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Writing a hypothesis using if and then

Anne Helmenstine, Ph.D. is an author and consultant with a broad scientific and medical background. Read more

Updated August 19, 2015.

Question: What Are Examples of a Hypothesis?

Answer: Although you could state a scientific hypothesis in various ways, most hypothesis are either "If, then" statements or else forms of the null hypothesis. The null hypothesis sometimes is called the "no difference" hypothesis. The null hypothesis is good for experimentation because it’;s simple to disprove.

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If you disprove a null hypothesis. that is evidence for a relationship between the variables you are examining. For example:

Examples of the Null Hypothesis

• Hyperactivity is unrelated to eating sugar.
• All daisies have the same number of petals.
• The number of pets in a household is unrelated to the number of people living in it.
• A person’;s preference for a shirt is unrelated to its color.

Examples of an If, Then Hypothesis

• If you get at least 6 hours of sleep, you will do better on tests than if you get less sleep.
• If you drop a ball, it will fall toward the ground.
• If you drink coffee before going to bed, then it will take longer to fall asleep.
• If you cover a wound with a bandage, then it will heal with less scarring.

Improving a Hypothesis To Make It Testable

While there are many ways to state a hypothesis, you may wish to revise your first hypothesis in order to make it easier to design an experiment to test it. For example, let’;s say you have a bad breakout the morning after eating a lot of greasy food. You may wonder if there is a correlation between eating greasy food and getting pimples.

You propose a hypothesis:

Eating greasy food causes pimples.

Next you need to design an experiment to test this hypothesis. Let’;s say you decide to eat greasy food every day for a week and record the effect on your face. Then, as a control, for the next week you’;ll avoid greasy food and see what happens. Now, this is not a very good experiment because it does not take into account other factors, such as hormone levels, stress, sun exposure, exercise or any number of other variables which might conceivably affect your skin. The problem is that you cannot assign cause to your effect. If you eat french fries for a week and suffer a breakout, can you definitely say it was the grease in the food that caused it? Maybe it was the salt. Maybe it was the potato. Maybe it was unrelated to diet.You can’;t prove your hypothesis. It’;s much easier to disprove a hypothesis. So, let’;s restate the hypothesis to make it easy to evaluate the data.

Getting pimples is unaffected by eating greasy food.

So, if you eat fatty food every day for a week and suffer breakouts and then don’;t breakout the week that you avoid greasy food, you can be pretty sure something is up. Can you disprove the hypothesis? Probably not, since it is so hard to assign cause and effect. However, you can make a strong case that there is some relationship between diet and acne.

A hypothesis is a description of a pattern in nature or an explanation about some real-world phenomenon that can be tested through observation and experimentation. The most common way a hypothesis is used in scientific research is as a tentative, testable, and falsifiable statement that explains some observed phenomenon in nature.ok ok [1] We more specifically call this kind of statement an explanatory hypothesis . However, a hypothesis can also be a statement that describes an observed pattern in nature. In this case we call the statement a generalizing hypothesis . [2] [3] Hypotheses can generate predictions . statements that propose that one variable will drive some effect on or change in another variable in the result of a controlled experiment. However, many science resources promote the myth that a hypothesis is simply an educated guess and no different from a prediction. [4] More on this misunderstanding below.

Many academic fields, from the physical sciences to the life sciences to the social sciences, use hypothesis testing as a means of testing ideas to learn about the world and advance scientific knowledge. Whether you are a beginning scholar or a beginning student taking a class in a science subject, understanding what hypotheses are and being able to generate hypotheses and predictions yourself is very important. These instructions will help get you started.

Part One of Two: Preparing to Write a Hypothesis Edit

Select a topic. Pick a topic that interests you, and that you think it would be good to know more about.

• If you are writing a hypothesis for a school assignment, this step may be taken care of for you.

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Read existing research. Gather all the information you can about the topic you’ve selected. You’ll need to become an expert on the subject and develop a good grasp of what is already known about the topic.

• Focus on academic and scholarly writing. You need to be certain that your information is unbiased, accurate, and comprehensive.
• You can find information in textbooks, at a library, and online. If you are in school, you can also ask for help from teachers, librarians, and your peers.

Analyze the literature. Spend some time reading the materials you’ve collected. As you do so, look for and make note of unanswered questions in the literature. These can provide excellent ideas for areas to investigate.

• For example, if you are interested in the effects of caffeine on the human body, but notice that nobody seems to have explored whether caffeine affects men differently than it does women, this could be something to formulate a hypothesis about. Or, if you are interested in organic farming, you might notice that no one has tested whether organic fertilizer results in different growth rates for plants than non-organic fertilizer.
• You can sometimes find holes in the existing literature by looking for statements like “it is unknown” or places where information is clearly missing. You might also find a claim in the literature that seems far-fetched, unlikely, or too good to be true, like that caffeine improves math skills. If the claim is testable, you could provide a great service to scientific knowledge by doing your own investigation. If you confirm the claim, the claim becomes even more credible. If you do not find support for the claim, you are helping with the necessary self-correcting aspect of science.
• Examining these types of questions provides an excellent way for you to set yourself apart by filling in important gaps in a field of study.

Generate questions. After studying the literature on your topic, generate one or more unanswered questions you’d be interested in exploring further. These are your research questions.

• Following the examples above, you might ask: “How does caffeine affect women as compared to men?” or “How does organic fertilizer affect plant growth compared to non-organic fertilizer?” The rest of your research will be aimed at answering these questions.

Look for clues as to what the answer might be. Once you have generated your research question or questions, look in the literature to see if the existing findings and/or theories about the topic provide any clues that would allow you to come up with ideas about what the answers to your research questions might be. If so, these clues can form the basis for your hypothesis.

• Following the examples above, if you discover in the literature that there is a pattern that some other types of stimulants seem to affect women more than men, this could be a clue that the same pattern might be true for caffeine. Similarly, if you observe the pattern that organic fertilizer seems to be associated with smaller plants overall, you might explain this pattern with the hypothesis that plants exposed to organic fertilizer grow more slowly than plants exposed to non-organic fertilizer.

Determine your variables. A generalizing hypothesis describes a pattern you think may exist between two variables: an independent variable and a dependent variable. If your experiments confirm the pattern, you may decide to suggest a reason that the pattern exists or a mechanism that generates the pattern. The reason or mechanism you suggest is an explanatory hypothesis .

• You can think of the independent variable as the one that is causing some kind of difference or effect to occur. In the examples, the independent variable would be gender, i.e. whether a person is male or female, and fertilizer type, i.e. whether the fertilizer is organic or non-organically-based.
• The dependent variable is what is affected by (i.e. “depends” on) the independent variable. In the examples above, the dependent variable would be the measured impact of caffeine or fertilizer.
• Your hypothesis should only suggest one relationship. Most importantly, it should only have one independent variable. If you have more than one, you won’t be able to determine which one is actually the source of any effects you might observe.

Generate a simple hypothesis. Once you’ve spent some time thinking about your research question and variables, write down your initial idea about how the variables might be related as a simple declarative statement.

• Don’t worry too much at this point about being precise or detailed.
• In the examples above, one hypothesis would make a statement about whether a person’s gender might impact the way the person is affected by caffeine; for example, at this point, your hypothesis might simply be: “a person’s gender is related to how caffeine affects his or her heart rate.” The other hypothesis would make a general statement about plant growth and fertilizer; for example your simple explanatory hypothesis might be “plants given different types of fertilizer are different sizes because they grow at different rates.”

Decide on direction. Hypotheses can either be directional or non-directional. A non-directional hypothesis simply says that one variable affects the other in some way, but does not say specifically in what way. A directional hypothesis provides more information about the nature (or “direction”) of the relationship, stating specifically how one variable affects the other.

• Using our example, our non-directional hypotheses would be “there is a relationship between a person’s gender and how much caffeine increases the person’s heart rate,” and “there is a relationship between fertilizer type and the speed at which plants grow.”
• Directional predictions using the same example hypotheses above would be. “Women will experience a greater increase in heart rate after consuming caffeine than will men,” and “plants fertilized with non-organic fertilizer will grow faster than those fertilized with organic fertilizer.” Indeed, these predictions and the hypotheses that allow for them are very different kinds of statements. More on this distinction below.
• If the literature provides any basis for making a directional prediction, it is better to do so, because it provides more information. Especially in the physical sciences, non-directional predictions are often seen as inadequate.

Get specific. Once you have an initial idea on paper, it’s time to start refining. Make your hypotheses as specific as you can, so it’s clear exactly what ideas you will be testing and make your predictions specific and measurable so that they provide evidence of a relationship between the variables.

• Where necessary, specify the population (i.e. the people or things) about which you hope to uncover new knowledge. For example, if you were only interested the effects of caffeine on elderly people, your prediction might read: “Women over the age of 65 will experience a greater increase in heart rate than will men of the same age.” If you were interested only in how fertilizer affects tomato plants, your prediction might read: “Tomato plants treated with non-organic fertilizer will grow faster in the first three months than will tomato plants treated with organic fertilizer.”

Make sure it is testable. Your hypothesis must suggest a relationship between two variables or a reason that two variables are related that can feasibly be observed and measured in the real and observable world .

• For example, you would not want to make the hypothesis: “red is the prettiest color.” This statement is an opinion and it cannot be tested with an experiment. However, proposing the generalizing hypothesis that red is the most popular color is testable with a simple random survey. If you do indeed confirm that red is the most popular color, your next step may be to ask: Why is red the most popular color? The answer you propose is your explanatory hypothesis .
• Often, hypotheses are stated in the form of if-then sentences. For example, “if children are given caffeine, then their heart rates will increase.” This statement is not a hypothesis. This kind of statement is a brief description of an experimental method followed by a prediction and is the most common way that hypotheses are misrepresented in science education. An easy way to get to the hypothesis for this method and prediction is to ask yourself why you think heart rates will increase if children are given caffeine. Your explanatory hypothesis in this case may be that caffeine is a stimulant. At this point, some scientists write what is called a research hypothesis . a statement that includes the hypothesis, the experiment, and the prediction all in one statement: If caffeine is a stimulant, and some children are given a drink with caffeine while others are given a drink without caffeine, then the heart rates of those children given a caffeinated drink will increase more than the heart rate of children given a non-caffeinated drink.
• It may sound strange, but researchers rarely ever prove that a hypothesis is right or wrong. Instead, they look for evidence that the opposite of their hypotheses is probably not true. If the opposite (caffeine is not a stimulant) is probably not true, the hypothesis (caffeine is a stimulant) probably is true.
• Using the above example, if you were to test the effects of caffeine on the heart rates of children, evidence that your hypothesis is not true, sometimes called the null hypothesis . could occur if the heart rates of both the children given the caffeinated drink and the children given the non-caffeinated drink (called the placebo control) did not change, or lowered or raised with the same magnitude, if there was no difference between the two groups of children. If you wanted to test the effects of different fertilizer types, evidence that your hypothesis was not true would be that the plants grew at the same rate, regardless of fertilizer, or if plants treated with organic fertilizer grew faster. It is important to note here that the null hypothesis actually becomes much more useful when researchers test the significance of their results with statistics. When statistics are used on the results of an experiment, a researcher is testing the idea of the null statistical hypothesis. For example, that there is no relationship between two variables or that there is no difference between two groups. [5]

Test your hypothesis. Make your observations or conduct your experiment. Your evidence may allow you to reject your null hypotheses, thus lending support to your experimental hypothesis. However, your evidence may not allow you to reject your null hypothesis and this is okay. Any result is important, even when your result sends you back to the drawing board. Constantly having to go “back to the drawing board” and refine your ideas is how authentic science really works! [6]

When examining the literature, look for research that is similar to what you want to do, and try to build on the findings of other researchers. But also look for claims that you think are suspicious, and test them yourself.

