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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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Controlled Experiment

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Associate Editor for Simply Psychology

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Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

This is when a hypothesis is scientifically tested.

In a controlled experiment, an independent variable (the cause) is systematically manipulated, and the dependent variable (the effect) is measured; any extraneous variables are controlled.

The researcher can operationalize (i.e., define) the studied variables so they can be objectively measured. The quantitative data can be analyzed to see if there is a difference between the experimental and control groups.

What is the control group?

In experiments scientists compare a control group and an experimental group that are identical in all respects, except for one difference – experimental manipulation.

Unlike the experimental group, the control group is not exposed to the independent variable under investigation and so provides a baseline against which any changes in the experimental group can be compared.

Since experimental manipulation is the only difference between the experimental and control groups, we can be sure that any differences between the two are due to experimental manipulation rather than chance.

Randomly allocating participants to independent variable groups means that all participants should have an equal chance of participating in each condition.

The principle of random allocation is to avoid bias in how the experiment is carried out and limit the effects of participant variables.

What are extraneous variables?

The researcher wants to ensure that the manipulation of the independent variable has changed the changes in the dependent variable.

Hence, all the other variables that could affect the dependent variable to change must be controlled. These other variables are called extraneous or confounding variables.

Extraneous variables should be controlled were possible, as they might be important enough to provide alternative explanations for the effects.

In practice, it would be difficult to control all the variables in a child’s educational achievement. For example, it would be difficult to control variables that have happened in the past.

A researcher can only control the current environment of participants, such as time of day and noise levels.

Why conduct controlled experiments?

Scientists use controlled experiments because they allow for precise control of extraneous and independent variables. This allows a cause-and-effect relationship to be established.

Controlled experiments also follow a standardized step-by-step procedure. This makes it easy for another researcher to replicate the study.

Key Terminology

Experimental group.

The group being treated or otherwise manipulated for the sake of the experiment.

Control Group

They receive no treatment and are used as a comparison group.

Ecological validity

The degree to which an investigation represents real-life experiences.

Experimenter effects

These are the ways that the experimenter can accidentally influence the participant through their appearance or behavior.

Demand characteristics

The clues in an experiment lead the participants to think they know what the researcher is looking for (e.g., the experimenter’s body language).

Independent variable (IV)

The variable the experimenter manipulates (i.e., changes) – is assumed to have a direct effect on the dependent variable.

Dependent variable (DV)

Variable the experimenter measures. This is the outcome (i.e., the result) of a study.

Extraneous variables (EV)

All variables that are not independent variables but could affect the results (DV) of the experiment. Extraneous variables should be controlled where possible.

Confounding variables

Variable(s) that have affected the results (DV), apart from the IV. A confounding variable could be an extraneous variable that has not been controlled.

Random Allocation

Randomly allocating participants to independent variable conditions means that all participants should have an equal chance of participating in each condition.

Order effects

Changes in participants’ performance due to their repeating the same or similar test more than once. Examples of order effects include:

(i) practice effect: an improvement in performance on a task due to repetition, for example, because of familiarity with the task;

(ii) fatigue effect: a decrease in performance of a task due to repetition, for example, because of boredom or tiredness.

What is the control in an experiment?

In an experiment , the control is a standard or baseline group not exposed to the experimental treatment or manipulation. It serves as a comparison group to the experimental group, which does receive the treatment or manipulation.

The control group helps to account for other variables that might influence the outcome, allowing researchers to attribute differences in results more confidently to the experimental treatment.

Establishing a cause-and-effect relationship between the manipulated variable (independent variable) and the outcome (dependent variable) is critical in establishing a cause-and-effect relationship between the manipulated variable.

What is the purpose of controlling the environment when testing a hypothesis?

Controlling the environment when testing a hypothesis aims to eliminate or minimize the influence of extraneous variables. These variables other than the independent variable might affect the dependent variable, potentially confounding the results.

By controlling the environment, researchers can ensure that any observed changes in the dependent variable are likely due to the manipulation of the independent variable, not other factors.

This enhances the experiment’s validity, allowing for more accurate conclusions about cause-and-effect relationships.

It also improves the experiment’s replicability, meaning other researchers can repeat the experiment under the same conditions to verify the results.

Why are hypotheses important to controlled experiments?

Hypotheses are crucial to controlled experiments because they provide a clear focus and direction for the research. A hypothesis is a testable prediction about the relationship between variables.

It guides the design of the experiment, including what variables to manipulate (independent variables) and what outcomes to measure (dependent variables).

The experiment is then conducted to test the validity of the hypothesis. If the results align with the hypothesis, they provide evidence supporting it.

The hypothesis may be revised or rejected if the results do not align. Thus, hypotheses are central to the scientific method, driving the iterative inquiry, experimentation, and knowledge advancement process.

What is the experimental method?

The experimental method is a systematic approach in scientific research where an independent variable is manipulated to observe its effect on a dependent variable, under controlled conditions.

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What Is a Control Variable? Definition and Examples

A control variable is any factor that is controlled or held constant during an experiment . For this reason, it’s also known as a controlled variable or a constant variable. A single experiment may contain many control variables . Unlike the independent and dependent variables , control variables aren’t a part of the experiment, but they are important because they could affect the outcome. Take a look at the difference between a control variable and control group and see examples of control variables.

Importance of Control Variables

Remember, the independent variable is the one you change, the dependent variable is the one you measure in response to this change, and the control variables are any other factors you control or hold constant so that they can’t influence the experiment. Control variables are important because:

• They make it easier to reproduce the experiment.
• The increase confidence in the outcome of the experiment.

For example, if you conducted an experiment examining the effect of the color of light on plant growth, but you didn’t control temperature, it might affect the outcome. One light source might be hotter than the other, affecting plant growth. This could lead you to incorrectly accept or reject your hypothesis. As another example, say you did control the temperature. If you did not report this temperature in your “methods” section, another researcher might have trouble reproducing your results. What if you conducted your experiment at 15 °C. Would you expect the same results at 5 °C or 35 5 °C? Sometimes the potential effect of a control variable can lead to a new experiment!

Sometimes you think you have controlled everything except the independent variable, but still get strange results. This could be due to what is called a “ confounding variable .” Examples of confounding variables could be humidity, magnetism, and vibration. Sometimes you can identify a confounding variable and turn it into a control variable. Other times, confounding variables cannot be detected or controlled.

Control Variable vs Control Group

A control group is different from a control variable. You expose a control group to all the same conditions as the experimental group, except you change the independent variable in the experimental group. Both the control group and experimental group should have the same control variables.

Control Variable Examples

Anything you can measure or control that is not the independent variable or dependent variable has potential to be a control variable. Examples of common control variables include:

• Duration of the experiment
• Size and composition of containers
• Temperature
• Sample volume
• Experimental technique
• Chemical purity or manufacturer
• Species (in biological experiments)

For example, consider an experiment testing whether a certain supplement affects cattle weight gain. The independent variable is the supplement, while the dependent variable is cattle weight. A typical control group would consist of cattle not given the supplement, while the cattle in the experimental group would receive the supplement. Examples of control variables in this experiment could include the age of the cattle, their breed, whether they are male or female, the amount of supplement, the way the supplement is administered, how often the supplement is administered, the type of feed given to the cattle, the temperature, the water supply, the time of year, and the method used to record weight. There may be other control variables, too. Sometimes you can’t actually control a control variable, but conditions should be the same for both the control and experimental groups. For example, if the cattle are free-range, weather might change from day to day, but both groups have the same experience. When you take data, be sure to record control variables along with the independent and dependent variable.

• Box, George E.P.; Hunter, William G.; Hunter, J. Stuart (1978). Statistics for Experimenters : An Introduction to Design, Data Analysis, and Model Building . New York: Wiley. ISBN 978-0-471-09315-2.
• Giri, Narayan C.; Das, M. N. (1979). Design and Analysis of Experiments . New York, N.Y: Wiley. ISBN 9780852269145.
• Stigler, Stephen M. (November 1992). “A Historical View of Statistical Concepts in Psychology and Educational Research”. American Journal of Education . 101 (1): 60–70. doi: 10.1086/444032

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• Methodology
• A Quick Guide to Experimental Design | 5 Steps & Examples

A Quick Guide to Experimental Design | 5 Steps & Examples

Published on 11 April 2022 by Rebecca Bevans . Revised on 5 December 2022.

Experiments are used to study causal relationships . You manipulate one or more independent variables and measure their effect on one or more dependent variables.

Experimental design means creating a set of procedures to systematically test a hypothesis . A good experimental design requires a strong understanding of the system you are studying. 

There are five key steps in designing an experiment:

• Consider your variables and how they are related
• Write a specific, testable hypothesis
• Design experimental treatments to manipulate your independent variable
• Assign subjects to groups, either between-subjects or within-subjects
• Plan how you will measure your dependent variable

For valid conclusions, you also need to select a representative sample and control any  extraneous variables that might influence your results. If if random assignment of participants to control and treatment groups is impossible, unethical, or highly difficult, consider an observational study instead.

Table of contents

Step 1: define your variables, step 2: write your hypothesis, step 3: design your experimental treatments, step 4: assign your subjects to treatment groups, step 5: measure your dependent variable, frequently asked questions about experimental design.

You should begin with a specific research question . We will work with two research question examples, one from health sciences and one from ecology:

To translate your research question into an experimental hypothesis, you need to define the main variables and make predictions about how they are related.

Start by simply listing the independent and dependent variables .

Then you need to think about possible extraneous and confounding variables and consider how you might control  them in your experiment.

Finally, you can put these variables together into a diagram. Use arrows to show the possible relationships between variables and include signs to show the expected direction of the relationships.

Here we predict that increasing temperature will increase soil respiration and decrease soil moisture, while decreasing soil moisture will lead to decreased soil respiration.

Prevent plagiarism, run a free check.

Now that you have a strong conceptual understanding of the system you are studying, you should be able to write a specific, testable hypothesis that addresses your research question.

The next steps will describe how to design a controlled experiment . In a controlled experiment, you must be able to:

• Systematically and precisely manipulate the independent variable(s).
• Precisely measure the dependent variable(s).
• Control any potential confounding variables.

If your study system doesn’t match these criteria, there are other types of research you can use to answer your research question.

How you manipulate the independent variable can affect the experiment’s external validity – that is, the extent to which the results can be generalised and applied to the broader world.

First, you may need to decide how widely to vary your independent variable.

• just slightly above the natural range for your study region.
• over a wider range of temperatures to mimic future warming.
• over an extreme range that is beyond any possible natural variation.

Second, you may need to choose how finely to vary your independent variable. Sometimes this choice is made for you by your experimental system, but often you will need to decide, and this will affect how much you can infer from your results.

