizations are not obligatory. If they are dropped, they are interpreted as definite and need to be pragmatically identifiable, just like the objects of verbs like win and notice . Since this is something common to all nominalizations and is not related to the verb involved, it must be specified by the nominalizing head, N in the structure above. Let us consider how this might work. There does not appear to be a null argument in the syntax in such cases, because it cannot be modified by a secondary predicate, unlike null internal arguments in recipe contexts:

In the analysis of passives and nominalizations in Bruening ( 2013 ), the argument of Voice is allowed to remain unprojected just when Voice combines with a head with the right properties, for instance a Pass(ive) head or the nominalizing head. Pass and the nominalizing head are able to satisfy the selectional requirements of Voice without it actually projecting an argument (see Bruening 2013 for a formalization). In the case of the internal argument of the verb, the verb appears to be too far away from the nominalizing head for it to perform this function. Take an example like the relocation , with no overt internal argument (but one which is pragmatically identifiable). I assume that the internal argument is simply not projected:

I will assume that the argument of the stem relocate is allowed to remain unprojected just because the V moves through Voice to N. At that point it combines locally with N. The N head checks off the so-far unsatisfied selectional requirement of the V (again, see Bruening 2013 for a formalization of this checking), and specifies that the unprojected argument of V is definite. As this is a property of the abstract nominalizing head N, N can do this with any V stem it combines with (even when it is pronounced as something other than -tion ).

This will not work with a raising clause, however. In (39), if the argument of the V stem declare is not projected, then there will be no clause and no subject of that clause. There will simply be a pragmatically identifiable proposition. It will be impossible to have an NP without projecting the TP that the NP started in. This is why the non-finite clause can never be dropped, leaving the NP behind. It will also be impossible to have TP without a subject for that TP: the nominalizing head N does not combine with the head that projects the embedded subject, so it cannot check off the selectional requirements of that head. This is why it is also not possible to drop the NP argument, leaving just the non-finite clause. Thus, we explain why argument drop is never possible with raising.

Finally, note that VP in the structures here provides an adjunction site for adverbs, yielding examples like the relocation of the refugees forcibly and God’s declaration of them so forcefully to be wrong . In my judgment, such adverbs are acceptable with nominalizations derived from VPs, but are not acceptable with underived nouns. So *his claim so forcefully that cheetahs are not cats is not acceptable. In this my judgments accord with those reported in Fu et al. ( 2001 ). These judgments have been disputed by Newmeyer ( 2009 ) and Ackema & Neeleman ( 2002: 119, (41) ), both of whom present examples of putatively underived nouns that also permit adverbs. Newmeyer’s examples all seem to be derived nouns, while Ackema and Neeleman’s examples are all unacceptable in my judgment (and the judgments of other speakers I have asked). I will have to leave full exploration of this matter to future research, but I will provide some data that I think indicate that derived nominals can be modified by adverbs while underived nominals cannot. Consider the following contrasting sets, using underived nouns that can be eventive from Newmeyer ( 2009 ) and Lieber ( 2016 ): 14

Bruening ( 2013 ) also claims that certain PP adjuncts like instrumentals and subject-oriented comitatives are acceptable with derived nominals, but not with underived nominals. If this is correct, it would again corroborate the presence of VP structure within nominalizations.

Fu et al. ( 2001 ) also claim that nominals derived from VPs can serve as the antecedent for the VP anaphor do so , but underived nominals cannot. They take this to also indicate that nominals derived from verbs include VP structure within them. It does indeed appear that there is a contrast along these lines. All of the attested examples that I have found of nominals anteceding do so involve derived nominals:

While the matter may not be settled yet, it appears to me that the weight of the existing evidence points to the presence of VP structure within derived nominals, exactly as in the analysis proposed here.

3.3 Summary

I have argued here that raising requires a syntactic account, not a lexical one, and I have also spelled out a minimal syntactic analysis of nominalization that is compatible with a syntactic account of raising. We can do without lexical processes altogether, and move in the direction of a more parsimonious theory, with only one component of grammar and not two.

4 Defending a syntactic account of nominalizations: coordination

One argument that has been presented against syntactic accounts of nominalizations like the one outlined above is that nominalizations of verbs can be coordinated with underived nouns and share arguments with them ( Wechsler 2008 ; Müller & Wechsler 2014 ). However, all the examples that I have been able to find (both in the literature and in corpora) involve coordination of derived nouns, like the following: 15

In fact, coordination of derived nouns and truly underived nouns seems to be ungrammatical:

It is possible that this incompatibility is semantic in nature, and so I will not make anything of it here.

However, Wechsler ( 2008 ) presents examples like those in (47) as problematic for specific accounts of nominalizations which ascribe very different structures to nominalizations like destruction and gerunds derived with -ing , like looting (e.g., Marantz 1997 ). The first response to this argument is that it is only an argument against accounts that treat -tion and -ing nominalizations very differently. Other syntactic accounts may not be subject to this criticism. For instance, we could give -ing nominalizations the exact same account as -tion nominalizations in (39), only with -ing in place of -tion . (An issue for such an account is that -ing nominalizations, unlike -tion nominalizations, permit particles but do not permit the logical object to appear as a prenominal possessor. An analysis that treated them the same would have to explain these differences.)