Be specific in your hypotheses, but not so specific that your hypothesis can’t be applied to anything outside your specific experiment. You definitely want to be clear about the population about which you are interested in drawing conclusions, but nobody (except your roommates) will be interested in reading a paper with the prediction: “my three roommates will each be able to do a different amount of pushups.”

Keep your feelings and opinions out of your research. Hypotheses should never say “I believe. ” “I think. ” “I feel. ” or “My opinion is that. “

Remember that science is not necessarily a linear process and can be approached in various ways. [7]

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Hypothesis If Then

In the vast universe of scientific inquiries, the “if-then” hypothesis structure stands out as an essential tool, bridging observation and prediction. This format not only simplifies complex scientific theories but also provides clarity to young learners and budding scientists. Whether you’re experimenting in a professional lab or just in your backyard, understanding and crafting a Thesis statement succinct “if-then” hypothesis can be the key to unlocking the secrets of the world around us. Dive in to explore, write, and refine!

What is If Then Hypothesis?

The “If-Then” hypothesis is a predictive statement that sets up a cause-and-effect relationship between two variables. It’s structured such that the “If” portion introduces a condition or a cause, and the “Then” portion predicts the effect or outcome of that condition. This format helps in clearly establishing a link between the independent and dependent variables in an experiment.

What is an example of a Hypothesis If Then Statement?

For instance, let’s consider a basic experiment related to plant growth:

• Hypothesis : If a plant is exposed to direct sunlight for at least 6 hours a day, then it will grow taller than a plant that is kept in the shade.

In this example, the exposure to sunlight (or the lack thereof) is the condition, while the growth of the plant is the predicted outcome. The statement concisely links the cause (sunlight exposure) to the effect (plant growth).

100 If Then Hypothesis Statement Examples

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The “If-Then” hypothesis elegantly captures a cause-and-effect relationship in scientific inquiries. This predictive format, with its concise clarity, bridges observation and anticipated outcome, guiding experiments in a myriad of domains.

• Plant Growth : If a plant receives fertilizer, then it will grow faster than one without fertilizer.
• Melting Points : If ice is exposed to temperatures above 0°C, then it will melt.
• Battery Life : If a battery is used continuously, then it will drain faster than if used intermittently.
• Sleep & Performance : If a person sleeps less than 6 hours a night, then their cognitive performance will decrease.
• Diet & Weight : If an individual consumes more calories than they burn, then they will gain weight.
• Hydration : If a person drinks less than 8 glasses of water daily, then they may experience dehydration.
• Light & Vision : If a room is darkened, then the pupils of one’s eyes will dilate.
• Sugar & Energy : If children consume sugary drinks, then they will show increased levels of energy.
• Study Habits : If a student revises regularly, then they will retain more information than those who cram.
• Exercise & Health : If a person exercises three times a week, then their cardiovascular health will improve.
• Noise & Concentration : If a room is noisy, then people inside will find it harder to concentrate.
• Medication & Pain : If an individual takes painkillers, then they will report reduced pain levels.
• Soil Quality : If soil is rich in nutrients, then plants grown in it will be healthier.
• Reading & Vocabulary : If a child reads daily, then their vocabulary will expand faster than a non-reading peer.
• Social Media : If a teenager spends over 5 hours on social media, then they may experience decreased sleep quality.
• Sunscreen : If sunscreen is applied, then the chances of getting sunburned decrease.
• Coffee & Alertness : If an individual drinks coffee in the morning, then they will feel more alert.
• Music & Productivity : If calming music is played in the workplace, then employees will be more productive.
• Temperature & Metabolism : If the ambient temperature is cold, then a person’s metabolism will increase.
• Pets & Stress : If an individual owns a pet, then their stress levels might decrease.
• Vegetation & Air Quality : If trees are planted in an urban area, then air quality will improve.
• Vaccination : If a child is vaccinated, then they will have a reduced risk of contracting certain diseases.
• E-learning : If students use e-learning platforms, then they will have flexible study hours.
• Recycling : If a community adopts recycling, then landfill waste will decrease.
• Fast Food : If an individual eats fast food regularly, then their cholesterol levels might rise.
• UV Light : If UV light is shone on a glow-in-the-dark material, then it will glow more brightly.
• Brushing Teeth : If a child brushes their teeth twice daily, then they will have fewer cavities than those who don’t.
• Bird Migration : If the climate becomes colder, then certain birds will migrate to warmer regions.
• Space Exploration : If astronauts go without gravity for long periods, then their bone density will decrease.
• Plastic Pollution : If we reduce single-use plastic consumption, then the amount of plastic in the ocean will decrease.
• Books & Imagination : If a child reads fantasy novels, then their imaginative skills will be enhanced.
• AI & Efficiency : If companies use artificial intelligence in operations, then their efficiency will improve.
• Video Games : If children play violent video games, then they might exhibit aggressive behavior.
• Healthy Diet : If someone consumes a balanced diet, then their overall health will benefit.
• Deforestation : If forests are cleared at the current rate, then global temperatures will rise due to reduced carbon sequestration.
• Renewable Energy : If a country invests in renewable energy, then its carbon footprint will decrease.
• Exercise & Mood : If an individual engages in regular physical activity, then their mood will generally improve.
• Microplastics : If microplastics enter the water system, then marine life will be at risk.
• Language Learning : If a person practices a new language daily, then they will become fluent faster.
• Organic Farming : If farmers use organic methods, then the pesticide residue in the food will decrease.
• Remote Work : If employees work remotely, then office costs will reduce.
• Yoga & Flexibility : If someone practices yoga regularly, then their flexibility will increase.
• Public Transport : If a city improves its public transportation system, then traffic congestion will decrease.
• Meditation & Stress : If an individual meditates daily, then their stress levels will be lower.
• Fish & Omega-3 : If someone includes fish in their diet weekly, then their omega-3 fatty acid intake will be adequate.
• Smartphones & Sleep : If a person uses their smartphone before bed, then their sleep quality might decrease.
• Waste Segregation : If households segregate waste, then recycling processes will be more efficient.
• E-Books : If students use e-books instead of paper ones, then paper consumption will decrease.
• Carpooling : If more people adopt carpooling, then urban air quality will improve due to fewer car emissions.
• Digital Payments : If digital payment systems are adopted widely, then cash handling costs will reduce.
• Online Learning : If students engage in online learning platforms, then their access to diverse educational resources will increase.
• Tree Planting : If a community plants more trees in urban areas, then the air quality will improve due to increased oxygen output.
• Pet Ownership : If an individual adopts a pet, then they may experience reduced feelings of loneliness.
• Recycling : If recycling is made mandatory in cities, then landfill waste will decrease significantly.
• Natural Cleaners : If households use natural cleaning agents, then water pollution from residential areas will decrease.
• Solar Panels : If a house installs solar panels, then its electricity bill will decrease.
• Music & Productivity : If workers listen to instrumental music while working, then their productivity might increase.
• Healthy Breakfast : If someone eats a nutritious breakfast daily, then their energy levels throughout the day will be higher.
• Water Conservation : If individuals reduce their shower time by 5 minutes, then significant water conservation can be achieved annually.
• Learning Instruments : If a child learns a musical instrument, then their cognitive and motor skills may improve.
• Reusable Bags : If shoppers use reusable bags, then the demand for plastic bags will reduce.
• Public Libraries : If a city invests in public libraries, then the literacy rate of its citizens may rise.
• Organ Donation : If awareness about organ donation increases, then the waiting list for organ transplants will decrease.
• Green Spaces : If urban areas increase green spaces, then residents’ mental well-being may improve.
• Sleep & Memory : If a student gets at least 8 hours of sleep, then their memory retention might be better.
• Digital Detox : If someone takes a weekly digital detox day, then their stress levels may decrease.
• Composting : If households start composting kitchen waste, then the amount of organic waste in landfills will reduce.
• Gardening & Health : If individuals engage in gardening activities, then they might experience improved mental health.
• Flu Vaccination : If a person gets a flu shot annually, then their chances of getting influenza will reduce.
• Hand Washing : If people wash their hands regularly, then the spread of common diseases may decrease.
• Diverse Diet : If someone consumes a diverse range of vegetables, then they will have a better nutrient intake.
• Physical Books : If a student reads from physical books instead of screens, then they might have better sleep patterns.
• Mindfulness & Anxiety : If an individual practices mindfulness exercises, then their anxiety levels may decrease.
• Green Vehicles : If a city promotes the use of electric vehicles, then air pollution levels will reduce.
• Walking & Health : If someone walks 10,000 steps daily, then their cardiovascular health might improve.
• Art & Creativity : If children are exposed to art classes from a young age, then their creative thinking skills may enhance.
• Dark Chocolate : If someone consumes dark chocolate regularly, then their antioxidant intake may increase.
• Yoga & Flexibility : If an individual practices yoga thrice a week, then their flexibility and posture may improve.
• Cooking at Home : If families cook meals at home more frequently, then their intake of processed foods might decrease.
• Local Tourism : If local tourism is promoted, then a region’s economy can benefit due to increased business opportunities.
• Reading Aloud : If parents read aloud to their children every night, then the children’s vocabulary and comprehension skills might expand.
• Public Transportation : If cities improve their public transportation system, then the number of cars on the road might decrease.
• Indoor Plants : If a person keeps indoor plants in their workspace, then their concentration and productivity may enhance due to better air quality.
• Bird Watching : If an individual engages in bird watching, then their patience and observation skills might develop.
• Biking to Work : If employees bike to work, then their cardiovascular health can improve and their carbon footprint might reduce.
• Aquariums & Stress : If someone spends time watching fish in an aquarium, then their stress levels may decrease.
• Meditation & Focus : If an individual meditates daily, then their attention span and focus might increase.
• Learning Languages : If a student learns a new language, then their cognitive flexibility and memory retention may improve.
• Community Gardens : If neighborhoods establish community gardens, then residents may benefit from fresh produce and community bonding.
• Journaling : If someone journals their thoughts regularly, then their self-awareness and emotional processing might improve.
• Volunteering : If an individual volunteers once a month, then their sense of purpose and community connection may strengthen.
• Eco-friendly Products : If consumers prefer eco-friendly products, then industries might adopt more sustainable manufacturing practices.
• Limiting Screen Time : If children limit their screen time to an hour a day, then their physical activity levels and sleep patterns may benefit.
• Outdoor Play : If kids play outdoors regularly, then their motor skills and social interactions might develop better.
• Therapy & Mental Health : If someone attends therapy sessions, then they may experience improved mental well-being and coping strategies.
• Natural Light : If workspaces are designed to allow more natural light, then employee morale and productivity might rise.
• Water Intake : If a person drinks at least 8 glasses of water daily, then their hydration levels and skin health may improve.
• Classical Music : If students listen to classical music while studying, then their concentration might increase.
• Home Composting : If households adopt composting, then garden soil quality might improve and organic waste in landfills may reduce.
• Green Roofs : If buildings adopt green roofs, then urban heat islands might decrease, and biodiversity may benefit.