• a categorical variable : either as binary (yes/no) or as levels of a factor (no phone use, low phone use, high phone use).
• a continuous variable (minutes of phone use measured every night).

How you apply your experimental treatments to your test subjects is crucial for obtaining valid and reliable results.

First, you need to consider the study size : how many individuals will be included in the experiment? In general, the more subjects you include, the greater your experiment’s statistical power , which determines how much confidence you can have in your results.

Then you need to randomly assign your subjects to treatment groups . Each group receives a different level of the treatment (e.g. no phone use, low phone use, high phone use).

You should also include a control group , which receives no treatment. The control group tells us what would have happened to your test subjects without any experimental intervention.

When assigning your subjects to groups, there are two main choices you need to make:

• A completely randomised design vs a randomised block design .
• A between-subjects design vs a within-subjects design .

Randomisation

An experiment can be completely randomised or randomised within blocks (aka strata):

• In a completely randomised design , every subject is assigned to a treatment group at random.
• In a randomised block design (aka stratified random design), subjects are first grouped according to a characteristic they share, and then randomly assigned to treatments within those groups.

Sometimes randomisation isn’t practical or ethical , so researchers create partially-random or even non-random designs. An experimental design where treatments aren’t randomly assigned is called a quasi-experimental design .

Between-subjects vs within-subjects

In a between-subjects design (also known as an independent measures design or classic ANOVA design), individuals receive only one of the possible levels of an experimental treatment.

In medical or social research, you might also use matched pairs within your between-subjects design to make sure that each treatment group contains the same variety of test subjects in the same proportions.

In a within-subjects design (also known as a repeated measures design), every individual receives each of the experimental treatments consecutively, and their responses to each treatment are measured.

Within-subjects or repeated measures can also refer to an experimental design where an effect emerges over time, and individual responses are measured over time in order to measure this effect as it emerges.

Counterbalancing (randomising or reversing the order of treatments among subjects) is often used in within-subjects designs to ensure that the order of treatment application doesn’t influence the results of the experiment.

Finally, you need to decide how you’ll collect data on your dependent variable outcomes. You should aim for reliable and valid measurements that minimise bias or error.

Some variables, like temperature, can be objectively measured with scientific instruments. Others may need to be operationalised to turn them into measurable observations.

• Ask participants to record what time they go to sleep and get up each day.
• Ask participants to wear a sleep tracker.

How precisely you measure your dependent variable also affects the kinds of statistical analysis you can use on your data.

Experiments are always context-dependent, and a good experimental design will take into account all of the unique considerations of your study system to produce information that is both valid and relevant to your research question.

Experimental designs are a set of procedures that you plan in order to examine the relationship between variables that interest you.

To design a successful experiment, first identify:

• A testable hypothesis
• One or more independent variables that you will manipulate
• One or more dependent variables that you will measure

When designing the experiment, first decide:

• How your variable(s) will be manipulated
• How you will control for any potential confounding or lurking variables
• How many subjects you will include
• How you will assign treatments to your subjects

The key difference between observational studies and experiments is that, done correctly, an observational study will never influence the responses or behaviours of participants. Experimental designs will have a treatment condition applied to at least a portion of participants.

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word ‘between’ means that you’re comparing different conditions between groups, while the word ‘within’ means you’re comparing different conditions within the same group.

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Controlled Experiment

Reviewed by: BD Editors

Controlled Experiment Definition

A controlled experiment is a scientific test that is directly manipulated by a scientist, in order to test a single variable at a time. The variable being tested is the independent variable , and is adjusted to see the effects on the system being studied. The controlled variables are held constant to minimize or stabilize their effects on the subject. In biology, a controlled experiment often includes restricting the environment of the organism being studied. This is necessary to minimize the random effects of the environment and the many variables that exist in the wild.

In a controlled experiment, the study population is often divided into two groups. One group receives a change in a certain variable, while the other group receives a standard environment and conditions. This group is referred to as the control group , and allows for comparison with the other group, known as the experimental group . Many types of controls exist in various experiments, which are designed to ensure that the experiment worked, and to have a basis for comparison. In science, results are only accepted if it can be shown that they are statistically significant . Statisticians can use the difference between the control group and experimental group and the expected difference to determine if the experiment supports the hypothesis , or if the data was simply created by chance.

Examples of Controlled Experiment

Music preference in dogs.

Do dogs have a taste in music? You might have considered this, and science has too. Believe it or not, researchers have actually tested dog’s reactions to various music genres. To set up a controlled experiment like this, scientists had to consider the many variables that affect each dog during testing. The environment the dog is in when listening to music, the volume of the music, the presence of humans, and even the temperature were all variables that the researches had to consider.

In this case, the genre of the music was the independent variable. In other words, to see if dog’s change their behavior in response to different kinds of music, a controlled experiment had to limit the interaction of the other variables on the dogs. Usually, an experiment like this is carried out in the same location, with the same lighting, furniture, and conditions every time. This ensures that the dogs are not changing their behavior in response to the room. To make sure the dogs don’t react to humans or simply the noise of the music, no one else can be in the room and the music must be played at the same volume for each genre. Scientist will develop protocols for their experiment, which will ensure that many other variables are controlled.

This experiment could also split the dogs into two groups, only testing music on one group. The control group would be used to set a baseline behavior, and see how dogs behaved without music. The other group could then be observed and the differences in the group’s behavior could be analyzed. By rating behaviors on a quantitative scale, statistics can be used to analyze the difference in behavior, and see if it was large enough to be considered significant. This basic experiment was carried out on a large number of dogs, analyzing their behavior with a variety of different music genres. It was found that dogs do show more relaxed and calm behaviors when a specific type of music plays. Come to find out, dogs enjoy reggae the most.

Scurvy in Sailors

In the early 1700s, the world was a rapidly expanding place. Ships were being built and sent all over the world, carrying thousands and thousands of sailors. These sailors were mostly fed the cheapest diets possible, not only because it decreased the costs of goods, but also because fresh food is very hard to keep at sea. Today, we understand that lack of essential vitamins and nutrients can lead to severe deficiencies that manifest as disease. One of these diseases is scurvy.

Scurvy is caused by a simple vitamin C deficiency, but the effects can be brutal. Although early symptoms just include general feeling of weakness, the continued lack of vitamin C will lead to a breakdown of the blood cells and vessels that carry the blood. This results in blood leaking from the vessels. Eventually, people bleed to death internally and die. Before controlled experiments were commonplace, a simple physician decided to tackle the problem of scurvy. James Lind, of the Royal Navy, came up with a simple controlled experiment to find the best cure for scurvy.

He separated sailors with scurvy into various groups. He subjected them to the same controlled condition and gave them the same diet, except one item. Each group was subjected to a different treatment or remedy, taken with their food. Some of these remedies included barley water, cider and a regiment of oranges and lemons. This created the first clinical trial , or test of the effectiveness of certain treatments in a controlled experiment. Lind found that the oranges and lemons helped the sailors recover fast, and within a few years the Royal Navy had developed protocols for growing small leafy greens that contained high amounts of vitamin C to feed their sailors.

Related Biology Terms

• Field Experiment – An experiment conducted in nature, outside the bounds of total control.
• Independent Variable – The thing in an experiment being changed or manipulated by the experimenter to see effects on the subject.
• Controlled Variable – A thing that is normalized or standardized across an experiment, to remove it from having an effect on the subject being studied.
• Control Group – A group of subjects in an experiment that receive no independent variable, or a normalized amount, to provide comparison.

1. Why is it necessary for scientist to conduct controlled experiments? A. They allow for more definite relationships of cause and effect to be established B. Without control, anything could happen in the experiment C. Safety first! Controls are just silly safety precautions

2. A population of birds is being studied. Which of the following describes a controlled experiment on the birds? A. The birds are subjected to a lighting strike, and the results observed. B. The birds are split in two groups, one left in the wild and one kept in captivity. After time, the effects are measured and compared. C. The birds are observed as they migrate from North to South America.

3. A scientist is interested in the effects of a pesticide on the eggs of certain birds. The scientist takes some eggs and coats them with pesticide, and does not coat a second group of eggs. He places them in an incubator for several days, then measures several chemical and physical properties of the eggs. Is this a good controlled experiment? A. Yes B. No C. Maybe, but there may be more to the picture

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• Knowledge Base

Methodology

• Guide to Experimental Design | Overview, Steps, & Examples

Guide to Experimental Design | Overview, 5 steps & Examples

Published on December 3, 2019 by Rebecca Bevans . Revised on June 21, 2023.

Experiments are used to study causal relationships . You manipulate one or more independent variables and measure their effect on one or more dependent variables.

Experimental design create a set of procedures to systematically test a hypothesis . A good experimental design requires a strong understanding of the system you are studying.

There are five key steps in designing an experiment:

• Consider your variables and how they are related
• Write a specific, testable hypothesis
• Design experimental treatments to manipulate your independent variable
• Assign subjects to groups, either between-subjects or within-subjects
• Plan how you will measure your dependent variable

For valid conclusions, you also need to select a representative sample and control any  extraneous variables that might influence your results. If random assignment of participants to control and treatment groups is impossible, unethical, or highly difficult, consider an observational study instead. This minimizes several types of research bias, particularly sampling bias , survivorship bias , and attrition bias as time passes.

Table of contents

Step 1: define your variables, step 2: write your hypothesis, step 3: design your experimental treatments, step 4: assign your subjects to treatment groups, step 5: measure your dependent variable, other interesting articles, frequently asked questions about experiments.

You should begin with a specific research question . We will work with two research question examples, one from health sciences and one from ecology:

To translate your research question into an experimental hypothesis, you need to define the main variables and make predictions about how they are related.

Start by simply listing the independent and dependent variables .

Then you need to think about possible extraneous and confounding variables and consider how you might control  them in your experiment.

Finally, you can put these variables together into a diagram. Use arrows to show the possible relationships between variables and include signs to show the expected direction of the relationships.

Here we predict that increasing temperature will increase soil respiration and decrease soil moisture, while decreasing soil moisture will lead to decreased soil respiration.

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

• Academic style
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Now that you have a strong conceptual understanding of the system you are studying, you should be able to write a specific, testable hypothesis that addresses your research question.

The next steps will describe how to design a controlled experiment . In a controlled experiment, you must be able to:

• Systematically and precisely manipulate the independent variable(s).
• Precisely measure the dependent variable(s).
• Control any potential confounding variables.

If your study system doesn’t match these criteria, there are other types of research you can use to answer your research question.

How you manipulate the independent variable can affect the experiment’s external validity – that is, the extent to which the results can be generalized and applied to the broader world.

First, you may need to decide how widely to vary your independent variable.

• just slightly above the natural range for your study region.
• over a wider range of temperatures to mimic future warming.
• over an extreme range that is beyond any possible natural variation.