The second, and more important, response to this argument is that there is evidence for an ellipsis account of coordination with argument sharing as in (47). For example, such coordinations can antecede elements that require plurals, as shown in (49):

The NPs here have the same interpretation as the hiring of faculty members into tenured positions and the promotion of faculty members into tenured positions , and the soldiers’ destruction of their home and the soldiers’ looting of their home . This points to an ellipsis account, with deletion of shared material in the first conjunct. See Chaves ( 2008 ) on this point with apparent coordination of word parts, and a deletion analysis. If a coordinate ellipsis account is correct, then coordination is not problematic for any syntactic theory of nominalizations. It is possible to give destruction a very different analysis from that given to a gerund like looting , and still have them coordinate, because the analysis will have full phrases in each conjunct ( the [destruction of their home] and [looting of their home] ).

I conclude that coordination is not problematic for any syntactic account of nominalization, contra claims in the Lexicalist literature. This clears the way for a purely syntactic account of word formation.

5 Conclusion

Since Chomsky ( 1970 ), it has been accepted that raising is ungrammatical in nominalizations, and some have argued that this points to a Lexicalist conception of grammar, with distinct components for word formation and phrasal syntax. I have shown here that this is not correct: raising to subject and raising to object are both grammatical in nominalizations. I have also argued that raising is better treated syntactically, as a lexical analysis cannot explain the need for a lower clause for a raised NP to have raised out of. This is true in both clauses and nominalizations: a raising to object interpretation is not possible without the full phrasal syntax to support it. This points to a purely syntactic account. We then also need a syntactic account of nominalizations. Recent arguments against such accounts from coordination were shown not to go through, since coordination requires an ellipsis analysis and so is compatible with fully phrasal analyses.

More generally, the results of this study point to a model of grammar where there is only one combinatorial component, not two. We can do without a lexical component altogether, and analyze everything, including word formation, with the phrasal syntax.

Additional File

The additional file for this article can be found as follows:

Experimental items for the acceptability survey. DOI: https://doi.org/10.5334/gjgl.470.s1

• References for the Lexicalist approach include, among many others, Chomsky ( 1970 ), Jackendoff ( 1972 ), Aronoff ( 1976 ), Lapointe ( 1980 ), Bresnan ( 1982b ), Kiparsky ( 1982 ), Simpson ( 1983 ), Mohanan ( 1986 ), Di Sciullo & Williams ( 1987 ), Bresnan & Mchombo ( 1995 ). Some more recent defenses of Lexicalism include Ackema & Neeleman ( 2004 ), Williams ( 2007 ), Newmeyer ( 2009 ), Müller ( 2013 ), Müller & Wechsler ( 2014 ). [ ^ ]
• References for the purely syntactic approach include, among others, Sadock ( 1980 ), Baker ( 1985 ), Sproat ( 1985 ), Lieber ( 1988 ; 1992 ), Hale & Keyser ( 1993 ), Halle & Marantz ( 1993 ), Marantz ( 1997 ), Borer ( 2005 ; 2013 ), Bruening ( 2014 ; 2018 ). [ ^ ]
• Actually, Chomsky and Kayne only addressed one of Postal’s counterexamples, examples like John’s tendency to leave . Postal produced several other counterexamples. These include Nixon’s likelihood of being reelected is minimal (328, (23b)), which Postal judged marginal, Nationalist China’s continuation as a Security Council member (330, (31)), cancer’s persistence as a frightening killer (328, (32–33)), the bomb’s failure to go off (354, (84)) on the raising to subject side, and your estimate of Bob’s weight to be/as being 200 pounds (348, (71)), your recognition of him as (being) the outstanding living malingerer (352, (77b)) on the raising to object side. I believe Postal to be correct that these are genuine examples of raising within nominalizations. Additionally, a recent publication ( Lieber 2016: 50 ) cites two attested examples of raising to subject: the adolescent’s tendency to feel invulnerable and his only child’s failure to marry . Lieber ( 2016 ) also calls into question many other claims that have been made about nominalizations in the syntactic literature (especially those from Grimshaw 1990 ). [ ^ ]
• When I have presented this material, multiple linguists have told me that they never really agreed with Chomsky’s judgments on raising to subject in (1b). With raising to object, Chomsky and others simply did not try enough verbs. [ ^ ]
• This was the scale that was provided with the free tools described in Gibson et al. ( 2011 ). Participants were not told what was meant by “(un)natural.” This is an area where the experimental setup could certainly be improved, but on the other hand, the results gleaned from using these tools indicate that participants are doing what the experimenters want them to (rate intuitive acceptability). [ ^ ]
• Mixed models that include subjects and items as random effects lead to different results depending on how they are set up. The one thing they all agree on is that the interaction between the two factors is significant. They differ on whether there are any main effects. [ ^ ]
• One might think from some of these examples that acceptability with of correlates with acceptability of the passive. For instance, most of the corresponding verbs in (15) cannot passivize. However, the house was surrounded by trees is acceptable (as an adjectival passive, at least). Conversely, NPs raised to object are fine as passivized subjects in clauses, although they are degraded with of to different degrees. [ ^ ]
• An anonymous reviewer offers the alternative suggestion that of , unlike for , strongly prefers to case-mark its sister and does not like to case-mark the specifier of its sister. In the analysis I propose below, of is just a marker of genitive case and is not a case assigner, so I cannot adopt this suggestion. [ ^ ]
• This is exactly like phrasal idioms like eat crow (‘be humiliated by having to admit being wrong’). No one would say that the fact that eat by itself cannot mean what eat crow does shows that the object of eat is obligatory. [ ^ ]
• I assume that missing complements are not present in the syntax at all. This is why neither the NP nor the complement clause can be dropped while the other is present. If the non-finite clause is missing, there was nothing for the NP to have raised out of. If the NP is missing, the non-finite clause is missing a subject, which violates both selectional requirements and the EPP in the lower clause. See below. [ ^ ]
• Pollard & Sag ( 1994: note 43 ) do state that VP ellipsis has to be treated differently from argument drop (or “null complement anaphora”). However, it is not clear that it is even possible to formulate a process of VP ellipsis in HPSG—which generally eschews null structure—in such a way that it can avoid violating the Raising Principle. The analysis of VP ellipsis in Sag et al. ( 2003: 416–419 ), for instance, seems to directly violate the Raising Principle. Moreover, Pollard & Sag 1994 go on to treat infinitival to as a raising verb exactly like seems , on their page 143, example (124). If to and other auxiliaries are raising verbs, there is no way their complements can be elided without violating the Raising Principle. Yet, as we see in (34a), the complement of to can be null. [ ^ ]
• I indicate the lower copy as also having of . I view the NP as starting with unvalued case features, which will only be pronounced as of once they are valued as genitive in the higher position. However, given that all copies in a movement chain are formally the same item, once the features are valued on the highest copy, they are valued on all lower copies as well. This is why I indicate the presence of of even in the lower copy. [ ^ ]
• It should be noted that expletives like there , one of the primary diagnostics of raising, are not possible in nominalizations when they are marked with of or with genitive’s (* acknowledgment of there to be dissent , * there’s likelihood to be protests ). Postal ( 1974: 325 ) suggests that this is due to a surface restriction against such NPs being marked with genitive case. Expletives are grammatical in nominalizations (gerunds) when they receive a different case ( there being likely to be vs. *there’s being likely to be ), so it does not appear that there is anything that blocks expletives in nominalizations in general. [ ^ ]
• Payne et al. ( 2010 ) show that certain types of adverbs can freely modify both derived and underived nouns. However, the semantic classes of adverbs that can do this are different from the manner and act-related adverbs at issue here, which seem to indicate a contrast. These types of adverbs are missing from corpora, as Payne et al. ( 2010 ) show, but it appears that a significant number of speakers judge them to be acceptable just with nouns derived from verbs. [ ^ ]