Hypothesis If Then Statement Examples in Research

The crux of experimental research revolves around predicting an outcome. An ‘If-Then’ hypothesis format succinctly conveys anticipated cause-and-effect relationships, enabling clearer comprehension and assessment.

• DNA Sequencing : If we utilize CRISPR technology for DNA sequencing, then the accuracy of detecting genetic mutations may increase.
• Drug Efficiency : If a new drug compound is introduced to malignant cells in vitro, then the proliferation rate of these cells might decrease.
• Digital Learning : If students are exposed to AI-driven educational tools, then their academic performance might significantly improve.
• Nano-technology : If nanoparticles are used in drug delivery, then the targeting of specific cells may become more efficient.
• Quantum Computing : If quantum bits replace traditional bits in computing, then the processing speed might witness a revolutionary acceleration.

Hypothesis If Then Statement Examples about Climate Change

Understanding climate change necessitates predicting outcomes based on varied actions or occurrences. These hypotheses present potential scenarios in the vast realm of climate studies.

• Deforestation : If deforestation rates continue at the current pace, then global carbon dioxide levels will rise significantly.
• Solar Energy : If solar energy adoption increases by 50% in the next decade, then global reliance on fossil fuels might decrease considerably.
• Ocean Temperatures : If the world’s oceans warm by another degree Celsius, then coral bleaching events may become twice as frequent.
• Carbon Taxation : If a global carbon tax is implemented, then emissions from industries might see a drastic reduction.
• Melting Ice Caps : If polar ice caps continue to melt at the current rate, then sea levels might rise to submerge several coastal cities by 2100.

Hypothesis If Then Statement Examples in Psychology

Psychology delves into understanding behaviors and mental processes. Formulating hypotheses in an ‘If-Then’ structure can streamline experimental setups and interpretations.

• Mindfulness Meditation : If individuals practice daily mindfulness meditation, then symptoms of anxiety and stress may decrease.
• Social Media : If teenagers spend over five hours daily on social media, then their self-esteem levels might drop.
• Cognitive Behavioral Therapy : If patients with depression undergo cognitive-behavioral therapy, then their coping mechanisms may strengthen.
• Sleep and Memory : If adults get less than six hours of sleep nightly, then their memory retention might deteriorate faster.
• Nature Exposure : If urban residents are exposed to natural settings weekly, then their mental well-being might improve.

Alternative If Then Hypothesis Statement Examples

Sometimes, researchers propose alternate scenarios to challenge or complement existing beliefs. These hypotheses capture such alternative insights.

• Vitamin Intake : If individuals consume Vitamin C supplements daily, then their immunity might not necessarily strengthen, contradicting popular belief.
• Digital Detox : If tech professionals take a monthly digital detox day, then their productivity may not diminish, countering the notion that constant connectivity boosts efficiency.
• Organic Foods : If consumers solely eat organic foods, then their overall health markers might remain unchanged, challenging the health superiority of organic diets.
• Exercise Routines : If gym-goers switch to calisthenics from weight training, then muscle mass gain might remain consistent, offering an alternative to traditional gym workouts.
• E-learning : If students transition from classroom learning to e-learning platforms, then their academic performance may not necessarily drop, challenging the indispensability of physical classrooms.

Hypothesis If Then Statement Examples in Biology

In biology, the interaction of living organisms and their environments often leads to distinct outcomes. The ‘If-Then’ hypothesis structure can efficiently predict these outcomes based on varying factors.

• Cell Division : If a cell is exposed to radiation, then the rate of its division might decrease significantly.
• Plant Growth : If plants are provided with blue light, then their growth rate might be faster compared to those exposed to red light.
• Enzyme Activity : If the temperature of a reaction involving enzymes rises by 10°C, then the activity of the enzymes might double.
• Animal Behavior : If nocturnal animals are exposed to continuous artificial light, then their feeding and reproductive behaviors might be disrupted.
• Genetic Modification : If crops are genetically modified for drought resistance, then their yield in arid regions might increase substantially.

Hypothesis If Then Statement Examples in Chemistry

The realm of chemistry is filled with reactions and interactions. Predicting outcomes based on specific conditions is crucial, and the ‘If-Then’ hypothesis structure provides clarity in such predictions.

• Acid-Base Reactions : If a solution has a pH below 7, then it might turn blue litmus paper red, indicating its acidic nature.
• Temperature and Reaction Rate : If the temperature of a chemical reaction is increased, then the rate of that reaction might speed up.
• Metal Reactivity : If zinc metal is placed in copper sulfate solution, then it might displace the copper, indicating its higher reactivity.
• Organic Synthesis : If an alkene is treated with bromine water, then the solution might decolorize, suggesting the presence of a double bond.
• Electrolysis : If an aqueous solution of sodium chloride undergoes electrolysis, then chlorine gas might be released at the anode.

Hypothesis If Then Statement Examples in Physics

Physics examines the fundamental principles governing our universe. ‘If-Then’ hypotheses help in determining cause-and-effect relationships amidst complex physical phenomena.

• Gravity : If an object is dropped from a certain height in a vacuum, then it might accelerate at 9.81 m/s^2, irrespective of its mass.
• Refraction : If light travels from air into water, then it might bend towards the normal due to the change in speed.
• Magnetism : If a magnetic field is applied to a moving charged particle, then the particle might experience a force perpendicular to its direction of motion.
• Thermal Expansion : If a metal rod is heated, then it might expand due to the increased kinetic energy of its atoms.
• Quantum Mechanics : If an electron is observed in a quantum system, then its wave function might collapse, determining its position.

What is an if-then because hypothesis?

An “if-then-because” hypothesis is a structured statement that predicts the outcome of an experiment based on a proposed cause and effect scenario. The structure usually goes as follows: “If [I do this specific action], then [this particular result will occur] because [of this scientific reason].”

For example: “If I water plants with sugar water, then they will grow taller than the ones watered with plain water because sugar provides additional nutrients to the plants.”

This type of simple hypothesis statement not only predicts the outcome but also provides a reasoning for the expected outcome, thereby setting the groundwork for the experimental procedure and its subsequent analysis.

Is a hypothesis typically an if-then statement?

Yes, a hypothesis is often framed as an “if-then” statement, especially in experimental studies. This format succinctly presents a proposed cause and its expected effect. By specifying a relationship between two variables, it offers clarity to the hypothesis and makes the intended testing straightforward. However, while common, not all hypotheses are written in the “if-then” format.

Is an if-then statement a hypothesis or prediction?

An “if-then” statement can be both a hypothesis and a prediction. However, their contexts differ:

• Hypothesis: It is a tentative explanation for an observation or phenomenon that can be tested experimentally. When written in the “if-then” format, it usually predicts a relationship between variables based on theoretical understanding.Example: “If a plant is given caffeine, then it will grow faster.”
• Prediction: It is a specific, testable statement about what will happen under particular conditions. It is based on the hypothesis and narrows down the expected outcomes of an experiment.Example: “If a bean plant is watered with a 1% caffeine solution daily, then after one month, it will be 10% taller than plants watered with plain water.”

How do you write an If Then Hypothesis Statement? – A Step by Step Guide

• Identify the Variables: Determine the independent variable (the factor you’ll change) and the dependent variable (the factor you’ll measure).
• Frame the Relationship: Using your understanding of the topic, establish a potential relationship between the identified variables.
• Start with “If”: Begin your hypothesis with “If” followed by your independent variable.
• Follow with “Then”: After stating your independent variable, include “then” followed by the potential outcome or change in the dependent variable you expect.
• Review for Clarity: Ensure your hypothesis is clear, concise, and testable. It should state a specific relationship between the variables.

Tips for Writing If Then Hypothesis

• Be Specific: Ensure your variables are clearly defined. Instead of “If I water plants more,” use “If I water plants twice daily.”
• Ensure Testability: Your hypothesis should propose a relationship that can be tested through an experiment.
• Avoid Conclusions: A hypothesis is a prediction, not a conclusion. It shouldn’t state a known fact but should be based on prior knowledge.
• Use Simple Language: Especially when the audience might not have a deep understanding of the topic. Keeping it straightforward ensures comprehension.
• Revise and Refine: After drafting your hypothesis, revisit it to check for clarity, specificity, and relevance to the research question at hand.

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What is a Research Hypothesis: How to Write it, Types, and Examples

Any research begins with a research question and a research hypothesis . A research question alone may not suffice to design the experiment(s) needed to answer it. A hypothesis is central to the scientific method. But what is a hypothesis ? A hypothesis is a testable statement that proposes a possible explanation to a phenomenon, and it may include a prediction. Next, you may ask what is a research hypothesis ? Simply put, a research hypothesis is a prediction or educated guess about the relationship between the variables that you want to investigate.  

It is important to be thorough when developing your research hypothesis. Shortcomings in the framing of a hypothesis can affect the study design and the results. A better understanding of the research hypothesis definition and characteristics of a good hypothesis will make it easier for you to develop your own hypothesis for your research. Let’s dive in to know more about the types of research hypothesis , how to write a research hypothesis , and some research hypothesis examples .  

Table of Contents

What is a hypothesis ?  

A hypothesis is based on the existing body of knowledge in a study area. Framed before the data are collected, a hypothesis states the tentative relationship between independent and dependent variables, along with a prediction of the outcome.  

What is a research hypothesis ?  

Young researchers starting out their journey are usually brimming with questions like “ What is a hypothesis ?” “ What is a research hypothesis ?” “How can I write a good research hypothesis ?”   