Second, you may need to choose how finely to vary your independent variable. Sometimes this choice is made for you by your experimental system, but often you will need to decide, and this will affect how much you can infer from your results.

• a categorical variable : either as binary (yes/no) or as levels of a factor (no phone use, low phone use, high phone use).
• a continuous variable (minutes of phone use measured every night).

How you apply your experimental treatments to your test subjects is crucial for obtaining valid and reliable results.

First, you need to consider the study size : how many individuals will be included in the experiment? In general, the more subjects you include, the greater your experiment’s statistical power , which determines how much confidence you can have in your results.

Then you need to randomly assign your subjects to treatment groups . Each group receives a different level of the treatment (e.g. no phone use, low phone use, high phone use).

You should also include a control group , which receives no treatment. The control group tells us what would have happened to your test subjects without any experimental intervention.

When assigning your subjects to groups, there are two main choices you need to make:

• A completely randomized design vs a randomized block design .
• A between-subjects design vs a within-subjects design .

Randomization

An experiment can be completely randomized or randomized within blocks (aka strata):

• In a completely randomized design , every subject is assigned to a treatment group at random.
• In a randomized block design (aka stratified random design), subjects are first grouped according to a characteristic they share, and then randomly assigned to treatments within those groups.

Sometimes randomization isn’t practical or ethical , so researchers create partially-random or even non-random designs. An experimental design where treatments aren’t randomly assigned is called a quasi-experimental design .

Between-subjects vs. within-subjects

In a between-subjects design (also known as an independent measures design or classic ANOVA design), individuals receive only one of the possible levels of an experimental treatment.

In medical or social research, you might also use matched pairs within your between-subjects design to make sure that each treatment group contains the same variety of test subjects in the same proportions.

In a within-subjects design (also known as a repeated measures design), every individual receives each of the experimental treatments consecutively, and their responses to each treatment are measured.

Within-subjects or repeated measures can also refer to an experimental design where an effect emerges over time, and individual responses are measured over time in order to measure this effect as it emerges.

Counterbalancing (randomizing or reversing the order of treatments among subjects) is often used in within-subjects designs to ensure that the order of treatment application doesn’t influence the results of the experiment.

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Finally, you need to decide how you’ll collect data on your dependent variable outcomes. You should aim for reliable and valid measurements that minimize research bias or error.

Some variables, like temperature, can be objectively measured with scientific instruments. Others may need to be operationalized to turn them into measurable observations.

• Ask participants to record what time they go to sleep and get up each day.
• Ask participants to wear a sleep tracker.

How precisely you measure your dependent variable also affects the kinds of statistical analysis you can use on your data.

Experiments are always context-dependent, and a good experimental design will take into account all of the unique considerations of your study system to produce information that is both valid and relevant to your research question.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval
• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Likert scale

Research bias

• Implicit bias
• Framing effect
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hindsight bias
• Affect heuristic

Experimental design means planning a set of procedures to investigate a relationship between variables . To design a controlled experiment, you need:

• A testable hypothesis
• At least one independent variable that can be precisely manipulated
• At least one dependent variable that can be precisely measured

When designing the experiment, you decide:

• How you will manipulate the variable(s)
• How you will control for any potential confounding variables
• How many subjects or samples will be included in the study
• How subjects will be assigned to treatment levels

Experimental design is essential to the internal and external validity of your experiment.

The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment .

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.

An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.

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Bevans, R. (2023, June 21). Guide to Experimental Design | Overview, 5 steps & Examples. Scribbr. Retrieved June 7, 2024, from https://www.scribbr.com/methodology/experimental-design/

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Rebecca Bevans

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Statistics By Jim

Making statistics intuitive

Control Variables: Definition, Uses & Examples

By Jim Frost 3 Comments

What is a Control Variable?

Control variables, also known as controlled variables, are properties that researchers hold constant for all observations in an experiment. While these variables are not the primary focus of the research, keeping their values consistent helps the study establish the true relationships between the independent and dependent variables. The capacity to control variables directly is highest in experiments that researchers conduct under lab conditions. In observational studies, researchers can’t directly control the variables. Instead, they record the values of control variables and then use statistical procedures to account for them.

In science, researchers assess the effects that the independent variables have on the dependent variable. However, other variables can also affect the outcome. If the scientists do not control these other variables, they can distort the primary results of interest. In other words, left uncontrolled, those other factors become confounders that can bias the findings. The uncontrolled variables may be responsible for the changes in the outcomes rather than your treatment or experimental variables. Consequently, researchers control the values of these other variables.

Suppose you are performing an experiment involving different types of fertilizers and plant growth. Those are your primary variables of interest. However, you also know that soil moisture, sunlight, and temperature affect plant growth. If you don’t hold these variables constant for all observations, they might explain the plant growth differences you observe. Consequently, moisture, sunlight, and temperature are essential control variables for your study.

If you perform the study in a controlled lab setting, you can control these environmental conditions and keep their values constant for all observations in your experiment. That way, if you do see plant growth differences, you can be more confident that the fertilizers caused them.

When researchers use control variables, they should identify them, record their values, and include the details in their write-up. This process helps other researchers understand and replicate the results.

Related posts : Independent and Dependent Variables and Confounding Variables

Control Variables and Internal Validity

By controlling variables, you increase the internal validity of your research. Internal validity is the degree of confidence that a causal relationship exists between the treatment and the difference in outcomes. In other words, how likely is it that your treatment caused the differences you observe? Are the researcher’s conclusions correct? Or, can changes in the outcome be attributed to other causes?

If the relevant variables are not controlled, you might need to attribute the changes to confounders rather than the treatment. Control variables reduce the impact of confounding variables.

Controlled Variable Examples

How to Control Variables in Science

Scientists can control variables using several methods. In some cases, variables can be controlled directly. For example, researchers can control the growing conditions for the fertilizer experiment. Or use standardized procedures and processes for all subjects to reduce other sources of variation. These efforts attempt to eliminate all differences between the treatment and control groups other than the treatments themselves.

However, sometimes that’s not possible. Fortunately, there are other approaches.

Random assignment

In some experiments, there can be too many variables to control. Additionally, the researchers might not even know all the potential confounding variables. In these cases, they can randomly assign subjects to the experimental groups. This process controls variables by averaging out all traits across the experimental groups, making them roughly equivalent when the experiment begins. The randomness helps prevent any systematic differences between the experimental groups. Learn more in my post about Random Assignment in Experiments .

Statistical control

Directly controlled variables and random assignment are methods that equalize the experimental groups. However, they aren’t always feasible. In some cases, there are too many variables to control. In other situations, random assignment might not be possible. Try randomly assigning people to smoking and non-smoking groups!

Fortunately, statistical techniques, such as multiple regression analysis , don’t balance the groups but instead use a model that statistically controls the variables. The model accounts for confounding variables.

In multiple regression analysis, including a variable in the model holds it constant while the treatment variable fluctuates. This process allows you to isolate the role of the treatment while accounting for confounders. You can also use ANOVA and ANCOVA.

For more information, read my posts, When to Use Regression and ANOVA Overview .

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Reader Interactions

February 28, 2024 at 2:09 pm

In your explanation of control variables you use the example of a research study of plant fertilizers and their growth, wanting to control for moisture, sunshine and temperature. You state “Consequently, moisture, sunlight, and temperature are essential control variables for your study. These variables can be controlled by keeping their values constant for all observations in your experiment. You do not go further as to how you control for these values, particularly when such variables are continually changing. Al Wassler

February 28, 2024 at 2:13 pm

Presumably, this experiment would occur in a lab setting where you can control these variables. Plants would be raised with the same humidity, soil moisture, and light conditions.

I’ll add some text to the article to clarify that. Thanks!

January 26, 2023 at 7:00 pm

I have a question please about when a control variable is also itself part of the dependent variable. I see this referred to in the medical research literature as ‘mathematical coupling’, where – for example – the beats per minute (BPM) is the dependent variable and researchers want to put minutes also as a control variable. This seems to create a problem because ‘minutes’ appears on both sides of the equation, and the medical literature talks about spurious correlation, and the model needing to be redesigned. But do you have a simple text or reference – ideally just plain statistics/OLS rather than linked to medical research – where this could be explained in theory terms ? What goes wrong in the regression when a variable is both a control variable and part of the dependent variable (perhaps as part of a ratio or measurement of change)? I just haven’t found a textbook reference that says definitively ‘you can’t have the same variable in both sides of the regression simultaneously’, so I’m not sure whether this violates OLS and so is something to avoid entirely (with a new model design or different research question) or to live with.

Any help would be great, thank you for your work,

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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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Home » Control Variable – Definition, Types and Examples

Control Variable – Definition, Types and Examples

Table of Contents

Control Variable

Definition :

Control variable, also known as a “constant variable,” is a variable that is held constant or fixed during an experiment or study to prevent it from affecting the outcome. In other words, a control variable is a variable that is kept the same or held constant to isolate the effects of the independent variable on the dependent variable.

For example, if you were conducting an experiment to test how temperature affects plant growth, you might want to control variables such as the amount of water, the amount of sunlight, and the type of soil to ensure that these variables do not interfere with the results. By controlling these variables, you can isolate the effect of temperature on plant growth and draw more accurate conclusions from the experiment.

Types of Control Variables

Types of Control Variables are as follows:

Environmental Control Variables

These are variables related to the physical environment in which the experiment is conducted, such as temperature, humidity, light, and sound.

Participant Control Variables

These are variables related to the participants in the experiment, such as age, gender, prior knowledge, or experience.

Experimental Control Variables

These are variables that the researcher manipulates or controls to ensure that they do not affect the outcome of the experiment. For example, in a study on the effects of a new medication, the researcher might control the dosage, frequency, or duration of the treatment.

Procedural Control Variables

These are variables related to the procedures or methods used in the experiment, such as the order in which tasks are completed, the timing of measurements, or the instructions given to participants.

Equipment Control Variables

These are variables related to the equipment or instruments used in the experiment, such as calibration, maintenance, or proper functioning.

How to Control a Variable

To control a variable in a scientific experiment, you need to ensure that it is kept constant or unchanged throughout the experiment. Here are some steps to help you control a variable:

Identify the Variable

Start by identifying the variable that you want to control. This can be an environmental, subject, procedural, or instrumentation variable.

Determine the Level of Control Needed

Depending on the variable, you may need to exert varying levels of control. For example, environmental variables may require you to control the temperature, humidity, and lighting in your experiment, while subject variables may require you to select a specific group of participants that meet certain criteria.

Establish a Standard Level

Determine the standard level or value of the variable that you want to control. For example, if you are controlling the temperature, you may set the temperature to a specific degree and ensure that it is maintained at that level throughout the experiment.