Acknowledgements

The author would like to thank the editors and anonymous reviewers of Glossa .

Competing Interests

The author has no competing interests to declare.

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Think about something strange and unexplainable in your life. Maybe you get a headache right before it rains, or maybe you think your favorite sports team wins when you wear a certain color. If you wanted to see whether these are just coincidences or scientific fact, you would form a hypothesis, then create an experiment to see whether that hypothesis is true or not.

But what is a hypothesis, anyway? If you’re not sure about what a hypothesis is--or how to test for one!--you’re in the right place. This article will teach you everything you need to know about hypotheses, including: 

• Defining the term “hypothesis” 
• Providing hypothesis examples 
• Giving you tips for how to write your own hypothesis

So let’s get started!

What Is a Hypothesis?

Merriam Webster defines a hypothesis as “an assumption or concession made for the sake of argument.” In other words, a hypothesis is an educated guess . Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it’s true or not. Keep in mind that in science, a hypothesis should be testable. You have to be able to design an experiment that tests your hypothesis in order for it to be valid. 

As you could assume from that statement, it’s easy to make a bad hypothesis. But when you’re holding an experiment, it’s even more important that your guesses be good...after all, you’re spending time (and maybe money!) to figure out more about your observation. That’s why we refer to a hypothesis as an educated guess--good hypotheses are based on existing data and research to make them as sound as possible.

Hypotheses are one part of what’s called the scientific method .  Every (good) experiment or study is based in the scientific method. The scientific method gives order and structure to experiments and ensures that interference from scientists or outside influences does not skew the results. It’s important that you understand the concepts of the scientific method before holding your own experiment. Though it may vary among scientists, the scientific method is generally made up of six steps (in order):

• Observation
• Asking questions
• Forming a hypothesis
• Analyze the data
• Communicate your results

You’ll notice that the hypothesis comes pretty early on when conducting an experiment. That’s because experiments work best when they’re trying to answer one specific question. And you can’t conduct an experiment until you know what you’re trying to prove!

Independent and Dependent Variables 

After doing your research, you’re ready for another important step in forming your hypothesis: identifying variables. Variables are basically any factor that could influence the outcome of your experiment . Variables have to be measurable and related to the topic being studied.

There are two types of variables:  independent variables and dependent variables. I ndependent variables remain constant . For example, age is an independent variable; it will stay the same, and researchers can look at different ages to see if it has an effect on the dependent variable. 

Speaking of dependent variables... dependent variables are subject to the influence of the independent variable , meaning that they are not constant. Let’s say you want to test whether a person’s age affects how much sleep they need. In that case, the independent variable is age (like we mentioned above), and the dependent variable is how much sleep a person gets. 

Variables will be crucial in writing your hypothesis. You need to be able to identify which variable is which, as both the independent and dependent variables will be written into your hypothesis. For instance, in a study about exercise, the independent variable might be the speed at which the respondents walk for thirty minutes, and the dependent variable would be their heart rate. In your study and in your hypothesis, you’re trying to understand the relationship between the two variables.

Elements of a Good Hypothesis

The best hypotheses start by asking the right questions . For instance, if you’ve observed that the grass is greener when it rains twice a week, you could ask what kind of grass it is, what elevation it’s at, and if the grass across the street responds to rain in the same way. Any of these questions could become the backbone of experiments to test why the grass gets greener when it rains fairly frequently.