A research hypothesis is a statement that proposes a possible explanation for an observable phenomenon or pattern. It guides the direction of a study and predicts the outcome of the investigation. A research hypothesis is testable, i.e., it can be supported or disproven through experimentation or observation.     

Characteristics of a good hypothesis  

Here are the characteristics of a good hypothesis :  

• Clearly formulated and free of language errors and ambiguity  
• Concise and not unnecessarily verbose  
• Has clearly defined variables  
• Testable and stated in a way that allows for it to be disproven  
• Can be tested using a research design that is feasible, ethical, and practical   
• Specific and relevant to the research problem  
• Rooted in a thorough literature search  
• Can generate new knowledge or understanding.  

How to create an effective research hypothesis  

A study begins with the formulation of a research question. A researcher then performs background research. This background information forms the basis for building a good research hypothesis . The researcher then performs experiments, collects, and analyzes the data, interprets the findings, and ultimately, determines if the findings support or negate the original hypothesis.  

Let’s look at each step for creating an effective, testable, and good research hypothesis :  

• Identify a research problem or question: Start by identifying a specific research problem.   
• Review the literature: Conduct an in-depth review of the existing literature related to the research problem to grasp the current knowledge and gaps in the field.   
• Formulate a clear and testable hypothesis : Based on the research question, use existing knowledge to form a clear and testable hypothesis . The hypothesis should state a predicted relationship between two or more variables that can be measured and manipulated. Improve the original draft till it is clear and meaningful.  
• State the null hypothesis: The null hypothesis is a statement that there is no relationship between the variables you are studying.   
• Define the population and sample: Clearly define the population you are studying and the sample you will be using for your research.  
• Select appropriate methods for testing the hypothesis: Select appropriate research methods, such as experiments, surveys, or observational studies, which will allow you to test your research hypothesis .  

Remember that creating a research hypothesis is an iterative process, i.e., you might have to revise it based on the data you collect. You may need to test and reject several hypotheses before answering the research problem.  

How to write a research hypothesis  

When you start writing a research hypothesis , you use an “if–then” statement format, which states the predicted relationship between two or more variables. Clearly identify the independent variables (the variables being changed) and the dependent variables (the variables being measured), as well as the population you are studying. Review and revise your hypothesis as needed.  

An example of a research hypothesis in this format is as follows:  

“ If [athletes] follow [cold water showers daily], then their [endurance] increases.”  

Population: athletes  

Independent variable: daily cold water showers  

Dependent variable: endurance  

You may have understood the characteristics of a good hypothesis . But note that a research hypothesis is not always confirmed; a researcher should be prepared to accept or reject the hypothesis based on the study findings.  

Research hypothesis checklist  

Following from above, here is a 10-point checklist for a good research hypothesis :  

• Testable: A research hypothesis should be able to be tested via experimentation or observation.  
• Specific: A research hypothesis should clearly state the relationship between the variables being studied.  
• Based on prior research: A research hypothesis should be based on existing knowledge and previous research in the field.  
• Falsifiable: A research hypothesis should be able to be disproven through testing.  
• Clear and concise: A research hypothesis should be stated in a clear and concise manner.  
• Logical: A research hypothesis should be logical and consistent with current understanding of the subject.  
• Relevant: A research hypothesis should be relevant to the research question and objectives.  
• Feasible: A research hypothesis should be feasible to test within the scope of the study.  
• Reflects the population: A research hypothesis should consider the population or sample being studied.  
• Uncomplicated: A good research hypothesis is written in a way that is easy for the target audience to understand.  

By following this research hypothesis checklist , you will be able to create a research hypothesis that is strong, well-constructed, and more likely to yield meaningful results.  

Types of research hypothesis  

Different types of research hypothesis are used in scientific research:  

1. Null hypothesis:

A null hypothesis states that there is no change in the dependent variable due to changes to the independent variable. This means that the results are due to chance and are not significant. A null hypothesis is denoted as H0 and is stated as the opposite of what the alternative hypothesis states.   

Example: “ The newly identified virus is not zoonotic .”  

2. Alternative hypothesis:

This states that there is a significant difference or relationship between the variables being studied. It is denoted as H1 or Ha and is usually accepted or rejected in favor of the null hypothesis.  

Example: “ The newly identified virus is zoonotic .”  

3. Directional hypothesis :

This specifies the direction of the relationship or difference between variables; therefore, it tends to use terms like increase, decrease, positive, negative, more, or less.   

Example: “ The inclusion of intervention X decreases infant mortality compared to the original treatment .”   

4. Non-directional hypothesis:

While it does not predict the exact direction or nature of the relationship between the two variables, a non-directional hypothesis states the existence of a relationship or difference between variables but not the direction, nature, or magnitude of the relationship. A non-directional hypothesis may be used when there is no underlying theory or when findings contradict previous research.  

Example, “ Cats and dogs differ in the amount of affection they express .”  

5. Simple hypothesis :

A simple hypothesis only predicts the relationship between one independent and another independent variable.  

Example: “ Applying sunscreen every day slows skin aging .”  

6 . Complex hypothesis :

A complex hypothesis states the relationship or difference between two or more independent and dependent variables.   

Example: “ Applying sunscreen every day slows skin aging, reduces sun burn, and reduces the chances of skin cancer .” (Here, the three dependent variables are slowing skin aging, reducing sun burn, and reducing the chances of skin cancer.)  

7. Associative hypothesis:  

An associative hypothesis states that a change in one variable results in the change of the other variable. The associative hypothesis defines interdependency between variables.  

Example: “ There is a positive association between physical activity levels and overall health .”  

8 . Causal hypothesis:

A causal hypothesis proposes a cause-and-effect interaction between variables.  

Example: “ Long-term alcohol use causes liver damage .”  

Note that some of the types of research hypothesis mentioned above might overlap. The types of hypothesis chosen will depend on the research question and the objective of the study.  

Research hypothesis examples  

Here are some good research hypothesis examples :  

“The use of a specific type of therapy will lead to a reduction in symptoms of depression in individuals with a history of major depressive disorder.”  

“Providing educational interventions on healthy eating habits will result in weight loss in overweight individuals.”  

“Plants that are exposed to certain types of music will grow taller than those that are not exposed to music.”  

“The use of the plant growth regulator X will lead to an increase in the number of flowers produced by plants.”  

Characteristics that make a research hypothesis weak are unclear variables, unoriginality, being too general or too vague, and being untestable. A weak hypothesis leads to weak research and improper methods.   

Some bad research hypothesis examples (and the reasons why they are “bad”) are as follows:  

“This study will show that treatment X is better than any other treatment . ” (This statement is not testable, too broad, and does not consider other treatments that may be effective.)  

“This study will prove that this type of therapy is effective for all mental disorders . ” (This statement is too broad and not testable as mental disorders are complex and different disorders may respond differently to different types of therapy.)  

“Plants can communicate with each other through telepathy . ” (This statement is not testable and lacks a scientific basis.)  

Importance of testable hypothesis  

If a research hypothesis is not testable, the results will not prove or disprove anything meaningful. The conclusions will be vague at best. A testable hypothesis helps a researcher focus on the study outcome and understand the implication of the question and the different variables involved. A testable hypothesis helps a researcher make precise predictions based on prior research.  

To be considered testable, there must be a way to prove that the hypothesis is true or false; further, the results of the hypothesis must be reproducible.  

Frequently Asked Questions (FAQs) on research hypothesis  

1. What is the difference between research question and research hypothesis ?  

A research question defines the problem and helps outline the study objective(s). It is an open-ended statement that is exploratory or probing in nature. Therefore, it does not make predictions or assumptions. It helps a researcher identify what information to collect. A research hypothesis , however, is a specific, testable prediction about the relationship between variables. Accordingly, it guides the study design and data analysis approach.

2. When to reject null hypothesis ?

A null hypothesis should be rejected when the evidence from a statistical test shows that it is unlikely to be true. This happens when the test statistic (e.g., p -value) is less than the defined significance level (e.g., 0.05). Rejecting the null hypothesis does not necessarily mean that the alternative hypothesis is true; it simply means that the evidence found is not compatible with the null hypothesis.  

3. How can I be sure my hypothesis is testable?  

A testable hypothesis should be specific and measurable, and it should state a clear relationship between variables that can be tested with data. To ensure that your hypothesis is testable, consider the following:  

• Clearly define the key variables in your hypothesis. You should be able to measure and manipulate these variables in a way that allows you to test the hypothesis.  
• The hypothesis should predict a specific outcome or relationship between variables that can be measured or quantified.   
• You should be able to collect the necessary data within the constraints of your study.  
• It should be possible for other researchers to replicate your study, using the same methods and variables.   
• Your hypothesis should be testable by using appropriate statistical analysis techniques, so you can draw conclusions, and make inferences about the population from the sample data.  
• The hypothesis should be able to be disproven or rejected through the collection of data.  

4. How do I revise my research hypothesis if my data does not support it?  

If your data does not support your research hypothesis , you will need to revise it or develop a new one. You should examine your data carefully and identify any patterns or anomalies, re-examine your research question, and/or revisit your theory to look for any alternative explanations for your results. Based on your review of the data, literature, and theories, modify your research hypothesis to better align it with the results you obtained. Use your revised hypothesis to guide your research design and data collection. It is important to remain objective throughout the process.  

5. I am performing exploratory research. Do I need to formulate a research hypothesis?  

As opposed to “confirmatory” research, where a researcher has some idea about the relationship between the variables under investigation, exploratory research (or hypothesis-generating research) looks into a completely new topic about which limited information is available. Therefore, the researcher will not have any prior hypotheses. In such cases, a researcher will need to develop a post-hoc hypothesis. A post-hoc research hypothesis is generated after these results are known.  

6. How is a research hypothesis different from a research question?

A research question is an inquiry about a specific topic or phenomenon, typically expressed as a question. It seeks to explore and understand a particular aspect of the research subject. In contrast, a research hypothesis is a specific statement or prediction that suggests an expected relationship between variables. It is formulated based on existing knowledge or theories and guides the research design and data analysis.

7. Can a research hypothesis change during the research process?

Yes, research hypotheses can change during the research process. As researchers collect and analyze data, new insights and information may emerge that require modification or refinement of the initial hypotheses. This can be due to unexpected findings, limitations in the original hypotheses, or the need to explore additional dimensions of the research topic. Flexibility is crucial in research, allowing for adaptation and adjustment of hypotheses to align with the evolving understanding of the subject matter.

8. How many hypotheses should be included in a research study?

The number of research hypotheses in a research study varies depending on the nature and scope of the research. It is not necessary to have multiple hypotheses in every study. Some studies may have only one primary hypothesis, while others may have several related hypotheses. The number of hypotheses should be determined based on the research objectives, research questions, and the complexity of the research topic. It is important to ensure that the hypotheses are focused, testable, and directly related to the research aims.