Monitor the Variable

Throughout the experiment, monitor the variable to ensure that it remains constant. Use appropriate equipment or instruments to measure the variable and make adjustments as necessary to maintain the desired level.

Document the Process

Document the process of controlling the variable to ensure that the experiment is replicable. This includes documenting the standard level, monitoring procedures, and any adjustments made during the experiment.

Examples of Control Variables

Here are some examples of control variables in Scientific Experiments and Research:

• Environmental Control Variables Example: Suppose you are conducting an experiment to study the effect of light on plant growth. You would want to control environmental factors such as temperature, humidity, and soil nutrients. In this case, you might keep the temperature and humidity constant and use the same type and amount of soil for all the plants.
• Subject Control Variables Example : If you are conducting an experiment to study the effect of a new medication on blood pressure, you would want to control subject variables such as age, gender, and health status. In this case, you might select a group of participants with similar ages, genders, and health conditions to ensure that these variables do not affect the results.
• Procedural Control Variables Example : Suppose you are conducting an experiment to study the effect of distraction on reaction time. You would want to control procedural variables such as the time of day, the order of the tasks, and the instructions given to the participants. In this case, you might ensure that all participants perform the tasks in the same order, at the same time of day, and receive the same instructions.
• Instrumentation Control Variables Example : If you are conducting an experiment to study the effect of a new measurement device on the accuracy of readings, you would want to control instrumentation variables such as the type and calibration of the device. In this case, you might use the same type and model of the device and ensure that it is calibrated before each use.

Applications of Control Variable

Control variables are widely used in scientific research across various fields, including physics, biology, psychology, and engineering. Here are some applications of control variables:

• In medical research , control variables are used to ensure that any observed effects of a new treatment or medication are due to the treatment and not some other variable. By controlling subject variables such as age, gender, and health status, researchers can isolate the effects of the treatment and determine its effectiveness.
• In environmental research , control variables are used to study the effects of changes in the environment on various species or ecosystems. By controlling environmental variables such as temperature, humidity, and lighting, researchers can determine how different species adapt to changes in the environment.
• In psychology research, control variables are used to study the effects of different interventions or therapies on cognitive or behavioral outcomes. By controlling procedural variables such as the order of tasks, the length of time allotted for each task, and the instructions given to participants, researchers can isolate the effects of the intervention and determine its effectiveness.
• In engineering research, control variables are used to study the effects of different design parameters on the performance of a system or device. By controlling instrumentation variables such as the type of measurement device used and the calibration of instruments, researchers can ensure that the measurements are accurate and reliable.

Purpose of Control Variable

The purpose of a control variable in an experiment is to ensure that any observed changes or effects are a result of the manipulation of the independent variable and not some other variable. By keeping certain variables constant, researchers can isolate the effects of the independent variable and determine whether it has a significant effect on the dependent variable.

Control variables are important because they help to increase the reliability and validity of the experiment. Reliability refers to the consistency and reproducibility of the results, while validity refers to the accuracy and truthfulness of the results. By controlling variables, researchers can reduce the potential for extraneous or confounding variables that can affect the outcome of the experiment and increase the likelihood that the results accurately reflect the effect of the independent variable on the dependent variable.

Characteristics of Control Variable

Control variables have the following characteristics:

• Constant : Control variables are kept constant or unchanged throughout the experiment. This means that their values do not vary or change during the experiment. Keeping control variables constant helps to ensure that any observed effects or changes are due to the manipulation of the independent variable and not some other variable.
• Independent : Control variables are independent of the independent variable being studied. This means that they do not affect the relationship between the independent and dependent variables. By controlling for independent variables, researchers can isolate the effect of the independent variable and determine its impact on the dependent variable.
• Documented: Control variables are documented in the experiment. This means that their values and methods of control are recorded and reported in the results section of the research paper. By documenting control variables, researchers can demonstrate the rigor and transparency of their study and allow other researchers to replicate their methods.
• Relevant: Control variables are relevant to the research question. This means that they are chosen based on their potential to affect the outcome of the experiment. By selecting relevant control variables, researchers can reduce the potential for extraneous or confounding variables that can affect the outcome of the experiment and increase the reliability and validity of the results.
• Varied : Control variables can be varied across different conditions or groups. This means that different levels of control may be needed depending on the research question or hypothesis being tested. By varying control variables, researchers can test different hypotheses and determine the factors that affect the outcome of the experiment.

Advantages of Control Variable

The advantages of using control variables in an experiment are:

• Increased accuracy : Control variables help to increase the accuracy of the results by reducing the potential for extraneous or confounding variables that can affect the outcome of the experiment. By controlling for these variables, researchers can isolate the effect of the independent variable on the dependent variable and determine whether it has a significant impact.
• Increased reliability : Control variables help to increase the reliability of the results by reducing the variability in the experiment. By keeping certain variables constant, researchers can ensure that any observed changes or effects are due to the manipulation of the independent variable and not some other variable.
• Reproducibility: Control variables help to increase the reproducibility of the results by ensuring that the same results can be obtained when the experiment is repeated. By documenting and reporting control variables, researchers can demonstrate the rigor and transparency of their study and allow other researchers to replicate their methods.
• Generalizability : Control variables help to increase the generalizability of the results by reducing the potential for bias and increasing the external validity of the experiment. By controlling for relevant variables, researchers can ensure that their findings are applicable to a broader population or context.
• Causality : Control variables help to establish causality by ensuring that any observed changes or effects are due to the manipulation of the independent variable and not some other variable. By controlling for confounding variables, researchers can increase the internal validity of the experiment and establish a cause-and-effect relationship between the independent and dependent variables.

Disadvantages of Control Variable

There are some potential disadvantages or limitations of using control variables in an experiment:

• Complexity : Controlling for multiple variables can make an experiment more complex and time-consuming. This can increase the likelihood of errors and reduce the feasibility of the experiment, especially if the control variables require a lot of resources or are difficult to measure.
• Artificiality : Controlling for variables can make the experimental conditions artificial and not reflective of real-world situations. This can reduce the external validity of the experiment and limit the generalizability of the findings to real-world settings.
• Limited scope : Controlling for specific variables can limit the scope of the experiment and make it difficult to generalize the results to other situations or populations. This can reduce the external validity of the experiment and limit its practical applications.
• Assumptions: Controlling for variables requires making assumptions about which variables are relevant and how they should be controlled. These assumptions may not be valid or accurate, and the results of the experiment may be affected by uncontrolled variables that were not considered.
• Cost : Controlling for variables can be costly, especially if the control variables require additional resources or equipment. This can limit the feasibility of the experiment, especially for researchers with limited funding or resources.

Limitations of Control Variable

There are several limitations of using control variables in an experiment, including:

• Not all variables can be controlled : There may be some variables that cannot be controlled or manipulated in an experiment. For example, some variables may be too difficult or expensive to measure or control, or they may be affected by factors outside of the researcher’s control.
• Interaction effects : Control variables can interact with each other, which can lead to unexpected results. For example, controlling for one variable may have a different effect when another variable is also controlled, or when the two variables interact with each other. These interaction effects can be difficult to predict or control for.
• Over-reliance on statistical significance: Controlling for variables can increase the statistical significance of the results, but this may not always translate to practical significance or real-world significance. Researchers should interpret the results of an experiment in light of the practical significance, not just the statistical significance.
• Limited generalizability : Controlling for variables can limit the generalizability of the results to other populations or situations. If the control variables are not representative of other populations or situations, the results of the experiment may not be applicable to those contexts.
• May mask important effects : Controlling for variables can mask important effects that are related to the independent variable. By controlling for certain variables, researchers may miss important interactions between the independent variable and the controlled variable, which can limit the understanding of the causal relationship between the two.

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Experimental Design - Independent, Dependent, and Controlled Variables

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Scientific experiments are meant to show cause and effect of a phenomena (relationships in nature).  The “ variables ” are any factor, trait, or condition that can be changed in the experiment and that can have an effect on the outcome of the experiment.

An experiment can have three kinds of variables: i ndependent, dependent, and controlled .

• The independent variable is one single factor that is changed by the scientist followed by observation to watch for changes. It is important that there is just one independent variable, so that results are not confusing.
• The dependent variable is the factor that changes as a result of the change to the independent variable.
• The controlled variables (or constant variables) are factors that the scientist wants to remain constant if the experiment is to show accurate results. To be able to measure results, each of the variables must be able to be measured.

For example, let’s design an experiment with two plants sitting in the sun side by side. The controlled variables (or constants) are that at the beginning of the experiment, the plants are the same size, get the same amount of sunlight, experience the same ambient temperature and are in the same amount and consistency of soil (the weight of the soil and container should be measured before the plants are added). The independent variable is that one plant is getting watered (1 cup of water) every day and one plant is getting watered (1 cup of water) once a week. The dependent variables are the changes in the two plants that the scientist observes over time.

Can you describe the dependent variable that may result from this experiment? After four weeks, the dependent variable may be that one plant is taller, heavier and more developed than the other. These results can be recorded and graphed by measuring and comparing both plants’ height, weight (removing the weight of the soil and container recorded beforehand) and a comparison of observable foliage.

Using What You Learned: Design another experiment using the two plants, but change the independent variable. Can you describe the dependent variable that may result from this new experiment?

Think of another simple experiment and name the independent, dependent, and controlled variables. Use the graphic organizer included in the PDF below to organize your experiment's variables.

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Examples of Independent and Dependent Variables

What Are Independent and Dependent Variables?

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Both the independent variable and dependent variable are examined in an experiment using the scientific method , so it's important to know what they are and how to use them.

In a scientific experiment, you'll ultimately be changing or controlling the independent variable and measuring the effect on the dependent variable. This distinction is critical in evaluating and proving hypotheses.

Below you'll find more about these two types of variables, along with examples of each in sample science experiments, and an explanation of how to graph them to help visualize your data.

What Is an Independent Variable?

An independent variable is the condition that you change in an experiment. In other words, it is the variable you control. It is called independent because its value does not depend on and is not affected by the state of any other variable in the experiment. Sometimes you may hear this variable called the "controlled variable" because it is the one that is changed. Do not confuse it with a control variable , which is a variable that is purposely held constant so that it can't affect the outcome of the experiment.

• What Is a Dependent Variable?

The dependent variable is the condition that you measure in an experiment. You are assessing how it responds to a change in the independent variable, so you can think of it as depending on the independent variable. Sometimes the dependent variable is called the "responding variable."