As you’re asking more questions about your first observation, make sure you’re also making more observations . If it doesn’t rain for two weeks and the grass still looks green, that’s an important observation that could influence your hypothesis. You'll continue observing all throughout your experiment, but until the hypothesis is finalized, every observation should be noted.

Finally, you should consult secondary research before writing your hypothesis . Secondary research is comprised of results found and published by other people. You can usually find this information online or at your library. Additionally, m ake sure the research you find is credible and related to your topic. If you’re studying the correlation between rain and grass growth, it would help you to research rain patterns over the past twenty years for your county, published by a local agricultural association. You should also research the types of grass common in your area, the type of grass in your lawn, and whether anyone else has conducted experiments about your hypothesis. Also be sure you’re checking the quality of your research . Research done by a middle school student about what minerals can be found in rainwater would be less useful than an article published by a local university.

Writing Your Hypothesis

Once you’ve considered all of the factors above, you’re ready to start writing your hypothesis. Hypotheses usually take a certain form when they’re written out in a research report.

When you boil down your hypothesis statement, you are writing down your best guess and not the question at hand . This means that your statement should be written as if it is fact already, even though you are simply testing it.

The reason for this is that, after you have completed your study, you'll either accept or reject your if-then or your null hypothesis. All hypothesis testing examples should be measurable and able to be confirmed or denied. You cannot confirm a question, only a statement! 

In fact, you come up with hypothesis examples all the time! For instance, when you guess on the outcome of a basketball game, you don’t say, “Will the Miami Heat beat the Boston Celtics?” but instead, “I think the Miami Heat will beat the Boston Celtics.” You state it as if it is already true, even if it turns out you’re wrong. You do the same thing when writing your hypothesis.

Additionally, keep in mind that hypotheses can range from very specific to very broad.  These hypotheses can be specific, but if your hypothesis testing examples involve a broad range of causes and effects, your hypothesis can also be broad.  

The Two Types of Hypotheses

Now that you understand what goes into a hypothesis, it’s time to look more closely at the two most common types of hypothesis: the if-then hypothesis and the null hypothesis.

#1: If-Then Hypotheses

First of all, if-then hypotheses typically follow this formula:

If ____ happens, then ____ will happen.

The goal of this type of hypothesis is to test the causal relationship between the independent and dependent variable. It’s fairly simple, and each hypothesis can vary in how detailed it can be. We create if-then hypotheses all the time with our daily predictions. Here are some examples of hypotheses that use an if-then structure from daily life: 

• If I get enough sleep, I’ll be able to get more work done tomorrow.
• If the bus is on time, I can make it to my friend’s birthday party. 
• If I study every night this week, I’ll get a better grade on my exam. 

In each of these situations, you’re making a guess on how an independent variable (sleep, time, or studying) will affect a dependent variable (the amount of work you can do, making it to a party on time, or getting better grades). 

You may still be asking, “What is an example of a hypothesis used in scientific research?” Take one of the hypothesis examples from a real-world study on whether using technology before bed affects children’s sleep patterns. The hypothesis read s:

“We hypothesized that increased hours of tablet- and phone-based screen time at bedtime would be inversely correlated with sleep quality and child attention.”

It might not look like it, but this is an if-then statement. The researchers basically said, “If children have more screen usage at bedtime, then their quality of sleep and attention will be worse.” The sleep quality and attention are the dependent variables and the screen usage is the independent variable. (Usually, the independent variable comes after the “if” and the dependent variable comes after the “then,” as it is the independent variable that affects the dependent variable.) This is an excellent example of how flexible hypothesis statements can be, as long as the general idea of “if-then” and the independent and dependent variables are present.

#2: Null Hypotheses

Your if-then hypothesis is not the only one needed to complete a successful experiment, however. You also need a null hypothesis to test it against. In its most basic form, the null hypothesis is the opposite of your if-then hypothesis . When you write your null hypothesis, you are writing a hypothesis that suggests that your guess is not true, and that the independent and dependent variables have no relationship .

One null hypothesis for the cell phone and sleep study from the last section might say: 

“If children have more screen usage at bedtime, their quality of sleep and attention will not be worse.” 

In this case, this is a null hypothesis because it’s asking the opposite of the original thesis! 

Conversely, if your if-then hypothesis suggests that your two variables have no relationship, then your null hypothesis would suggest that there is one. So, pretend that there is a study that is asking the question, “Does the amount of followers on Instagram influence how long people spend on the app?” The independent variable is the amount of followers, and the dependent variable is the time spent. But if you, as the researcher, don’t think there is a relationship between the number of followers and time spent, you might write an if-then hypothesis that reads:

“If people have many followers on Instagram, they will not spend more time on the app than people who have less.”

In this case, the if-then suggests there isn’t a relationship between the variables. In that case, one of the null hypothesis examples might say:

“If people have many followers on Instagram, they will spend more time on the app than people who have less.”

You then test both the if-then and the null hypothesis to gauge if there is a relationship between the variables, and if so, how much of a relationship. 

4 Tips to Write the Best Hypothesis

If you’re going to take the time to hold an experiment, whether in school or by yourself, you’re also going to want to take the time to make sure your hypothesis is a good one. The best hypotheses have four major elements in common: plausibility, defined concepts, observability, and general explanation.

#1: Plausibility

At first glance, this quality of a hypothesis might seem obvious. When your hypothesis is plausible, that means it’s possible given what we know about science and general common sense. However, improbable hypotheses are more common than you might think. 