9. Can research hypotheses be used in qualitative research?

Yes, research hypotheses can be used in qualitative research, although they are more commonly associated with quantitative research. In qualitative research, hypotheses may be formulated as tentative or exploratory statements that guide the investigation. Instead of testing hypotheses through statistical analysis, qualitative researchers may use the hypotheses to guide data collection and analysis, seeking to uncover patterns, themes, or relationships within the qualitative data. The emphasis in qualitative research is often on generating insights and understanding rather than confirming or rejecting specific research hypotheses through statistical testing.

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Part Five: Evaluating Deductive Logic

Chapter Eleven: If–Then Arguments

“Contrariwise,” continued Tweedledee, “if it was so, it might be; and if it were so, it would be: but as it isn’t, it ain’t. That’s logic.” —Lewis Carroll, Through the Looking-Glass

• Forms of If–Then Arguments
• Evaluating the Truth of If–Then Premises
• If–Then Arguments with Implicit Statements
• Bringing It All Together

If–then arguments , also known as conditional arguments or hypothetical syllogisms, are the workhorses of deductive logic. They make up a loosely defined family of deductive arguments that have an if–then statement —that is, a conditional —as a premise. The conditional has the standard form If P then Q. The if portion, since it typically comes first, is called the antecedent ; the then portion is called the consequent .

These arguments—often with implicit premises or conclusions—are pressed into service again and again in everyday communication. In The De-Valuing of America, for example, William Bennett gives this brief if–then argument:

If we believe that good art, good music, and good books will elevate taste and improve the sensibilities of the young—which they certainly do—then we must also believe that bad music, bad art, and bad books will degrade.

The if–then premise—lightly paraphrased—is this:

If good art, good music, and good books elevate taste and improve the sensibilities of the young, then bad music, bad art, and bad books degrade taste and degrade the sensibilities of the young.

The second premise—set off in the original by dashes—is:

Good art, good music, and good books elevate taste and improve the sensibilities of the young.

And the implicit conclusion is this:

Bad music, bad art, and bad books degrade taste and degrade the sensibilities of the young.

Whether the argument is sound depends on whether the logic of the argument is successful and whether the premises are true. We now look at each of these two categories of evaluation.

11.1 Forms of If–Then Arguments

The arguments of this chapter are deductive, so the success of their logic is entirely a matter of form. The form of Bennett’s argument in the preceding paragraph is the most common and the most obviously valid. It is normally termed affirming the antecedent ; a common Latin term for this form is modus ponens, which means “the method (or mode, from modus ) of affirming (or propounding, from ponens ).”

• If P then Q.

Almost as common is the valid form denying the consequent ; the Latin term for this is modus tollens, which means “the method of denying.”

This is the form of my argument if I say to you, “If you decide to adopt that puppy, then you’re going to be stuck at home for a long time. But you could never accept that—you live for your trips. This pup’s adorable, but it’s not for you.”

Each of these two valid forms may be contrasted with an invalid form that unsuccessfully mimics it. The invalid form that is tempting due to its similarity to affirming the antecedent is the fallacy of affirming the consequent ; its structure is this:

• If P then Q .

I’ve committed this fallacy if I argue, “If you decide to adopt that puppy, then you’re going to be stuck at home for a long time. Fortunately you hate to sleep in any bed other than your own. So, this pup’s for you!” After all, you may love staying at home but also have a severe allergy to dog hair; the conclusion surely does not follow.

And deceptively similar to denying the consequent is the fallacy of denying the antecedent ; this invalid form is as follows:

I made this mistake in the following argument: “If you decide to adopt that puppy, then you’re going to be stuck at home for a long time. But, knowing you, of course you’re not going to decide to adopt the puppy. So, it follows that you’re not going to be such a homebody anymore.” If you pass on the puppy because of your asthma, that has no bearing on your travel plans one way or the other. Again, the conclusion does not follow.

Recall that when you find these fallacious forms, there is normally no need to apply the principle of charity in your paraphrase. The ease with which such mistakes are made (thus earning each fallacy a name of its own) is usually reason to think that the arguer might have been truly mistaken in his or her thinking, and thus is reason to clarify the argument in the invalid form. [1]

Another form of argument, a valid one, that belongs to the if–then family is often termed transitivity of implication. This form of argument links if–then statements into a chain, as follows:

• If Q then R.
• ∴ If P then R.

I’ve given an argument of this form if I contend, “If you decide to adopt that puppy, then you’re going to be stuck at home for a long time. But if you’re stuck at home for a long time, you’d better fix your toaster oven. So, if you decide to adopt that puppy, you’d better fix your toaster oven.” There is no limit to the number of if–then links that this chain could contain and still be valid. [2]

Incidentally, Lewis Carroll’s argument at the chapter’s opening presents some interesting evaluative possibilities. Here is one reasonable paraphrase:

• If it is, then it is.
• ∴ It is not.

On the one hand, it has the form of the fallacy of denying the antecedent, which is invalid; on the other hand, it has the form of denying the consequent, which is valid. Further, it also has the form of repetition—looking only at 2 and C —which is also valid. The solution to the puzzle is that it is valid—not because the two valid forms outnumber the one invalid one, but because we should charitably suppose that the valid form is the one that was intended. Charity, unfortunately, cannot prevent us from noting that whatever the form, this argument probably commits the fallacy of begging the question. And if it does, then it does.

If–Then Arguments

EXERCISES Chapter 11, set (a)

Create a brief argument that takes the specified form.

Sample exercise. Transitivity of implication.

Sample answer. If I run out of gas I’ll be late. And if I’m late I’ll get fired. So, if I run out of gas I’ll get fired.

• Affirming the antecedent
• Affirming the consequent
• Denying the consequent
• Denying the antecedent
• Transitivity of implication

11.1.1 Stylistic Variants for If–Then

If–then arguments, as we have seen, make crucial use of statements of the form If P then Q as premises. Using the terminology of Chapter 6, the expression if–then is the logical constant of such statements, while P and Q are the variables— sentential variables, you will recall—replaceable by declarative sentences as the content of the argument.

These constants are anything but constant in ordinary language; a wide variety of everyday English expressions are used to express if–then. In the structuring phase of the clarifying process, it is important that you translate them into standard constants. This helps bring the structure of the argument close to the surface and makes it much easier to tell whether the argument is logically successful.

All of the expressions listed below—and many more—can be used as stylistic variants for if–then. More precisely, each of the expressions can be translated, for logical purposes, into If P then Q.

Stylistic Variants for if P then Q

Q if P. P only if Q. Only if Q, P. Assuming P, Q. Q assuming P. Supposing P, Q. Q supposing P. Given P, Q. Q given P. That P is a sufficient condition for that Q. That Q is a necessary condition for that P.

This list includes some of the most obvious variants, but it is not comprehensive. Unexpected variants for if–then statements show up with regularity. A politician says, for example, “Vote for my bill and I’ll vote for yours.” This can be taken as a stylistic variant for, “If you vote for my bill, then I’ll vote for yours.” A story about new television shows says, “ With good summer ratings, the series will end up on the fall schedule of NBC.” This translates into, “If the series gets good summer ratings, then it will end up on the fall schedule of NBC.” And language watcher Thomas Middleton, complaining in the Los Angeles Times about a tendency he has noticed among teens to use expressions like “and then my friend goes so-and-so” instead of “and then my friend said so-and-so,” presses his point thus:

The ability to say things . . . is consummately precious, and to describe “saying” as “going” is to debase this glorious gift. It is to treat speech as though it were no more than, as Random House says, making a certain sound—like a cat’s purr.

This passage, it seems, translates into something like the following:

If someone describes “saying” as “going,” then that person debases the gift of speech and treats it as though it were no more than making a sound.

Be very careful, however, with words like with, and, and to ; they are rarely stylistic variants for if–then. It is only when they are used in these distinctive kinds of contexts that they should be taken this way.

EXERCISES Chapter 11, set (b)

Translate the stylistic variant in each of the following if–then statements.

Sample exercise. As long as history textbooks make white racism invisible in the 19th century, students will never be able to analyze racism intelligently in the present.—James Loewen, Lies My Teacher Told Me

Sample answer. If history textbooks make white racism invisible in the 19th century, then students will never be able to analyze racism intelligently in the present.

• Oxygen is necessary for combustion.
• The governor agreed Tuesday to a legislative compromise for ending the community colleges’ financial troubles—but only if lawmakers can find another $121 million.
• Teachers should assign passages and require students to summarize the passages in their own words. Do that consistently, and students will not only learn to write a lot better, they will also learn to analyze, evaluate, sort out, and synthesize information.
• Those who are not willing to give to everyone else the same intellectual rights they claim for themselves are dishonest, selfish, and brutal. —from Robert Ingersoll, Ingersoll: The Immortal Infidel
• “To address kids in masses, you have to be an entertainer, which I’m not,” Dr. Seuss said, sounding a little like the Grinch.— Los Angeles Times
• “Strip a woman’s body of its breasts and hips, of all of its nurturing curves, and replace it with enough stringy, sinewy muscle, and a lot of people will simply not know what to make of what you have left.” — Pumping Iron II: The Women

EXERCISES Chapter 11, set (c)

Clarify each of the if–then arguments. Then state whether the argument is valid and provide the name of the valid or invalid form.

Sample exercise. “I submit that the author is thoroughly wrong to criticize analogical argumentation, that if argument by analogy were really as weak as he allows we would not use it as extensively as we do.”—book review in Teaching Philosophy

Sample answer.

• If argument by analogy is as weak as the author allows, then we do not use argument by analogy as extensively as we do.
• [We do use argument by analogy as extensively as we do.]
• ∴ Argument by analogy is not as weak as the author allows. Valid, denying the consequent.
• Universal mandatory screening for AIDS can be justified on the basis of beneficence when a therapeutic intervention is available or when an infectious state puts others at risk merely by casual contact. However, neither is the case with AIDS. Thus, there is no demonstrable public health benefit that justifies universal mandatory screening.—N. F. McKenzie, ed., The AIDS Reader (Even though an extremely charitable reading of this argument might suggest otherwise, go ahead and clarify it as a fallacy.)
• “The prolonged study of ethics does not by itself make you a better person. If it did, philosophy professors would in general be better people than average. But they aren’t.”—William Bennett, The De-Valuing of America
• “If the North Koreans are smart—and we know they are smart—they will move in the direction of reform.”—Daryl Plank, Korea expert and visiting fellow at Washington’s Heritage Foundation
• “If, instead of offering the occasional high-profile prize of $35 million, New York awarded 350 prizes of $100,000, making not one multimillionaire, but a great number of $100,000 winners, it would create an environment where far more people would know, or know of, large prize winners. More people will buy tickets if they know large prize winners. So experimenting with such a format should reverse the current negative trend.” —letter to the editor, New York Times
• “Ladies and Gentlemen, I’ll be brief. The issue here is not whether we broke a few rules or took a few liberties with our female party guests. We did. But you can’t hold a whole fraternity responsible for the behavior of a few sick perverted individuals. For if you do, then shouldn’t we blame the whole fraternity system? And if the whole fraternity system is guilty, then isn’t this an indictment of our educational institutions in general? I put it to you, Greg: Isn’t this an indictment of our entire American society? Well, you can do what you want to us, but we’re not going to sit here and listen to you badmouth the entire United States of America.”—Eric “Otter” Stratton, in the film Animal House (This is a complex argument with the subconclusion If the fraternity is guilty, then the entire American society is guilty. )
• “And if, for example, antiabortionism required the perverting of natural reason and normal sensibilities by a system of superstitions, then the liberal could discredit it—but it doesn’t, so he can’t.”—Roger Wertheimer, Philosophy and Public Affairs

11.1.2 Singular Inferences

One common variation on the preceding forms is worth our attention. Note the remark made by legendary heavyweight boxing champ Joe Frazier to the short-lived and less legendary title holder, Jimmy Ellis:

You ain’t no champ. You won’t fight anybody. A champ’s got to fight everybody.