Independent and Dependent Variable Examples

• In a study to determine whether the amount of time a student sleeps affects test scores, the independent variable is the amount of time spent sleeping while the dependent variable is the test score.
• You want to compare brands of paper towels to see which holds the most liquid. The independent variable in your experiment would be the brand of paper towels. The dependent variable would be the amount of liquid absorbed by the paper towel.
• In an experiment to determine how far people can see into the infrared part of the spectrum, the wavelength of light is the independent variable and whether the light is observed (the response) is the dependent variable.
• If you want to know whether caffeine affects your appetite, the presence or absence of a given amount of caffeine would be the independent variable. How hungry you are would be the dependent variable.
• You want to determine whether a chemical is essential for rat nutrition, so you design an experiment. The presence or absence of the chemical is the independent variable. The health of the rat (whether it lives and can reproduce) is the dependent variable. If you determine the substance is necessary for proper nutrition, a follow-up experiment might determine how much of the chemical is needed. Here, the amount of the chemical would be the independent variable, and the rat's health would be the dependent variable.

How Do You Tell Independent and Dependent Variables Apart?

If you are having a hard time identifying which variable is the independent variable and which is the dependent variable, remember the dependent variable is the one affected by a change in the independent variable. If you write out the variables in a sentence that shows cause and effect, the independent variable causes the effect on the dependent variable. If you have the variables in the wrong order, the sentence won't make sense.

Independent variable causes an effect on the dependent variable.

Example : How long you sleep (independent variable) affects your test score (dependent variable).

This makes sense, but:

Example : Your test score affects how long you sleep.

This doesn't really make sense (unless you can't sleep because you are worried you failed a test, but that would be a different experiment).

How to Plot Variables on a Graph

There is a standard method for graphing independent and dependent variables. The x-axis is the independent variable, while the y-axis is the dependent variable. You can use the DRY MIX acronym to help remember how to graph variables:

D  = dependent variable R  = responding variable Y  = graph on the vertical or y-axis

M  = manipulated variable I  = independent variable X  = graph on the horizontal or x-axis

Test your understanding with the scientific method quiz .

Key Takeaways

• In scientific experiments, the independent variable is manipulated while the dependent variable is measured.
• The independent variable, controlled by the experimenter, influences the dependent variable, which responds to changes. This dynamic forms the basis of cause-and-effect relationships.
• Graphing independent and dependent variables follows a standard method in which the independent variable is plotted on the x-axis and the dependent variable on the y-axis.
• Difference Between Independent and Dependent Variables
• Null Hypothesis Examples
• Dependent Variable Definition and Examples
• Independent Variable Definition and Examples
• Popular Math Terms and Definitions
• Scientific Variable
• What Is a Variable in Science?
• DRY MIX Experiment Variables Acronym
• What Is an Experiment? Definition and Design
• Six Steps of the Scientific Method
• The Significance of Negative Slope
• The Differences Between Explanatory and Response Variables
• What Is a Hypothesis? (Science)
• What Are the Elements of a Good Hypothesis?
• Scientific Method Vocabulary Terms

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7.1: Basics of Hypothesis Testing

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To understand the process of a hypothesis tests, you need to first have an understanding of what a hypothesis is, which is an educated guess about a parameter. Once you have the hypothesis, you collect data and use the data to make a determination to see if there is enough evidence to show that the hypothesis is true. However, in hypothesis testing you actually assume something else is true, and then you look at your data to see how likely it is to get an event that your data demonstrates with that assumption. If the event is very unusual, then you might think that your assumption is actually false. If you are able to say this assumption is false, then your hypothesis must be true. This is known as a proof by contradiction. You assume the opposite of your hypothesis is true and show that it can’t be true. If this happens, then your hypothesis must be true. All hypothesis tests go through the same process. Once you have the process down, then the concept is much easier. It is easier to see the process by looking at an example. Concepts that are needed will be detailed in this example.

Example \(\PageIndex{1}\) basics of hypothesis testing

Suppose a manufacturer of the XJ35 battery claims the mean life of the battery is 500 days with a standard deviation of 25 days. You are the buyer of this battery and you think this claim is inflated. You would like to test your belief because without a good reason you can’t get out of your contract.

What do you do?

Well first, you should know what you are trying to measure. Define the random variable.

Let x = life of a XJ35 battery

Now you are not just trying to find different x values. You are trying to find what the true mean is. Since you are trying to find it, it must be unknown. You don’t think it is 500 days. If you did, you wouldn’t be doing any testing. The true mean, \(\mu\), is unknown. That means you should define that too.

Let \(\mu\)= mean life of a XJ35 battery

You may want to collect a sample. What kind of sample?

You could ask the manufacturers to give you batteries, but there is a chance that there could be some bias in the batteries they pick. To reduce the chance of bias, it is best to take a random sample.

How big should the sample be?

A sample of size 30 or more means that you can use the central limit theorem. Pick a sample of size 30.

Example \(\PageIndex{1}\) contains the data for the sample you collected:

Now what should you do? Looking at the data set, you see some of the times are above 500 and some are below. But looking at all of the numbers is too difficult. It might be helpful to calculate the mean for this sample.

The sample mean is \(\overline{x} = 490\) days. Looking at the sample mean, one might think that you are right. However, the standard deviation and the sample size also plays a role, so maybe you are wrong.

Before going any farther, it is time to formalize a few definitions.

You have a guess that the mean life of a battery is less than 500 days. This is opposed to what the manufacturer claims. There really are two hypotheses, which are just guesses here – the one that the manufacturer claims and the one that you believe. It is helpful to have names for them.

Definition \(\PageIndex{1}\)

Null Hypothesis : historical value, claim, or product specification. The symbol used is \(H_{o}\).

Definition \(\PageIndex{2}\)

Alternate Hypothesis : what you want to prove. This is what you want to accept as true when you reject the null hypothesis. There are two symbols that are commonly used for the alternative hypothesis: \(H_{A}\) or \(H_{I}\). The symbol \(H_{A}\) will be used in this book.

In general, the hypotheses look something like this:

\(H_{o} : \mu=\mu_{o}\)

\(H_{A} : \mu<\mu_{o}\)

where \(\mu_{o}\) just represents the value that the claim says the population mean is actually equal to.

Also, \(H_{A}\) can be less than, greater than, or not equal to.

For this problem:

\(H_{o} : \mu=500\) days, since the manufacturer says the mean life of a battery is 500 days.

\(H_{A} : \mu<500\) days, since you believe that the mean life of the battery is less than 500 days.

Now back to the mean. You have a sample mean of 490 days. Is this small enough to believe that you are right and the manufacturer is wrong? How small does it have to be?

If you calculated a sample mean of 235, you would definitely believe the population mean is less than 500. But even if you had a sample mean of 435 you would probably believe that the true mean was less than 500. What about 475? Or 483? There is some point where you would stop being so sure that the population mean is less than 500. That point separates the values of where you are sure or pretty sure that the mean is less than 500 from the area where you are not so sure. How do you find that point?

Well it depends on how much error you want to make. Of course you don’t want to make any errors, but unfortunately that is unavoidable in statistics. You need to figure out how much error you made with your sample. Take the sample mean, and find the probability of getting another sample mean less than it, assuming for the moment that the manufacturer is right. The idea behind this is that you want to know what is the chance that you could have come up with your sample mean even if the population mean really is 500 days.

You want to find \(P\left(\overline{x}<490 | H_{o} \text { is true }\right)=P(\overline{x}<490 | \mu=500)\)

To compute this probability, you need to know how the sample mean is distributed. Since the sample size is at least 30, then you know the sample mean is approximately normally distributed. Remember \(\mu_{\overline{x}}=\mu\) and \(\sigma_{\overline{x}}=\dfrac{\sigma}{\sqrt{n}}\)

A picture is always useful.

Before calculating the probability, it is useful to see how many standard deviations away from the mean the sample mean is. Using the formula for the z-score from chapter 6, you find

\(z=\dfrac{\overline{x}-\mu_{o}}{\sigma / \sqrt{n}}=\dfrac{490-500}{25 / \sqrt{30}}=-2.19\)

This sample mean is more than two standard deviations away from the mean. That seems pretty far, but you should look at the probability too.

On TI-83/84:

\(P(\overline{x}<490 | \mu=500)=\text { normalcdf }(-1 E 99,490,500,25 \div \sqrt{30}) \approx 0.0142\)

\(P(\overline{x}<490 \mu=500)=\text { pnorm }(490,500,25 / \operatorname{sqrt}(30)) \approx 0.0142\)

There is a 1.42% chance that you could find a sample mean less than 490 when the population mean is 500 days. This is really small, so the chances are that the assumption that the population mean is 500 days is wrong, and you can reject the manufacturer’s claim. But how do you quantify really small? Is 5% or 10% or 15% really small? How do you decide?

Before you answer that question, a couple more definitions are needed.

Definition \(\PageIndex{3}\)

Test Statistic : \(z=\dfrac{\overline{x}-\mu_{o}}{\sigma / \sqrt{n}}\) since it is calculated as part of the testing of the hypothesis.

Definition \(\PageIndex{4}\)

p – value : probability that the test statistic will take on more extreme values than the observed test statistic, given that the null hypothesis is true. It is the probability that was calculated above.

Now, how small is small enough? To answer that, you really want to know the types of errors you can make.

There are actually only two errors that can be made. The first error is if you say that \(H_{o}\) is false, when in fact it is true. This means you reject \(H_{o}\) when \(H_{o}\) was true. The second error is if you say that \(H_{o}\) is true, when in fact it is false. This means you fail to reject \(H_{o}\) when \(H_{o}\) is false. The following table organizes this for you:

Type of errors:

Definition \(\PageIndex{5}\)

Type I Error is rejecting \(H_{o}\) when \(H_{o}\) is true, and

Definition \(\PageIndex{6}\)

Type II Error is failing to reject \(H_{o}\) when \(H_{o}\) is false.

Since these are the errors, then one can define the probabilities attached to each error.

Definition \(\PageIndex{7}\)

\(\alpha\) = P(type I error) = P(rejecting \(H_{o} / H_{o}\) is true)

Definition \(\PageIndex{8}\)

\(\beta\) = P(type II error) = P(failing to reject \(H_{o} / H_{o}\) is false)

\(\alpha\) is also called the level of significance .

Another common concept that is used is Power = \(1-\beta \).

Now there is a relationship between \(\alpha\) and \(\beta\). They are not complements of each other. How are they related?

If \(\alpha\) increases that means the chances of making a type I error will increase. It is more likely that a type I error will occur. It makes sense that you are less likely to make type II errors, only because you will be rejecting \(H_{o}\) more often. You will be failing to reject \(H_{o}\) less, and therefore, the chance of making a type II error will decrease. Thus, as \(\alpha\) increases, \(\beta\) will decrease, and vice versa. That makes them seem like complements, but they aren’t complements. What gives? Consider one more factor – sample size.