Imagine you’re studying weight gain and television watching habits. If you hypothesize that people who watch more than  twenty hours of television a week will gain two hundred pounds or more over the course of a year, this might be improbable (though it’s potentially possible). Consequently, c ommon sense can tell us the results of the study before the study even begins.

Improbable hypotheses generally go against  science, as well. Take this hypothesis example: 

“If a person smokes one cigarette a day, then they will have lungs just as healthy as the average person’s.” 

This hypothesis is obviously untrue, as studies have shown again and again that cigarettes negatively affect lung health. You must be careful that your hypotheses do not reflect your own personal opinion more than they do scientifically-supported findings. This plausibility points to the necessity of research before the hypothesis is written to make sure that your hypothesis has not already been disproven.

#2: Defined Concepts

The more advanced you are in your studies, the more likely that the terms you’re using in your hypothesis are specific to a limited set of knowledge. One of the hypothesis testing examples might include the readability of printed text in newspapers, where you might use words like “kerning” and “x-height.” Unless your readers have a background in graphic design, it’s likely that they won’t know what you mean by these terms. Thus, it’s important to either write what they mean in the hypothesis itself or in the report before the hypothesis.

Here’s what we mean. Which of the following sentences makes more sense to the common person?

If the kerning is greater than average, more words will be read per minute.

If the space between letters is greater than average, more words will be read per minute.

For people reading your report that are not experts in typography, simply adding a few more words will be helpful in clarifying exactly what the experiment is all about. It’s always a good idea to make your research and findings as accessible as possible. 

Good hypotheses ensure that you can observe the results. 

#3: Observability

In order to measure the truth or falsity of your hypothesis, you must be able to see your variables and the way they interact. For instance, if your hypothesis is that the flight patterns of satellites affect the strength of certain television signals, yet you don’t have a telescope to view the satellites or a television to monitor the signal strength, you cannot properly observe your hypothesis and thus cannot continue your study.

Some variables may seem easy to observe, but if you do not have a system of measurement in place, you cannot observe your hypothesis properly. Here’s an example: if you’re experimenting on the effect of healthy food on overall happiness, but you don’t have a way to monitor and measure what “overall happiness” means, your results will not reflect the truth. Monitoring how often someone smiles for a whole day is not reasonably observable, but having the participants state how happy they feel on a scale of one to ten is more observable. 

In writing your hypothesis, always keep in mind how you'll execute the experiment.

#4: Generalizability 

Perhaps you’d like to study what color your best friend wears the most often by observing and documenting the colors she wears each day of the week. This might be fun information for her and you to know, but beyond you two, there aren’t many people who could benefit from this experiment. When you start an experiment, you should note how generalizable your findings may be if they are confirmed. Generalizability is basically how common a particular phenomenon is to other people’s everyday life.

Let’s say you’re asking a question about the health benefits of eating an apple for one day only, you need to realize that the experiment may be too specific to be helpful. It does not help to explain a phenomenon that many people experience. If you find yourself with too specific of a hypothesis, go back to asking the big question: what is it that you want to know, and what do you think will happen between your two variables?

Hypothesis Testing Examples

We know it can be hard to write a good hypothesis unless you’ve seen some good hypothesis examples. We’ve included four hypothesis examples based on some made-up experiments. Use these as templates or launch pads for coming up with your own hypotheses.

Experiment #1: Students Studying Outside (Writing a Hypothesis)

You are a student at PrepScholar University. When you walk around campus, you notice that, when the temperature is above 60 degrees, more students study in the quad. You want to know when your fellow students are more likely to study outside. With this information, how do you make the best hypothesis possible?

You must remember to make additional observations and do secondary research before writing your hypothesis. In doing so, you notice that no one studies outside when it’s 75 degrees and raining, so this should be included in your experiment. Also, studies done on the topic beforehand suggested that students are more likely to study in temperatures less than 85 degrees. With this in mind, you feel confident that you can identify your variables and write your hypotheses:

If-then: “If the temperature in Fahrenheit is less than 60 degrees, significantly fewer students will study outside.”

Null: “If the temperature in Fahrenheit is less than 60 degrees, the same number of students will study outside as when it is more than 60 degrees.”

These hypotheses are plausible, as the temperatures are reasonably within the bounds of what is possible. The number of people in the quad is also easily observable. It is also not a phenomenon specific to only one person or at one time, but instead can explain a phenomenon for a broader group of people.

To complete this experiment, you pick the month of October to observe the quad. Every day (except on the days where it’s raining)from 3 to 4 PM, when most classes have released for the day, you observe how many people are on the quad. You measure how many people come  and how many leave. You also write down the temperature on the hour. 

After writing down all of your observations and putting them on a graph, you find that the most students study on the quad when it is 70 degrees outside, and that the number of students drops a lot once the temperature reaches 60 degrees or below. In this case, your research report would state that you accept or “failed to reject” your first hypothesis with your findings.

Experiment #2: The Cupcake Store (Forming a Simple Experiment)

Let’s say that you work at a bakery. You specialize in cupcakes, and you make only two colors of frosting: yellow and purple. You want to know what kind of customers are more likely to buy what kind of cupcake, so you set up an experiment. Your independent variable is the customer’s gender, and the dependent variable is the color of the frosting. What is an example of a hypothesis that might answer the question of this study?

Here’s what your hypotheses might look like: 

If-then: “If customers’ gender is female, then they will buy more yellow cupcakes than purple cupcakes.”