This provides several opportunities for following the rules of paraphrasing arguments—a stylistic variant for if–then, the need to follow the principle of charity (because of the rather extreme words everybody, anybody, and even what Frazier means by being a champ), wording to be matched, and emptiness to be avoided (because of the word you ). The result of clarifying it is something like this:

• If any person deserves to be the heavyweight boxing champion, then that person will fight all worthy contenders.
• Jimmy Ellis will not fight all worthy contenders.
• ∴ Jimmy Ellis does not deserve to be the heavyweight boxing champion.

This looks very much like denying the consequent—that is, it seems to depend on this form:

But the Q of premise 1 and the Q of premise 2 do not really match, nor do the P of premise 1 and the P of C. For there is no mention of Jimmy Ellis anywhere in premise 1, yet Jimmy Ellis is the subject of premise 2 and of the conclusion. This certainly does not harm the argument’s logic, however, since Jimmy Ellis is included—as a single person—among those encompassed by the term any person in the first premise. So, for practical purposes, we can continue to call this form denying the consequent, but with a slight difference. It will be identified as singular denying the consequent

The same modification is permitted for every form of sentential logic that we cover, assuming two things hold. First, there must be a universal statement as a premise—that is, a premise with a term like all, none, anything, or nothing, to mention a few examples. If any person deserves to be the heavyweight boxing champion, then that person will fight all worthy contenders is universal, since it applies to any person. Second, there must be a conclusion in which a single instance is specified that is encompassed by the universal term. Jimmy Ellis will not fight all worthy contenders provides an example, since Jimmy Ellis is encompassed by any person. All the if–then forms mentioned above can be modified in this way. Singular affirming the antecedent and singular transitivity of implication are also valid forms, while the fallacy of singular affirming the consequent and the fallacy of singular denying the antecedent are invalid ones.

Singular If–Then Arguments

EXERCISES Chapter 11, set (d)

Clarify the following arguments as examples of singular if–then arguments. Then state whether the argument is valid and provide the name of the valid or invalid form.

Sample exercise. “ Q : You mentioned that Bundy was mentally ill? A : Sane people do not go round killing dozens of women, and the person that the state of Florida strapped in the electric chair was a man who was severely mentally ill.”—I. Gray and M. Stanley, eds., A Punishment in Search of a Crime: Americans Speak Out Against the Death Penalty

• If anyone is sane, that person does not kill dozens of women.
• [Bundy killed dozens of women.]
• ∴ Bundy was not sane. Valid, singular denying the consequent.
• If someone is in Birmingham, then that person is in Alabama. And if someone is in Alabama, then that person is in America. So, if I am in Birmingham, then I am in America.
• I conceded that speeding is sufficient reason for getting pulled over by a police officer. But I wasn’t speeding. So I should not have been pulled over.
• One argument for the immorality of adultery might go something like this: it involves the breaking of a promise, and it is immoral to break a promise.—from a lecture by philosopher Richard Wasserstrom
• I refer you to the verdict in the English Court sustaining Whistler’s contention that a man did not wholly own a picture by simply buying it. So, although I may have sold my painting to him, I have a right to protect my picture from the vandalism of his cleaning it.—from American artist Albert Pinkham Ryder

11.2 Evaluating the Truth of If–Then Premises

If–then statements usually propose a special connection between the if-clause and then-clause. Identifying the specific nature of the connection is usually the key to judging the truth of such a statement and to successfully defending that judgment. [3]

Sometimes the proposed connection is causal, as in the case of the statement If you push the ignition button, then the car will start. Pushing the button would cause the car to start. But in other cases the proposed connection is broadly logical ; the if-clause does not cause the then-clause but is offered as counting toward or even guaranteeing its truth. [4] Consider the statement that became a book and movie title— If it’s Tuesday, this must be Belgium. It’s being Tuesday cannot cause this to be Belgium, but could presumably (combined with other statements about the itinerary) count in favor of the belief that this is Belgium. Or consider the statement If there is intelligent life on other planets, then we are not alone in the universe. That there is intelligent life elsewhere in the universe is just what we mean by not being alone in the universe. So the connection here is also a logical one—and in this case it is such a tight connection that we can safely call it self-evidently true.

Whether the proposed connection is causal or logical, it is helpful to think of the if-clause as not being offered as alone sufficient for the then-clause. When we use if–then statements we are typically allowing for other relevant factors as well. We have simply picked out the if-clause for special mention because it is the one factor that happens to be most important in the context. These implicit assumptions about other relevant factors are termed secondary assumptions (or auxiliary hypotheses).

Return to the if–then statement If you push the ignition button, then the car will start. Behind such a statement there usually are implicit secondary assumptions about many other factors that contribute to the starting of the car—but that are presumed to be already in place, and thus do not merit mention. They may include assumptions about the specific situation, such as these:

There is a functioning engine in the car. There is gas in the tank and the starter battery is not dead (if it has an internal combustion engine). The battery pack is charged (if it has an electric engine). The key fob is nearby. The ignition system is not defective.

They may also include more general assumptions about the relation between the if-clause and then-clause, such as this:

Ignition systems are designed to start properly functioning cars.

And they may include even broader principles that guide much of our reasoning, such as this:

The laws of nature will not suddenly change.

When you judge an if–then statement to be true, a good way to defend your judgment is to identify the secondary assumptions that are most likely to be in question, given the circumstances, and to point out their truth. You might say, for example,

I judge this premise to be very probably true because this is what ignition systems are designed to do, and there is no reason to think that this car is out of fuel or is defective in some other way.

Thus a connection between if-clause and then-clause is affirmed.

Alternatively, if you judge the if–then statement to be false, a good defense is to point out that a secondary assumption is false; for example,

This premise is probably false, since the headlights were left on all day and the battery is dead by now.

Thus you have denied one of the secondary assumptions and shown that the connection between if-clause and then-clause is severed.

The same strategy works well for if–then statements in which the connection is broadly logical rather than causal. Consider If you are reading this book, then you understand English. One important secondary assumption is This book is written in English. Another is Reading something just means that you understand it. (You might wonder whether this, or the earlier life on other planets example, should count as a secondary assumption, since it is part of the very meaning of the terms used—what we have in preceding chapters called self-evidently true. It will nevertheless make good practical sense in this text for us to count it so.) So here is an exemplary defense of the statement:

This premise is certainly true, since the book is written in English, and part of what it means to read something is to understand it.

Again, its truth is defended by pointing out the cords that connect if-clause to then-clause.

Consider, finally, If New York City were in Quebec, then it would still be in the United States. There is, unfortunately, no way of knowing what secondary assumptions are supposed to connect this if-clause and then-clause. Is New York City to be located further north, or Quebec further south? And, on either scenario, what historical events would have caused such a difference—and would they, perhaps, have resulted in Quebec’s being included within the United States? There is simply not enough information to decide. The best evaluation of this premise, then, would be something like this:

I can’t decide whether this premise is true or false. There is no way of knowing whether New York City is to be located further north, Quebec further south, or what relevant historical events might have led to it.

The daughter of Rudolf Carnap, one of the great philosophers and logicians of the 20th century, tells of asking her father, when she was a young child, “If you were offered a million dollars, would you be willing to have your right arm amputated?” “I don’t know,” he replied. “Would I be given an anesthetic?” Lack of information about relevant secondary assumptions can sometimes make it impossible for any of us, even Carnap, to say any more than “can’t decide” in evaluating if–then statements.

EXERCISES Chapter 11, set (e)

For each of the following if–then statements, list the most plausible and relevant secondary assumptions (or explain why you cannot do so). Then provide a judgment of the premise’s truth by reference to your list. (They are not provided with any context, so you will have to use your imagination.)

Sample exercise. If there were more solar panels available, then air pollution would decrease.

Sample answer. Secondary assumptions: Consumers will buy and install more solar panels if they become available. Solar panels produce less air pollution than the more conventional forms of energy production. Probably false, since, at least currently, in much of the world consumers do not have enough economic incentive to convert to solar energy.

• If there were more classical music on the radio, then there would be more appreciation of classical music among the public.
• If George W. Bush was the 45th president, then Barack Obama was the 46th.
• If it rains tomorrow, then you should take your umbrella to work.
• If people recycled more, the environment would be in better shape.
• If I were two feet taller, I would have played in the NBA.
• If it’s Tuesday, this must be Belgium.
• If the stock market rises next year, then Alphabet stock will rise in value.
• If all private ownership of guns were made illegal, then violence in our country would drop dramatically.
• If you can do 20 pushups, then you are in good shape.
• If you are planning to go to medical school, then you can expect to take several science courses.

11.2.1 The Retranslation Mistake

Consider the statement If New York City is in the state of New York, then it is in the United States. It is certainly true, but it is tempting to defend that judgment by more or less repeating the if–then statement in slightly different words, as follows:

My view is that the premise is certainly true, since New York City has to be in the United States, given that it is in the state of New York.

You have said nothing that goes beyond the premise itself, thus nothing that would be enlightening to the reasonable objector over your shoulder. You have merely retranslated the if–then constant back into one of its stylistic variants! Be careful to avoid this sort of defense. (I’ll leave it as an exercise for you to identify the simple secondary assumption that provides the crucial connection for this if–then statement.)

11.2.2 Truth Counterexamples

It can be especially tempting to ignore mention of secondary assumptions when the if-clause is clearly true and the then-clause is clearly false. These are the most straightforward cases, for if you know that the if-clause is true and the then-clause is false, you know that the if–then statement is false. The if–then statement has vividly failed to deliver on its promise.