Consider if you have a larger sample that is representative of the population, then it makes sense that you have more accuracy then with a smaller sample. Think of it this way, which would you trust more, a sample mean of 490 if you had a sample size of 35 or sample size of 350 (assuming a representative sample)? Of course the 350 because there are more data points and so more accuracy. If you are more accurate, then there is less chance that you will make any error. By increasing the sample size of a representative sample, you decrease both \(\alpha\) and \(\beta\).

Summary of all of this:

• For a certain sample size, n , if \(\alpha\) increases, \(\beta\) decreases.
• For a certain level of significance, \(\alpha\), if n increases, \(\beta\) decreases.

Now how do you find \(\alpha\) and \(\beta\)? Well \(\alpha\) is actually chosen. There are only three values that are usually picked for \(\alpha\): 0.01, 0.05, and 0.10. \(\beta\) is very difficult to find, so usually it isn’t found. If you want to make sure it is small you take as large of a sample as you can afford provided it is a representative sample. This is one use of the Power. You want \(\beta\) to be small and the Power of the test is large. The Power word sounds good.

Which pick of \(\alpha\) do you pick? Well that depends on what you are working on. Remember in this example you are the buyer who is trying to get out of a contract to buy these batteries. If you create a type I error, you said that the batteries are bad when they aren’t, most likely the manufacturer will sue you. You want to avoid this. You might pick \(\alpha\) to be 0.01. This way you have a small chance of making a type I error. Of course this means you have more of a chance of making a type II error. No big deal right? What if the batteries are used in pacemakers and you tell the person that their pacemaker’s batteries are good for 500 days when they actually last less, that might be bad. If you make a type II error, you say that the batteries do last 500 days when they last less, then you have the possibility of killing someone. You certainly do not want to do this. In this case you might want to pick \(\alpha\) as 0.10. If both errors are equally bad, then pick \(\alpha\) as 0.05.

The above discussion is why the choice of \(\alpha\) depends on what you are researching. As the researcher, you are the one that needs to decide what \(\alpha\) level to use based on your analysis of the consequences of making each error is.

If a type I error is really bad, then pick \(\alpha\) = 0.01.

If a type II error is really bad, then pick \(\alpha\) = 0.10

If neither error is bad, or both are equally bad, then pick \(\alpha\) = 0.05

The main thing is to always pick the \(\alpha\) before you collect the data and start the test.

The above discussion was long, but it is really important information. If you don’t know what the errors of the test are about, then there really is no point in making conclusions with the tests. Make sure you understand what the two errors are and what the probabilities are for them.

Now it is time to go back to the example and put this all together. This is the basic structure of testing a hypothesis, usually called a hypothesis test. Since this one has a test statistic involving z, it is also called a z-test. And since there is only one sample, it is usually called a one-sample z-test.

Example \(\PageIndex{2}\) battery example revisited

• State the random variable and the parameter in words.
• State the null and alternative hypothesis and the level of significance.
• A random sample of size n is taken.
• The population standard derivation is known.
• The sample size is at least 30 or the population of the random variable is normally distributed.
• Find the sample statistic, test statistic, and p-value.
• Interpretation

1. x = life of battery

\(\mu\) = mean life of a XJ35 battery

2. \(H_{o} : \mu=500\) days

\(H_{A} : \mu<500\) days

\(\alpha = 0.10\) (from above discussion about consequences)

3. Every hypothesis has some assumptions that be met to make sure that the results of the hypothesis are valid. The assumptions are different for each test. This test has the following assumptions.

• This occurred in this example, since it was stated that a random sample of 30 battery lives were taken.
• This is true, since it was given in the problem.
• The sample size was 30, so this condition is met.

4. The test statistic depends on how many samples there are, what parameter you are testing, and assumptions that need to be checked. In this case, there is one sample and you are testing the mean. The assumptions were checked above.

Sample statistic:

\(\overline{x} = 490\)

Test statistic:

Using TI-83/84:

\(P(\overline{x}<490 | \mu=500)=\text { normalcdf }(-1 \mathrm{E} 99,490,500,25 / \sqrt{30}) \approx 0.0142\)

\(P(\overline{x}<490 | \mu=500)=\operatorname{pnorm}(490,500,25 / \operatorname{sqrt}(30)) \approx 0.0142\)

5. Now what? Well, this p-value is 0.0142. This is a lot smaller than the amount of error you would accept in the problem -\(\alpha\) = 0.10. That means that finding a sample mean less than 490 days is unusual to happen if \(H_{o}\) is true. This should make you think that \(H_{o}\) is not true. You should reject \(H_{o}\).

In fact, in general:

Reject \(H_{o}\) if the p-value < \(\alpha\) and

Fail to reject \(H_{o}\) if the p-value \(\geq \alpha\).

6. Since you rejected \(H_{o}\), what does this mean in the real world? That is what goes in the interpretation. Since you rejected the claim by the manufacturer that the mean life of the batteries is 500 days, then you now can believe that your hypothesis was correct. In other words, there is enough evidence to show that the mean life of the battery is less than 500 days.

Now that you know that the batteries last less than 500 days, should you cancel the contract? Statistically, there is evidence that the batteries do not last as long as the manufacturer says they should. However, based on this sample there are only ten days less on average that the batteries last. There may not be practical significance in this case. Ten days do not seem like a large difference. In reality, if the batteries are used in pacemakers, then you would probably tell the patient to have the batteries replaced every year. You have a large buffer whether the batteries last 490 days or 500 days. It seems that it might not be worth it to break the contract over ten days. What if the 10 days was practically significant? Are there any other things you should consider? You might look at the business relationship with the manufacturer. You might also look at how much it would cost to find a new manufacturer. These are also questions to consider before making any changes. What this discussion should show you is that just because a hypothesis has statistical significance does not mean it has practical significance. The hypothesis test is just one part of a research process. There are other pieces that you need to consider.

That’s it. That is what a hypothesis test looks like. All hypothesis tests are done with the same six steps. Those general six steps are outlined below.

• State the random variable and the parameter in words. This is where you are defining what the unknowns are in this problem. x = random variable \(\mu\) = mean of random variable, if the parameter of interest is the mean. There are other parameters you can test, and you would use the appropriate symbol for that parameter.
• State the null and alternative hypotheses and the level of significance \(H_{o} : \mu=\mu_{o}\), where \(\mu_{o}\) is the known mean \(H_{A} : \mu<\mu_{o}\) \(H_{A} : \mu>\mu_{o}\), use the appropriate one for your problem \(H_{A} : \mu \neq \mu_{o}\) Also, state your \(\alpha\) level here.
• State and check the assumptions for a hypothesis test. Each hypothesis test has its own assumptions. They will be stated when the different hypothesis tests are discussed.
• Find the sample statistic, test statistic, and p-value. This depends on what parameter you are working with, how many samples, and the assumptions of the test. The p-value depends on your \(H_{A}\). If you are doing the \(H_{A}\) with the less than, then it is a left-tailed test, and you find the probability of being in that left tail. If you are doing the \(H_{A}\) with the greater than, then it is a right-tailed test, and you find the probability of being in the right tail. If you are doing the \(H_{A}\) with the not equal to, then you are doing a two-tail test, and you find the probability of being in both tails. Because of symmetry, you could find the probability in one tail and double this value to find the probability in both tails.
• Conclusion This is where you write reject \(H_{o}\) or fail to reject \(H_{o}\). The rule is: if the p-value < \(\alpha\), then reject \(H_{o}\). If the p-value \(\geq \alpha\), then fail to reject \(H_{o}\).
• Interpretation This is where you interpret in real world terms the conclusion to the test. The conclusion for a hypothesis test is that you either have enough evidence to show \(H_{A}\) is true, or you do not have enough evidence to show \(H_{A}\) is true.

Sorry, one more concept about the conclusion and interpretation. First, the conclusion is that you reject \(H_{o}\) or you fail to reject \(H_{o}\). Why was it said like this? It is because you never accept the null hypothesis. If you wanted to accept the null hypothesis, then why do the test in the first place? In the interpretation, you either have enough evidence to show \(H_{A}\) is true, or you do not have enough evidence to show \(H_{A}\) is true. You wouldn’t want to go to all this work and then find out you wanted to accept the claim. Why go through the trouble? You always want to show that the alternative hypothesis is true. Sometimes you can do that and sometimes you can’t. It doesn’t mean you proved the null hypothesis; it just means you can’t prove the alternative hypothesis. Here is an example to demonstrate this.

Example \(\PageIndex{3}\) conclusion in hypothesis tests

In the U.S. court system a jury trial could be set up as a hypothesis test. To really help you see how this works, let’s use OJ Simpson as an example. In the court system, a person is presumed innocent until he/she is proven guilty, and this is your null hypothesis. OJ Simpson was a football player in the 1970s. In 1994 his ex-wife and her friend were killed. OJ Simpson was accused of the crime, and in 1995 the case was tried. The prosecutors wanted to prove OJ was guilty of killing his wife and her friend, and that is the alternative hypothesis

\(H_{0}\): OJ is innocent of killing his wife and her friend

\(H_{A}\): OJ is guilty of killing his wife and her friend

In this case, a verdict of not guilty was given. That does not mean that he is innocent of this crime. It means there was not enough evidence to prove he was guilty. Many people believe that OJ was guilty of this crime, but the jury did not feel that the evidence presented was enough to show there was guilt. The verdict in a jury trial is always guilty or not guilty!

The same is true in a hypothesis test. There is either enough or not enough evidence to show that alternative hypothesis. It is not that you proved the null hypothesis true.

When identifying hypothesis, it is important to state your random variable and the appropriate parameter you want to make a decision about. If count something, then the random variable is the number of whatever you counted. The parameter is the proportion of what you counted. If the random variable is something you measured, then the parameter is the mean of what you measured. (Note: there are other parameters you can calculate, and some analysis of those will be presented in later chapters.)

Example \(\PageIndex{4}\) stating hypotheses

Identify the hypotheses necessary to test the following statements:

• The average salary of a teacher is more than $30,000.
• The proportion of students who like math is less than 10%.
• The average age of students in this class differs from 21.

a. x = salary of teacher

\(\mu\) = mean salary of teacher

The guess is that \(\mu>\$ 30,000\) and that is the alternative hypothesis.

The null hypothesis has the same parameter and number with an equal sign.

\(\begin{array}{l}{H_{0} : \mu=\$ 30,000} \\ {H_{A} : \mu>\$ 30,000}\end{array}\)

b. x = number od students who like math

p = proportion of students who like math

The guess is that p < 0.10 and that is the alternative hypothesis.

\(\begin{array}{l}{H_{0} : p=0.10} \\ {H_{A} : p<0.10}\end{array}\)

c. x = age of students in this class

\(\mu\) = mean age of students in this class

The guess is that \(\mu \neq 21\) and that is the alternative hypothesis.