Null: “If customers’ gender is female, then they will be just as likely to buy purple cupcakes as yellow cupcakes.”

This is a pretty simple experiment! It passes the test of plausibility (there could easily be a difference), defined concepts (there’s nothing complicated about cupcakes!), observability (both color and gender can be easily observed), and general explanation ( this would potentially help you make better business decisions ).

Experiment #3: Backyard Bird Feeders (Integrating Multiple Variables and Rejecting the If-Then Hypothesis)

While watching your backyard bird feeder, you realized that different birds come on the days when you change the types of seeds. You decide that you want to see more cardinals in your backyard, so you decide to see what type of food they like the best and set up an experiment. 

However, one morning, you notice that, while some cardinals are present, blue jays are eating out of your backyard feeder filled with millet. You decide that, of all of the other birds, you would like to see the blue jays the least. This means you'll have more than one variable in your hypothesis. Your new hypotheses might look like this: 

If-then: “If sunflower seeds are placed in the bird feeders, then more cardinals will come than blue jays. If millet is placed in the bird feeders, then more blue jays will come than cardinals.”

Null: “If either sunflower seeds or millet are placed in the bird, equal numbers of cardinals and blue jays will come.”

Through simple observation, you actually find that cardinals come as often as blue jays when sunflower seeds or millet is in the bird feeder. In this case, you would reject your “if-then” hypothesis and “fail to reject” your null hypothesis . You cannot accept your first hypothesis, because it’s clearly not true. Instead you found that there was actually no relation between your different variables. Consequently, you would need to run more experiments with different variables to see if the new variables impact the results.

Experiment #4: In-Class Survey (Including an Alternative Hypothesis)

You’re about to give a speech in one of your classes about the importance of paying attention. You want to take this opportunity to test a hypothesis you’ve had for a while: 

If-then: If students sit in the first two rows of the classroom, then they will listen better than students who do not.

Null: If students sit in the first two rows of the classroom, then they will not listen better or worse than students who do not.

You give your speech and then ask your teacher if you can hand out a short survey to the class. On the survey, you’ve included questions about some of the topics you talked about. When you get back the results, you’re surprised to see that not only do the students in the first two rows not pay better attention, but they also scored worse than students in other parts of the classroom! Here, both your if-then and your null hypotheses are not representative of your findings. What do you do?

This is when you reject both your if-then and null hypotheses and instead create an alternative hypothesis . This type of hypothesis is used in the rare circumstance that neither of your hypotheses is able to capture your findings . Now you can use what you’ve learned to draft new hypotheses and test again! 

Key Takeaways: Hypothesis Writing

The more comfortable you become with writing hypotheses, the better they will become. The structure of hypotheses is flexible and may need to be changed depending on what topic you are studying. The most important thing to remember is the purpose of your hypothesis and the difference between the if-then and the null . From there, in forming your hypothesis, you should constantly be asking questions, making observations, doing secondary research, and considering your variables. After you have written your hypothesis, be sure to edit it so that it is plausible, clearly defined, observable, and helpful in explaining a general phenomenon.

Writing a hypothesis is something that everyone, from elementary school children competing in a science fair to professional scientists in a lab, needs to know how to do. Hypotheses are vital in experiments and in properly executing the scientific method . When done correctly, hypotheses will set up your studies for success and help you to understand the world a little better, one experiment at a time.

What’s Next?

If you’re studying for the science portion of the ACT, there’s definitely a lot you need to know. We’ve got the tools to help, though! Start by checking out our ultimate study guide for the ACT Science subject test. Once you read through that, be sure to download our recommended ACT Science practice tests , since they’re one of the most foolproof ways to improve your score. (And don’t forget to check out our expert guide book , too.)

If you love science and want to major in a scientific field, you should start preparing in high school . Here are the science classes you should take to set yourself up for success.

If you’re trying to think of science experiments you can do for class (or for a science fair!), here’s a list of 37 awesome science experiments you can do at home

Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

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Universities Face an Urgent Question: What Makes a Protest Antisemitic?

Pro-Palestinian student activists say their movement is anti-Zionist but not antisemitic. It is not a distinction that everyone accepts.

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By Katherine Rosman

Katherine Rosman reported from the Columbia University campus.

Follow our live coverage of the college protests at U.C.L.A. and other universities.

In a video shared widely online, a leader of the pro-Palestinian student movement at Columbia University stands near the center of a lawn on the campus and calls out, “We have Zionists who have entered the camp.”

Dozens of protesters, who have created a tent village called the “Gaza Solidarity Encampment,” repeat his words back to him: “We have Zionists who have entered the camp.”

“Walk and take a step forward,” the leader says, as the students continue to repeat his every utterance, “so that we can start to push them out of the camp. ”

The protesters link arms and march in formation toward three Jewish students who have come inside the encampment.

“It was really scary because we had like 75 people quickly gathered around, encircling us, doing exactly what he said to do,” Avi Weinberg, one of the Jewish students, said in an interview. He and his friends had gone to see the encampment, not intending to provoke, he said. When it began to feel tense, one of the students started to record the encounter. They are not sure precisely how the protest leader determined they were supportive of Israel.

“Suddenly we are being called ‘the Zionists’ in their encampment,” Mr. Weinberg said. “He put a target on our back.”

On Thursday, the incident took on new significance when a video from January resurfaced on social media showing the same protest leader, Khymani James, saying “Zionists don’t deserve to live” and “Be grateful that I’m not just going out and murdering Zionists.”