But even here it is better, if possible, to show the severed connection between the two by identifying the false secondary assumption. Take, for example, If New York City is in the state of New York, then it is in Canada. You might defend your judgment as follows:

I consider the premise to be certainly false since, based on my experience in my own travels and based on the testimony of every authority I’ve ever encountered, New York City is in the state of New York and it is not in Canada (but in the United States).

But this makes no mention of any connection between the if-clause and then-clause. If there is supposed to be one, it is the assumption that the state of New York is itself in Canada. And your defense is stronger if you include the rejection of this assumption, as follows:

Further, the state of New York is wholly located within the United States, not Canada.

There can be, however, exceptions to this rule. One exception applies when it is a universal if–then statement that is false. Universal if–then statements, recall, are if–then statements with a universal term like anything, anyone, nothing, or nobody in the if-clause. An example we have already seen is If any person deserves to be the heavyweight boxing champion, then that person will fight all worthy contenders. A property—such as deserving to be champ —is applied universally—to any person —rather than to a single instance. When such statements are false, the method of truth counterexample can be a simple and effective way of defending that judgment. This method identifies a single instance in which the if-clause is obviously true and the then-clause is obviously false.

A newspaper story on the homeless, for example, contains the line, “No one is poor by choice.” This is a stylistic variant of the universal if–then statement, “If anyone is poor, then it is not by choice.” Yet the same newspaper, on the facing page, has a story about Mother Theresa’s religious order, stating, “These nuns have voluntarily taken an oath of poverty.” Here we have a ready-made truth counterexample. The nuns are instances of the if-clause’s truth—they are poor—and at the same time are instances of the then-clause’s falsity—their poverty is by choice. Thus armed, your defense of your judgment of the universal if–then statement can be stated simply as follows: “The premise is certainly false, since certain orders of nuns are poor by choice.”

EXERCISES Chapter 11, set (f)

Provide a truth counterexample for each of these false universal if–then statements. If necessary, first translate stylistic variants into the standard constant.

Sample exercise. Only animals that can fly are endowed with wings.

Sample answer. If any animal has wings, then it can fly. Certainly false; the ostrich has wings but cannot fly.

• No major-party presidential or vice presidential candidate has been a female.
• If any substance is made of metal, then it is attracted to a magnet.
• Everything reported in the newspaper is true.
• Nice guys finish last.
• What goes up must come down.

11.2.3 The Educated Ignorance Defense

Another occasion for ignoring secondary assumptions—also occurring under the true if-clause/false then-clause scenario—is when the evidence for the truth of the if-clause and the evidence for the falsity of the then-clause are each stronger than the evidence for the truth of the if–then statement. In these cases, even though you may not know which secondary assumption is at fault, it can be reasonable to say that the premise is false “because some secondary assumption—not yet identified—is mistaken.” This we will term the educated ignorance defense (“Ignorance” because you admit ignorance regarding which secondary assumption is faulty; “educated” because you nevertheless have good evidence that the if-clause is true and the then-clause is false.)

Return, for example, to our car-starting example. Imagine that when you pick up your car after extensive repairs your mechanic says to you, “If you push the ignition button, then the car will start.” He has extremely good reasons to believe this is true. He has checked out all of the systems—in short, his experience and expert judgment support the truth of any secondary assumption that might be reasonably questioned. You push the ignition button. But the car does not start.

Something has to give. There are three statements for which you apparently have very good evidence:

If you push the ignition button, then the car will start. You push the ignition button. (The if-clause is true.) The car will not start. (The then-clause is false.)

They cannot all be true at the same time. You will probably quickly give up on the truth of the if–then statement, not knowing what went wrong but knowing quite well that you pushed the button and the car didn’t start. But the mechanic, who has especially good reasons to believe the if–then statement—he did the work, and he has his reputation to think about—will probably start off by doubting the if-clause, asking you suspiciously, “Are you sure you pushed the ignition button?” “I’m sure,” you reply, anxiously pushing it again and again. “Let me see,” he says with a hint of disdain and gets in to push the button himself. Only when it does not start for him does he say, “Well, OK, I was mistaken, but I just can’t figure out what’s wrong with it.”

The mechanic’s initial reluctance to give up the truth of the if–then statement is because he cannot imagine which secondary assumption is mistaken. And he only concedes that the if–then statement is false when he sees that evidence in favor of the if-clause—that the button has been pushed—is conclusive. (The evidence that the then-clause is false—that the car did not start—is already conclusive.) He is still ignorant of which secondary assumption to blame, but now that he is duly educated—about the truth of the if-clause and falsity of the then-clause— he can reasonably resort to the educated ignorance defense. Eventually something better than educated ignorance will be required if the car is to be driven away.

Science provides many examples of this defense. In the 18th century, for example, astronomers used the new Newtonian mechanics to accurately predict the orbits of many of the planets in our solar system. The following if–then statement describes the general shape of these predictions:

If Newtonian mechanics is true, then the orbit of planet A will be observed to be F.

(In this case, A is the name of the planet and F is a mathematical description of the predicted observed orbit of the planet around Earth.) After many successes, the astronomers did their work on the orbit of Uranus and discovered, to everyone’s surprise, that the predicted orbit did not accord with their observations. They thus found themselves with good evidence for the following three statements, not all of which could be true:

If Newtonian mechanics is true, then the orbit of Uranus will be observed to be F. Newtonian mechanics is true. (The if-clause is true.) It is not the case that the orbit of Uranus is observed to be F. (The then-clause is false).

They checked and rechecked their equipment to be sure of their evidence that the then-clause was false, but they found their surprising observations to be accurate. They reminded themselves of the mountains of other evidence in favor of the if-clause. And they checked and rechecked their calculations, in the futile hope of finding some faulty secondary assumption that would falsify the if–then statement. In the end, the only reasonable thing to do was to reject the if–then statement with a defense something like this:

This premise is probably false; the support for Newtonian theory is so strong, and the quality of this observation so good, that it is most likely that some not-yet-identified faulty secondary assumption lies behind its falsity.

Incidentally, that is where things stood until the 19th century, when the Englishman John Adams and the Frenchman Urbain Leverier, working independently, realized that the mistake had been in assuming Uranus is the outermost planet. Due to this secondary assumption, the earlier Newtonians had not factored into their calculations any gravitational pull from the other side of Uranus. They each reworked the calculations and predicted where they should be able to observe an outer planet exercising gravitational attraction on Uranus. In 1846 they independently observed this planet, later named Neptune, in the predicted location.

The strategy of saying, “There is some unidentified secondary assumption that is mistaken” should be employed with great care. Again, it works only when there is independent strong evidence in favor of the truth of the if-clause and against the truth of the then-clause. These lines are from the final letter written to his wife by one of the doomed soldiers of the German Sixth Army outside Stalingrad:

“If there is a God,” you wrote me in your last letter, “then he will bring you back to me soon and healthy.” But, dearest, if your words are weighed now you will have to make a difficult and great decision.

Her own words, quoted by her husband, committed her to the statement If God exists, then the soldier will return to his wife soon and healthy. The report of his death that she later received supported this statement: The soldier will not return to his wife soon and healthy. But by a valid denying the consequent argument, these two premises entail God does not exist. This, then, presented his wife with the difficult and great decision that the soldier foretold—she must stop believing in God, or she must go back on her own words.

Let’s set this up in the same way as we did with the auto mechanic and the Newtonians. There are three statements before her, at least one of which must be false:

If God exists, then the soldier will return to his wife soon and healthy. God exists. (The if-clause is true.) The soldier will not return to his wife soon and healthy. (The then-clause is false.)

Let’s suppose that instead of giving up her belief in God, she chose the option of going back on her words and rejecting her if–then statement. Her most reasonable defense, as we have seen, would be for her to sever the connection between the if-clause and the then-clause by identifying and rejecting the false secondary assumption. Candidates might include:

God cares about human suffering. God cares about the suffering of this particular soldier and his wife. God is able to prevent this suffering. God knows about this suffering.

But let’s further suppose that she insisted on continuing to embrace all these secondary assumptions, on the grounds that to do otherwise would be to unsuitably diminish God. Instead, she took the step that many believers in God take—the step of saying, “God’s ways are beyond the understanding of man. When I get to heaven he will reveal to me his reasons. Until then, I will continue to believe in him.” This is an attempt to use the educated ignorance defense. We give up on the if–then statement in the expectation that we will eventually discover the car’s mechanical defect, the flaw in our astronomical calculations, or the hidden mysteries of God.

Whether this is a reasonable move for the soldier’s wife depends on one condition: it is educated ignorance—and thus a reasonable defense—only if the wife has independent strong evidence that God exists (evidence for the if-clause). If she does not—if she accepts by faith alone not only God’s mysterious ways but also his very existence—then she cannot reasonably defend her rejection of the if–then statement unless she identifies and rejects the false secondary assumption.

EXERCISES Chapter 11, set (g)

In each problem there are three statements, at least one of which must be false. Provide an “educated ignorance” defense for the claim that the if–then statement is false; you’ll need to state evidence for the if-clause and against the then-clause in your defense.

Sample exercise. If the instructor is fair, then he will not give higher grades to males than to females. The instructor is fair. The instructor gave higher grades to males than females.

Sample answer. The if–then statement is probably false, although I can’t say exactly what the mistaken assumption is. Even though the record shows that in this class the males did much better than the females, he has a widespread reputation for bending over backward to treat everyone fairly. It seems likely that his reputation is deserved and that in this case there is an explanation that will eventually emerge.

• If you patch that hole, then the roof will stop leaking. You patch the hole. The roof does not stop leaking.
• If your boyfriend loves you, then he will be on time tonight. Your boyfriend loves you. He is not on time tonight.
• If you are the most talented, then you will win the talent show. You are the most talented. You do not win the talent show.
• If it is impossible to move physical objects by only thinking about it, then when Uri Geller concentrates on bending the spoon it will not bend. It is impossible to move physical objects by only thinking about it. When Uri Geller concentrates on bending the spoon it does bend.

Strategies for Evaluating the Truth of If–Then Statements

11.2.4 Secondary Assumptions and Indirect Arguments

Secondary assumptions can also play an important role in the evaluation of indirect arguments (which we have also called reductios ). Introduced in Chapter 10, such arguments, in their simplest form, exhibit the structure of denying the consequent. They begin with a statement that may seem quite innocuous and attempt to show that it is false by pointing out, in what amounts to an if–then premise, an absurd consequence that it forces on you. You accept the absurdity of the consequence by accepting a premise that says the then-clause is false. You must then conclude, by the valid form of denying the consequent, that the seemingly innocuous if-clause must be rejected. [5] An example is found in these remarks by David Wilson (no known relation to the author), adapted from a newspaper report:

Melina Mercouri, Greece’s minister of culture, swept into the staid old British Museum to examine what she called the soul of the Greek people—the Elgin Marbles. Lord Elgin took them from the Parthenon in Athens in the early 19th century. Mercouri is expected to make a formal request soon for the marbles’ return. But Dr. David Wilson, director of the British Museum, opposes the idea. “If we start dismantling our collection,” Wilson said, “it will be the beginning of the end of the museum as an international cultural institution. The logical conclusion of the forced return of the Elgin Marbles would be the utter stripping of the great museums of the world.”