\(\begin{array}{c}{H_{0} : \mu=21} \\ {H_{A} : \mu \neq 21}\end{array}\)

Example \(\PageIndex{5}\) Stating Type I and II Errors and Picking Level of Significance

• The plant-breeding department at a major university developed a new hybrid raspberry plant called YumYum Berry. Based on research data, the claim is made that from the time shoots are planted 90 days on average are required to obtain the first berry with a standard deviation of 9.2 days. A corporation that is interested in marketing the product tests 60 shoots by planting them and recording the number of days before each plant produces its first berry. The sample mean is 92.3 days. The corporation wants to know if the mean number of days is more than the 90 days claimed. State the type I and type II errors in terms of this problem, consequences of each error, and state which level of significance to use.
• A concern was raised in Australia that the percentage of deaths of Aboriginal prisoners was higher than the percent of deaths of non-indigenous prisoners, which is 0.27%. State the type I and type II errors in terms of this problem, consequences of each error, and state which level of significance to use.

a. x = time to first berry for YumYum Berry plant

\(\mu\) = mean time to first berry for YumYum Berry plant

\(\begin{array}{l}{H_{0} : \mu=90} \\ {H_{A} : \mu>90}\end{array}\)

Type I Error: If the corporation does a type I error, then they will say that the plants take longer to produce than 90 days when they don’t. They probably will not want to market the plants if they think they will take longer. They will not market them even though in reality the plants do produce in 90 days. They may have loss of future earnings, but that is all.

Type II error: The corporation do not say that the plants take longer then 90 days to produce when they do take longer. Most likely they will market the plants. The plants will take longer, and so customers might get upset and then the company would get a bad reputation. This would be really bad for the company.

Level of significance: It appears that the corporation would not want to make a type II error. Pick a 10% level of significance, \(\alpha = 0.10\).

b. x = number of Aboriginal prisoners who have died

p = proportion of Aboriginal prisoners who have died

\(\begin{array}{l}{H_{o} : p=0.27 \%} \\ {H_{A} : p>0.27 \%}\end{array}\)

Type I error: Rejecting that the proportion of Aboriginal prisoners who died was 0.27%, when in fact it was 0.27%. This would mean you would say there is a problem when there isn’t one. You could anger the Aboriginal community, and spend time and energy researching something that isn’t a problem.

Type II error: Failing to reject that the proportion of Aboriginal prisoners who died was 0.27%, when in fact it is higher than 0.27%. This would mean that you wouldn’t think there was a problem with Aboriginal prisoners dying when there really is a problem. You risk causing deaths when there could be a way to avoid them.

Level of significance: It appears that both errors may be issues in this case. You wouldn’t want to anger the Aboriginal community when there isn’t an issue, and you wouldn’t want people to die when there may be a way to stop it. It may be best to pick a 5% level of significance, \(\alpha = 0.05\).

Hypothesis testing is really easy if you follow the same recipe every time. The only differences in the various problems are the assumptions of the test and the test statistic you calculate so you can find the p-value. Do the same steps, in the same order, with the same words, every time and these problems become very easy.

Exercise \(\PageIndex{1}\)

For the problems in this section, a question is being asked. This is to help you understand what the hypotheses are. You are not to run any hypothesis tests and come up with any conclusions in this section.

• Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made in a given time period and found that 11% of all lenses had defects of some type. Looking at the type of defects, they found in a three-month time period that out of 34,641 defective lenses, 5865 were due to scratches. Are there more defects from scratches than from all other causes? State the random variable, population parameter, and hypotheses.
• According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the random variable, population parameter, and hypotheses.
• The Kyoto Protocol was signed in 1997, and required countries to start reducing their carbon emissions. The protocol became enforceable in February 2005. In 2004, the mean CO2 emission was 4.87 metric tons per capita. Is there enough evidence to show that the mean CO2 emission is lower in 2010 than in 2004? State the random variable, population parameter, and hypotheses.
• The FDA regulates that fish that is consumed is allowed to contain 1.0 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish. The data for the average amount of mercury in each lake is in Example \(\PageIndex{5}\) ("Multi-disciplinary niser activity," 2013). Do the data provide enough evidence to show that the fish in Florida lakes has more mercury than the allowable amount? State the random variable, population parameter, and hypotheses.
• Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made in a given time period and found that 11% of all lenses had defects of some type. Looking at the type of defects, they found in a three-month time period that out of 34,641 defective lenses, 5865 were due to scratches. Are there more defects from scratches than from all other causes? State the type I and type II errors in this case, consequences of each error type for this situation from the perspective of the manufacturer, and the appropriate alpha level to use. State why you picked this alpha level.
• According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the type I and type II errors in this case, consequences of each error type for this situation from the perspective of the state of Arizona, and the appropriate alpha level to use. State why you picked this alpha level.
• The Kyoto Protocol was signed in 1997, and required countries to start reducing their carbon emissions. The protocol became enforceable in February 2005. In 2004, the mean CO2 emission was 4.87 metric tons per capita. Is there enough evidence to show that the mean CO2 emission is lower in 2010 than in 2004? State the type I and type II errors in this case, consequences of each error type for this situation from the perspective of the agency overseeing the protocol, and the appropriate alpha level to use. State why you picked this alpha level.
• The FDA regulates that fish that is consumed is allowed to contain 1.0 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish. The data for the average amount of mercury in each lake is in Example \(\PageIndex{5}\) ("Multi-disciplinary niser activity," 2013). Do the data provide enough evidence to show that the fish in Florida lakes has more mercury than the allowable amount? State the type I and type II errors in this case, consequences of each error type for this situation from the perspective of the FDA, and the appropriate alpha level to use. State why you picked this alpha level.

1. \(H_{o} : p=0.11, H_{A} : p>0.11\)

3. \(H_{o} : \mu=4.87 \text { metric tons per capita, } H_{A} : \mu<4.87 \text { metric tons per capita }\)

5. See solutions

7. See solutions

How To Use “Controlled Experiment” In A Sentence: undefined

Controlled experiments are a powerful tool in the realm of scientific research, allowing researchers to test hypotheses and gain valuable insights. But how exactly should one use the term “controlled experiment” in a sentence? Let’s explore the proper way to incorporate this term into your scientific discourse.

When discussing controlled experiments, it is important to provide a concise yet informative definition. A controlled experiment refers to a scientific investigation in which variables are carefully manipulated and controlled to determine cause-and-effect relationships. By isolating and controlling certain variables, researchers can draw reliable conclusions about the effects of specific factors.

Now, let’s delve deeper into the various contexts in which you can effectively utilize the term “controlled experiment” in your scientific discussions.

Definition Of Controlled Experiment

A controlled experiment is a scientific study or test that is designed to carefully manipulate and control certain variables in order to observe and measure the effects of those variables on a specific outcome or phenomenon. It is a fundamental tool used in various fields of research, including but not limited to biology, psychology, physics, and medicine.

In a controlled experiment, the researcher intentionally alters one or more variables, known as the independent variables, while keeping all other factors constant. This allows them to isolate the effects of the manipulated variables and determine their causal relationship with the dependent variable, which is the outcome or behavior being measured.

Historical Evolution:

The concept of controlled experiments can be traced back to the scientific revolution of the 17th century when notable figures such as Francis Bacon and Galileo Galilei emphasized the importance of systematic observation and experimentation in the pursuit of scientific knowledge. However, it was not until the late 19th and early 20th centuries that controlled experiments became more widely adopted as a standard research method.

Different Meanings in Different Contexts:

While the fundamental concept of a controlled experiment remains consistent across various fields, there may be slight variations in terminology and application depending on the specific context.

In the field of biology, for example, controlled experiments often involve the use of control groups, which are groups that are not subjected to the experimental treatment or intervention. This allows researchers to compare the results of the experimental group with those of the control group, providing a baseline for evaluating the effectiveness of the independent variable.

In psychology, controlled experiments are frequently conducted in laboratory settings to investigate human behavior. Researchers carefully manipulate variables such as environmental conditions, stimuli, or participant characteristics, while controlling for confounding factors, to better understand the underlying mechanisms and influences on human cognition and behavior.

In physics, controlled experiments are crucial for testing hypotheses and theories. By manipulating variables such as temperature, pressure, or electric current, physicists can observe and measure the resulting changes in physical phenomena, helping to validate or refine existing theories.

How To Properly Use Controlled Experiment In A Sentence

When it comes to incorporating the term “controlled experiment” into a sentence, it is essential to adhere to the grammatical rules to ensure clarity and precision. This section will delve into the guidelines for using this phrase effectively, while also exploring the various parts of speech it can assume.

Grammatical Rules

1. Subject-Verb Agreement:

When constructing a sentence with “controlled experiment,” it is crucial to ensure that the subject and verb agree in number. For example:

• Correct: The researchers conducted a controlled experiment to test their hypothesis.
• Incorrect: The researchers conducts a controlled experiment to test their hypothesis.

2. Proper Punctuation:

It is important to use appropriate punctuation marks when incorporating “controlled experiment” into a sentence. Commas, colons, and semicolons can be employed to enhance clarity and structure. Consider the following examples:

• Correct: The scientists meticulously designed the controlled experiment, ensuring accurate data collection.
• Correct: The team implemented a variety of methodologies: surveys, interviews, and a controlled experiment.
• Correct: The results of the controlled experiment were inconclusive; therefore, further investigation is warranted.

Parts Of Speech

The term “controlled experiment” can function as different parts of speech depending on its usage within a sentence. Here are a few examples:

By understanding the potential parts of speech that “controlled experiment” can assume, writers can employ this term with precision and convey their intended meaning effectively.

Examples Of Using Controlled Experiment In A Sentence

When it comes to understanding the concept of a controlled experiment, it can be helpful to explore various examples that illustrate its application in different contexts. By examining sentences that incorporate the term “controlled experiment,” we can gain a deeper understanding of its nuances and how it is used in practice.

1. In Scientific Research:

– “The scientists conducted a controlled experiment to investigate the effects of a new drug on patients with a specific medical condition.”

– “By comparing the results of the control group with those of the experimental group, the researchers were able to draw conclusions based on the controlled experiment.”

– “In this controlled experiment, the independent variable was manipulated while keeping all other factors constant to determine its impact on the dependent variable.”

2. In Educational Settings:

– “The teacher designed a controlled experiment to assess the effectiveness of different teaching methods on students’ learning outcomes.”

– “By randomly assigning students to either the control or experimental group, the researcher ensured a well-controlled experiment.”

– “In this controlled experiment, the students were exposed to varying levels of background noise to examine its influence on their concentration.”

3. In Product Testing:

– “The company conducted a controlled experiment to compare the performance of their new product against a competitor’s product.”