The next day, Columbia officials announced they had barred Mr. James from campus.

Columbia has been ground zero in a national student movement against Israel’s treatment of Palestinians, with protesters setting up encampments on campuses across the country. Hundreds of demonstrators — at Columbia, Yale, Emerson College, the University of Southern California and beyond — have been arrested.

Protesters occupied

Hamilton Hall early

Tuesday morning

West 114th St.

Tent encampment at

Columbia University

Faculty and staff

members guarding

access to the tents

Amsterdam Ave.

Source: Google Earth

Note: Photograph taken Monday, April 29

By Leanne Abraham; Photograph by Bing Guan

Pro-Palestinian demonstrators across the country say Israel is committing what they see as genocide against the Palestinian people, and they aim to keep a spotlight on the suffering. But some Jewish students who support Israel and what they see as its right to defend itself against Hamas say the protests have made them afraid to walk freely on campus. They hear denunciations of Zionism and calls for a Palestinian uprising as an attack on Jews themselves.

The tension goes to the heart of a question that has touched off debate among observers and critics of the protests: At what point does pro-Palestinian political speech in a time of war cross the line into the type of antisemitism colleges have vowed to combat?

If this is a matter that has vexed political leaders, university administrators and some Jewish college students, inside the encampments the very notion of antisemitism is barely discussed, in part because the demonstrators do not believe the label applies to their activism. Protest leaders point to the involvement of Jewish student activists and challenge the idea that the comfort of Israel’s supporters should be a concern.

And they draw a distinction between anti-Zionism, which describes opposition to the Jewish state of Israel, and hatred toward Jewish people in general. It is an argument many Jews see as a fig leaf for bigotry.

In a letter to Columbia students last week, university officials made clear the challenge they are facing. “We know that many of you feel threatened by the atmosphere and the language being used and have had to leave campus,” they wrote. “That is unacceptable.”

They continued, “Chants, signs, taunts and social media posts from our own students that mock and threaten to ‘kill’ Jewish people are totally unacceptable, and Columbia students who are involved in such incidents will be held accountable.”

A call for divestment

The protests beyond New York City have been inspired by the Columbia students, but they are largely diffuse, spreading via social media much like other recent movements, including Black Lives Matter and the Arab Spring.

At Columbia, the demonstration is led by a group known as CUAD — Columbia University Apartheid Divest — a coalition representing more than 100 Columbia student organizations including Students for Justice in Palestine and Jewish Voice for Peace. Leadership is amorphous. The organizers communicate on the Telegram messaging app and provide media training to the activists they make available to speak to the press.

It is unclear what financial support the group receives, and from whom. When asked, one student leader declined to comment.

But supporters from across New York have responded to the group’s Instagram pleas for water, blankets, gloves and cigarettes. Last week, Palestine Legal, an advocacy group, filed a federal civil rights complaint on behalf of the protesters, arguing that they have been subjected to anti-Palestinian and anti-Islamic harassment on campus.

Student demonstrators are specifically calling for their universities to make transparent all financial holdings and divest from companies and funds they say are profiting from or supporting Israel and its government’s policies. They also want “amnesty” for students and faculty who have been disciplined by the university as a result of their protest.

At Columbia, students are also calling on the university to end its five-year-old dual-degree program with Tel Aviv University. Some also object to the presence on the university board of Jeh Johnson, who served as homeland security secretary during the Obama administration and sits on the board of Lockheed Martin , a supplier of fighter jets to the Israel Defense Force.

Mr. Johnson declined to comment.

At encampments around the country, signs also point to the broader politics of many of the protesters. They support the anti-Israel Boycott, Divestment and Sanctions movement, which predates the war in Gaza. The students invoke historical issues of colonialism and apartheid.

Student activists who are not themselves Palestinian say that they have joined the movement for a wide variety of reasons: anguish over a humanitarian crisis in Gaza ; a rebuke of university and police response to protests; a commitment to intersectional justice where any group’s fight should be everyone’s fight; the idealistic desire to be a part of a community effort; and a sense that the fight for Palestinians is a continuation of the work started on behalf of oppressed people during the Black Lives Matter movement.

Many Jewish students taking part in the current protests say they are doing so as an expression of their Jewish values that emphasize social justice and equality. Encampments have hosted Shabbat dinners and Passover seders. At Columbia, one student said that donors have supplied kosher meals.

Samuel Law, a graduate student at the University of Texas at Austin who is Jewish and involved in the protests, was inspired by the encampments popping up around the country. “I strongly believe that the university should be there for us to care about what we care about,” he said.

‘They don’t feel safe’

Outside the pro-Palestinian encampments, the movement has drawn accusations of anti-Jewish bigotry and harassment — from political leaders as well as from some students, Jewish and not.

Jimmy Hayward, a Columbia freshman who is not Jewish, said that he has many friends studying at the Columbia-affiliated Jewish Theological Seminary who are unnerved. “I have friends in JTS that need to be walked to campus,” he said. “They want me to walk them because they don’t feel safe walking alone.”

Signs in and around the Columbia encampment include inspirational quotes, including “The world belongs to the people, and the future belongs to us,” attributed to Jiang Qing, a Chinese communist revolutionary. But there are also celebrations of violence, like “Whoever is in solidarity with our corpses but not our rockets is a hypocrite and not one of us.”

At the University of Michigan, some Jewish students said they felt rattled as they walked to class passing by protesters chanting, “Long live the intifada,” using the word for “uprising” in Arabic, which has been used to describe periods of violent protests by Palestinians against Israelis.

Tessa Veksler, a Jewish student at the University of California Santa Barbara was alarmed to see, at the school’s multicultural center, a sign on the door to a student lounge that said, “Zionist Not Allowed.”

Campus protesters dispute the notion that their movement has made pro-Israel students unsafe.

Nas Issa, a Columbia graduate who is supporting and advising protest organizers, sees a difference between feeling uncomfortable and feeling that you are in danger — “especially if you feel that your identity is tied to the practices of a particular state or to a political ideology.”

“That can be personally affecting and I think that’s understandable,” said Ms. Issa, who is Palestinian. “But I think the conflation between that and safety — it can be a bit misleading.”

When pressed, the protesters say they are anti-Zionist but not antisemitic.

It is not a distinction everyone buys.

“Let’s take any other ethnic or religious minority,” said Eden Yadegar, a junior at Columbia. “Would you only accept them if they were willing to denounce an integral part of their religious or ethnic identity? The answer is absolutely not. So how come it’s OK to say, you know, we accept Jews, but only if you denounce your religious and social and ethnic connection to your homeland? It’s ridiculous.”

Last Tuesday afternoon, Isidore Karten, an Israeli Jew, hopped a fence and entered the pro-Palestinian encampment at Columbia.

“I think it’s super important to go and show our side also,” said Mr. Karten, a 2022 Columbia graduate. “We should be allowed to be there as much as anyone else .”

Once inside, he unfurled an Israeli flag. A friend who had come with him toted a poster showing the faces and names of Israelis who were kidnapped into Gaza by Hamas on Oct. 7.

As they did, they were trailed by pro-Palestinian protesters holding a large black sheet to keep journalists from seeing them and the flag.

A few students, Mr. Karten said, chanted, “Burn Tel Aviv to the ground.”

And as he tried to talk with the demonstrators, he said, his efforts were blocked by protest leaders.

One of them was Khymani James, the student who was later barred from campus for his incendiary video. “We don’t engage with Zionists,” he said, according to Mr. Karten.

‘A wake-up call’

Mr. James’s video , which was publicized by a right-wing outlet on Thursday and then reported on by The New York Times and others, drew wide attention, including from President Biden, whose spokesman issued a statement saying, “These dangerous, appalling statements turn the stomach and should serve as a wake-up call.”

Others cautioned not to use the words of one activist to define a much larger group.

The Rev. Michael McBride , a founder of Black Church PAC, who has pressed for a cease-fire in Gaza, said Mr. James’s comments were not representative of the antiwar movement.

“You can go to a protest and find anything you’re looking for,” said the Rev. McBride, who leads a church in Berkeley, Calif. “If you’re looking for that, then you’ll find it.”

At Columbia, the CUAD student protest organization on Friday posted a statement on Instagram that said, “Khymani’s words in January do not reflect his view, our values, nor the encampment’s community agreements.” The statement added, “In the same way some of us were once Zionists and are now anti-Zionists, we believe unlearning is always possible.”

But for university administrators, Mr. James’s case has presented a serious challenge.

He made some of his comments about killing Zionists — including that “taking someone’s life in certain case scenarios is necessary and better for the overall world” — during a college disciplinary hearing in January.

But he was not barred from campus until the January video began to spread last week. A notification sent to Mr. James by the university and shared with The New York Times by one of his friends described it as an “interim suspension.” Mr. James, who said in a statement last week that his words were “wrong,” could not be reached for comment.

“When leadership learned of the video, it took immediate steps to ban James from campus,” a Columbia spokesman said this weekend. “We initiated disciplinary proceedings which encompass this and additional potential violations of university policies.”

It is not clear whether the Columbia administrator conducting the disciplinary hearing alerted a superior or public safety official to Mr. James’s remarks at the time — or whether Columbia policy dictated that the administrator should have.

A spokesman for the university declined to comment further.

The episode left Avi Weinberg, the pro-Israel student who was surrounded by Mr. James and other protesters at the encampment, distressed. “The university was aware that this is his mind-set, and the university put their students in danger,” he said. “That is very present on my mind.”

Eryn Davis, Neelam Bohra, Katie Glueck, Stephanie Saul, Olivia Bensimon and Karla Marie Sanford contributed reporting.

Katherine Rosman covers newsmakers, power players and individuals making an imprint on New York City. More about Katherine Rosman

Our Coverage of the U.S. Campus Protests

News and Analysis

Duke: Dozens of students walked out  of Duke University’s commencement ceremony as Jerry Seinfeld, who has been vocal about his support for Israel, received an honorary degree.

U.C. Berkeley:  Befitting a campus synonymous with student protest, the graduation ceremony at the University of California, Berkeley, blurred the lines between pomp and pro-Palestinian activism .

U.S.C.: Asna Tabassum, the valedictorian at the University of Southern California whose speech was canceled by school administrators, received her degree to cheers and loud applause  from students and parents.

Turning to Al Jazeera :  Students active in campus protests value the Arab news network’s on-the-ground coverage  and its perspective on the Israel-Hamas war. They draw distinctions between it and major American outlets.

Black Colleges :  The White House appears anxious about President Biden’s speech at Morehouse College, a historically Black institution. But for complex reasons, such campuses have had far less visible Gaza tensions .

A Different Approach :  University leaders in Britain have so far adopted a more permissive attitude to pro-Palestinian encampments than their U.S. counterparts. Here’s why .