– “By using a control group that did not receive the product, the company was able to measure the true impact of their intervention in the controlled experiment.”

– “In this controlled experiment, the participants were asked to rate their satisfaction levels after using the product for a designated period of time.”

4. In Agricultural Studies:

– “The researchers implemented a controlled experiment to determine the optimal amount of fertilizer required for maximum crop yield.”

– “By maintaining identical conditions for each plot except for the varying levels of fertilizer, the team ensured a well-controlled experiment.”

– “In this controlled experiment, the growth rate of the plants was measured to assess the impact of different fertilizer treatments.”

5. In Psychology Research:

– “The psychologists conducted a controlled experiment to investigate the influence of positive reinforcement on behavior change.”

– “By randomly assigning participants to either the control or experimental group, the researchers were able to establish a well-controlled experiment.”

– “In this controlled experiment, the participants’ behavior was observed and recorded under different reinforcement conditions.”

These examples demonstrate the versatility of the term “controlled experiment” across various fields and disciplines. Whether it’s in scientific research, educational settings, product testing, agricultural studies, or psychology research, the concept of a controlled experiment remains a fundamental tool for gaining reliable and valid results.

Edge Cases Or Things To Consider

When it comes to using controlled experiments, there are a few edge cases and important considerations that need to be taken into account. By understanding these factors, you can ensure the validity and reliability of your experiments, leading to more accurate and meaningful results.

Common Mistakes People Make When Using Controlled Experiment

While controlled experiments are a powerful tool for scientific research and decision-making, there are several common mistakes that people often make when conducting them. It is crucial to be aware of these pitfalls to avoid compromising the integrity of your experiment and the validity of your findings.

Here are some of the most frequent mistakes to watch out for:

• Insufficient sample size: One of the fundamental principles of a controlled experiment is the need for an adequate sample size. Failing to include a sufficient number of participants can lead to biased or inconclusive results. It is essential to determine the appropriate sample size based on statistical calculations to ensure the accuracy and generalizability of your findings.
• Selection bias: Another common mistake is unintentional bias in participant selection. If the participants in your experiment are not representative of the target population, the results may not be applicable beyond the specific group involved. Randomization and proper sampling techniques can help mitigate selection bias and increase the external validity of your experiment.
• Failure to control confounding variables: In a controlled experiment, it is crucial to isolate the effect of the independent variable by controlling for other factors that may influence the outcome. Neglecting to identify and control confounding variables can introduce unwanted variability and undermine the internal validity of your experiment. Careful experimental design and meticulous data analysis are necessary to minimize the impact of confounders.
• Lack of clear hypothesis: A well-defined hypothesis is the foundation of any controlled experiment. Without a clear and testable hypothesis, it becomes challenging to determine the success or failure of the experiment accurately. Clearly stating the expected outcome and defining the variables of interest are essential for conducting a meaningful controlled experiment.
• Ignoring ethical considerations: Ethical concerns should always be taken into account when conducting controlled experiments involving human subjects. Respecting participants’ rights, obtaining informed consent, and ensuring their well-being are paramount. Neglecting ethical considerations not only compromises the integrity of your experiment but also raises ethical concerns that can have legal and reputational consequences.

By being aware of these common mistakes and taking proactive measures to avoid them, you can enhance the rigor and validity of your controlled experiments, leading to more reliable and insightful results.

Cultural Or Regional Differences

While the principles of controlled experiments remain consistent regardless of geographical location, cultural or regional differences can introduce unique challenges and considerations. It is important to acknowledge and address these differences to ensure the applicability and generalizability of your experiment’s findings.

Cultural factors can influence participants’ behavior, attitudes, and responses, which may impact the outcomes of your experiment. Therefore, when designing and conducting controlled experiments, it is crucial to consider the cultural context and tailor your approach accordingly.

Here are some key points to consider:

• Language and communication: Language barriers can affect participants’ understanding of instructions, questionnaires, or stimuli used in the experiment. Translating materials accurately and using culturally appropriate language can help minimize potential misunderstandings and ensure participants comprehend the experiment’s requirements.
• Social norms and values: Cultural norms and values can significantly influence individual behavior and decision-making. It is important to be cognizant of these differences and consider their potential impact on participants’ responses. Adapting experimental procedures to align with cultural expectations can help mitigate any potential bias or confounding effects.

Synonyms Or Alternates To Use

When it comes to discussing controlled experiments, there are several synonyms or alternate words that can be used to convey a similar meaning. These alternatives may have subtle differences in meaning or usage, making them suitable for specific contexts. Here, we explore four synonyms for controlled experiment:

1. Randomized Trial

A randomized trial is an alternate term often used interchangeably with controlled experiment. While both refer to a scientific investigation that involves manipulating variables and comparing outcomes, a randomized trial specifically emphasizes the random allocation of participants to different groups or conditions. This randomization helps minimize bias and ensures a fair distribution of characteristics among the groups being compared.

Contexts where “randomized trial” might be preferred over “controlled experiment” include medical research, clinical trials, and studies aiming to evaluate the effectiveness of interventions or treatments.

2. Experimental Study

An experimental study is another synonym for controlled experiment, highlighting the core aspect of experimentation. It involves the deliberate manipulation of variables to observe the resulting effects or outcomes. While controlled experiments typically involve manipulating one or more independent variables while keeping other factors constant, experimental studies may also explore the impact of multiple variables simultaneously.

The term “experimental study” is often used in fields such as psychology, sociology, and education, where researchers seek to establish cause-and-effect relationships. It may be preferred over “controlled experiment” when emphasizing the active manipulation of variables or when studying complex interactions among multiple factors.

3. Quasi-experiment

A quasi-experiment shares similarities with a controlled experiment but lacks the element of random assignment. In a quasi-experiment, researchers still manipulate variables and compare outcomes, but they do not randomly assign participants to different groups. Instead, pre-existing groups or naturally occurring conditions are used.

This term is commonly employed in social sciences, economics, and education, where randomization may be impractical or unethical. “Quasi-experiment” is preferred when studying phenomena in real-world settings, analyzing existing data, or when random assignment is not feasible.

4. Comparative Study

A comparative study involves comparing two or more groups, conditions, or variables to assess their differences or similarities. While not strictly synonymous with a controlled experiment, comparative studies often employ controlled experimental designs to ensure valid comparisons. However, comparative studies can also involve observational or non-experimental approaches.

This term is widely used across various disciplines, including sociology, anthropology, and economics. “Comparative study” may be preferred when the focus is on examining differences or similarities between groups or conditions, regardless of the specific experimental design used.

By using these synonyms or alternate words, researchers and writers can add variety to their language while conveying the essence of a controlled experiment. Selecting the most appropriate term depends on the specific context, emphasizing certain aspects of the experiment, and the nature of the research being conducted.

Related Phrases Or Idioms

When it comes to incorporating the concept of a controlled experiment into our everyday language, there are several related phrases and idioms that have emerged. These expressions not only reflect the significance of conducting experiments in a controlled manner but also provide a glimpse into how this approach is perceived in different contexts. Let’s explore a few of these phrases and idioms:

1. Play By The Rules

This phrase emphasizes the importance of adhering to a set of predetermined guidelines or protocols, much like how a controlled experiment operates within predefined parameters. When someone is said to be “playing by the rules,” it implies that they are following the established procedures or regulations without deviation.

Example sentence: “In order to obtain accurate results, it is crucial to play by the rules and conduct the controlled experiment exactly as outlined in the research protocol.”

2. Tinker With Variables

This phrase implies making small adjustments or modifications to certain factors or elements, just like scientists do when conducting controlled experiments. By “tinkering with variables,” individuals or researchers attempt to observe the effects of these changes on the overall outcome.

Example sentence: “To truly understand the impact of different marketing strategies, it is necessary to tinker with variables and conduct controlled experiments to identify the most effective approach.”

3. Leave No Stone Unturned

Although not directly related to controlled experiments, this idiom signifies the meticulous and thorough nature of such experiments. Just as scientists leave no stone unturned in their pursuit of knowledge, a controlled experiment leaves no aspect unexamined, ensuring that all potential variables are accounted for.

Example sentence: “To gain a comprehensive understanding of the disease, the researchers left no stone unturned and meticulously designed a controlled experiment to explore every possible factor.”

4. Trial And Error

While not specifically mentioning controlled experiments, this phrase encapsulates the iterative process of testing and refining hypotheses, which is at the core of any well-designed controlled experiment. It highlights the importance of learning from mistakes and making incremental improvements.

Example sentence: “Through a series of trial and error, the scientists were able to fine-tune their experimental design and eventually conduct a successful controlled experiment.”

These phrases and idioms offer glimpses into how the concept of a controlled experiment has permeated our language and culture. By incorporating these expressions into our conversations, we can further appreciate the significance of this scientific approach and its application in various domains.

In conclusion, the correct utilization of controlled experiments holds immense significance in various fields of study and research. By employing this methodological approach, researchers are able to establish a cause-and-effect relationship between variables, thereby enhancing the reliability and validity of their findings. The controlled experiment allows for the elimination of confounding factors and ensures that any observed changes can be attributed to the manipulated variable alone.

Furthermore, the controlled experiment provides a systematic framework for testing hypotheses and making informed decisions. It enables researchers to gather empirical evidence and draw logical conclusions based on the data collected. This rigorous approach not only enhances the credibility of scientific research but also fosters innovation and progress in diverse disciplines.

As readers, it is essential to recognize the value of using controlled experiments correctly. By incorporating this method into our own work, whether it be in academia, industry, or everyday life, we can elevate the quality of our investigations and problem-solving endeavors. Practicing the art of constructing well-designed experiments and utilizing appropriate control groups will undoubtedly enhance the accuracy and reliability of our conclusions.

So, let us embrace the power of controlled experiments and unleash their potential in our own sentences. By employing this methodological tool effectively, we can unlock new insights, challenge assumptions, and contribute to the advancement of knowledge in our respective fields.

Shawn Manaher is the founder and CEO of The Content Authority. He’s one part content manager, one part writing ninja organizer, and two parts leader of top content creators. You don’t even want to know what he calls pancakes.

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Biology library

Course: biology library   >   unit 1, the scientific method.

• Controlled experiments
• The scientific method and experimental design

Introduction

• Make an observation.
• Ask a question.
• Form a hypothesis , or testable explanation.
• Make a prediction based on the hypothesis.
• Test the prediction.
• Iterate: use the results to make new hypotheses or predictions.

Scientific method example: Failure to toast

1. make an observation., 2. ask a question., 3. propose a hypothesis., 4. make predictions., 5. test the predictions..

• If the toaster does toast, then the hypothesis is supported—likely correct.
• If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.

Logical possibility

Practical possibility, building a body of evidence, 6. iterate..

• If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
• If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.

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