Wilson’s argument can be clarified thus:

• If it is acceptable to force the British to return the Elgin Marbles to Greece, then it is acceptable to strip the great museums of the world.
• [It is not acceptable to strip the great museums of the world.]
• ∴ It is not acceptable to force the British to return the Elgin Marbles to Greece.

Melina Mercouri must avoid the conclusion without rejecting premise 2, so her only recourse is to reject the if–then premise. But when she does reject it, she is no position to respond with the educated ignorance defense; the evidence for the if-clause is exactly what is in question, so for her to simply say the if-clause is obviously true would be to beg the question. In short, her only reasonable strategy is to reject the if–then premise by identifying a faulty secondary assumption that it depends on. Here is a strong candidate for the role of faulty secondary assumption:

The only principle for returning the Elgin Marbles would be that any item, great or small, removed from its original culture, whether by consent or by force, must be returned to that culture.

This secondary assumption is clearly false. So Mercouri might defend her rejection of premise 1 as follows:

Premise 1 is almost certainly false, since it assumes that all items must be returned to their original culture; but the return of the Elgin Marbles only depends on a principle calling for the return of great national treasures that have been forcibly removed.

What Mercouri would be doing is accusing Wilson of committing the fallacy of non causa pro causa (introduced in Chapter 10). This is the fallacy of blaming the absurd consequence ( It is acceptable to strip the great museums of the world ) on what is set forth as its cause ( It is acceptable to force the British to return the Elgin Marbles to Greece ) instead of blaming the unnoticed assumption that is the real cause of the absurdity ( All items must be returned to their original culture ).

Because indirect arguments are typically offered in support of controversial conclusions, only rarely can the educated ignorance approach be used in evaluating them without begging the question. Be especially watchful for faulty secondary assumptions behind the if–then premise of indirect arguments; when there is such an assumption, the indirect argument can be criticized for committing the fallacy of non causa pro causa.

EXERCISES Chapter 11 set (h)

Clarify each of these simple indirect arguments; then evaluate only the if–then premise, on the grounds that it commits the fallacy of non causa pro causa. (Use the Elgin Marbles case as your sample.)

• If you are right in your claim that income taxes should be eliminated, then you must accept the consequence that the government will be left with no money to do even its most important business. But we would all agree that government cannot be done away with. So income taxes must remain.
• If children who misbehave are not immediately and severely punished, they will grow up with the belief that misbehavior has no negative consequences. We all agree, of course, that our children cannot be allowed to grow up with that belief. So don’t spare the rod with your children.

EXERCISES Chapter 11, set (i)

Each of the passages below indicates what could be seen as a misuse of secondary assumptions. In the Kelvin case, clarify the denying the consequent argument and identify the secondary assumption that, perhaps, Kelvin should have questioned. In the Azande case, clarify the affirming the antecedent argument that the Azande are trying to avoid, and identify the secondary assumption that they, perhaps, too readily reject to show that the if–then premise is false.

• Lord Kelvin, the leading British physicist of his day, dismissed Darwin’s work on the ground that it violated the principles of thermodynamics. The sun could be no more than 100 million years old; evolution demanded a much longer period in which to operate; therefore evolution must be rejected. Kelvin wasted no time pursuing the minutiae of the geological and palaeontological evidence on which evolution was based. Physics in the guise of thermodynamics had spoken clearly and whatever failed to fit into its scheme had to be rejected. Kelvin’s thermodynamics were later shown to be wrong. Unaware of radioactivity, he had inevitably failed to allow for its effect in his calculations.—Derek Gjertsen, Science and Philosophy
• According to the Azande, witchcraft is inherited unilinearly, from father to son, and mother to daughter. How, therefore, can I accept that my brother is a witch and yet deny that I am also infected? To prevent this absurdity arising, the Azande adopt further “elaborations of belief.” They argue, for example, that if a man is proven a witch beyond all doubt, his kin, to establish their innocence, deny that he is a member of their clan. They say he was a bastard, for among Azande a man is always of the clan of his genitor [natural father] and not of his pater [mother’s legal husband]. In this and other ways, Evans-Pritchard concluded, the Azande freed themselves from “the logical consequences of belief in biological transmission of witchcraft.”—Derek Gjertsen, Science and Philosophy

11.3 If–Then Arguments With Implicit Statements

If–then arguments, like any other sort of arguments, frequently have implicit premises or conclusions. To use a term from earlier in the book, they are frequently enthymemes. In extreme cases, only the if–then premise is explicit. Suppose, for example, that you’ve complained for the 10th time that the party across the hall is too loud, and I say to you, “Hey, if you can’t beat ‘em, join ‘em.” What I’ve actually given is an affirming the antecedent argument. I’ve explicitly provided the if–then premise; the implicit premise, obviously, is You can’t beat them; and the implicit conclusion is You should join them.

Consider the following, more sophisticated example, from a New York Review of Books review of a book of film criticism by Stanley Cavell:

When Katharine Hepburn in The Philadelphia Story brightly says, “I think men are wonderful,” Cavell hears an “allusion” to The Tempest that amounts “almost to an echo” of Miranda’s saying, “How beauteous mankind is!” If this is an echo, then Irene Dunne’s saying of her marriage, “It was pretty swell while it lasted” is a reminiscence of Gibbon’s Decline and Fall.

This argument is an example of denying the consequent. But only one statement of the argument is explicit. The full clarification proceeds thus:

• If Hepburn’s remark “I think men are wonderful” in The Philadelphia Story is an echo of Miranda’s “How beauteous mankind is” in The Tempest, then Irene Dunne’s saying of her marriage, “It was pretty swell while it lasted” is a reminiscence of Gibbon’s Decline and Fall.
• [Irene Dunne’s saying of her marriage, “It was pretty swell while it lasted” is not a reminiscence of Gibbon’s Decline and Fall. ]
• ∴ [Hepburn’s remark “I think men are wonderful” in The Philadelphia Story is not an echo of Miranda’s “How beauteous mankind is” in The Tempest. ]

This is the reviewer’s sideways—but effective—way of saying that perhaps Cavell takes himself a bit too seriously.

11.3.1 If–Then Bridges

In the preceding examples, only the if–then premise was explicit. But in other cases, only the if–then premise is implicit. Note, for example, this episode recorded by Jean Piaget in his book, The Child’s Conception of the World :

A little girl of nine asked: “Daddy, is there really God?” The father answered that it wasn’t very certain, to which the child retorted: “There must be really, because he has a name!”

This does not look, on the face of it, like an if–then argument. But there must be an implicit premise connecting the two parts of her retort. A good clarification, it seems, is this:

• [If any name exists, then the thing it names exists.]
• God has a name.
• ∴ God exists.

Premise 1 serves as a universal if–then bridge. It is a universal if–then statement (note the term any ) and serves as a bridge of sorts between 2 and C. We might have proposed a more specific sort of bridge, as follows:

1*. [If God has a name, then God exists.]

Either bridge produces a valid argument—the first one by singular affirming the antecedent, the second one by affirming the antecedent. But the second doesn’t produce an argument that will convince us—after all, you can add a premise to any argument that says, “If the premises are true, then the conclusion is true,” and thereby say something that the arguer surely intended, without saying anything illuminating. (There is a specialized term for such an if–then statement, namely, the corresponding conditional of an argument.) When the conditional is expressed in its universal form, on the other hand, we get some idea of the general principle being assumed by the arguer.

EXERCISES Chapter 11, set (j)

Clarify each of these arguments, proposing for each a universal if–then bridge.

Sample exercise. “An idealist is one who, on noticing that a rose smells better than a cabbage, concludes that it will also make better soup.”—H. L. Mencken

• [If anything smells better than another thing, then it also tastes better.]
• A rose smells better than a cabbage.
• ∴ A rose tastes better than a cabbage.
• Twitter, as another high-tech innovation, will inevitably fragment community rather than enhance it.
• “Spirituality turns out to be central to cognitive psychology, and therefore to artificial intelligence, and therefore to computer science, and therefore to the whole history of science and technology.” —David Gelernter, The Muse in the Machine
• Most striking of their claims is that among the 7,000 people executed in this century, at least 23 people, and possibly many more, have been innocent. This alone is reason, the authors conclude, that the death penalty should be abolished.—review of Hugo Bedau and Michael Radelet, In Spite of Innocence
• “There will always be books. You can show them off on the shelf behind you during a Zoom meeting, and you still can’t do that with your iPhone.”—Robert Maxwell
• “Although these textbooks purport to be a universal guide to learning of great worth and importance, there is a single clue that points to another direction. In the six years I taught in city and country schools, no one ever stole a textbook.”—W. Ron Jones, Changing Education

11.4 Bringing It All Together

After learning a wide array of distinct skills, you now have the opportunity to use all of them together. If–then arguments provide us with our first of six groupings of arguments that can be substantial and interesting. And you are now equipped to fully clarify and evaluate them.

There is nothing new to be said, but a few things bear repeating. In your evaluation, separately evaluate the truth of the premises (considering each premise individually), the logic of the argument (naming the form if it has a name, and providing a validity counterexample if it is invalid), the soundness of the argument (which depends entirely on truth and logic), and, if necessary, the conversational relevance of the argument. Always provide a defense of your judgment, and do so as if there were a reasonable objector over your shoulder whom you were trying to persuade.

I’ll provide a sample clarification and evaluation of this brief argument found in Gilbert Harman’s The Nature of Morality :

Total pacifism might be a good principle if everyone were to follow it. But not everyone is, so it isn’t.

CLARIFICATION

• If everyone followed total pacifism, then total pacifism would be a good principle.
• Not everyone follows total pacifism.
• ∴ Total pacifism is not a good principle.

Premise 1 is probably true, since the main objection to total pacifism is that it leaves you with no defense against those who are not pacifists. But if everyone were a pacifist, that would be no problem. (This seems to be the main secondary assumption of the premise.)

Premise 2 is certainly true. We all have firsthand experience with violent people, not to mention the experience of them that we have via the media.

Invalid, fallacy of denying the antecedent. Here is a validity counterexample:

• If anything is a chihuahua, then it is a dog.
• Uga, the Georgia Bulldogs mascot, is not a chihuahua.
• ∴ Uga, the Georgia Bulldogs mascot, is not a dog

Unsound, due to invalidity.

EXERCISES Chapter 11, set (k)

Clarify and evaluate. Where appropriate, provide implicit statements in the clarification (including universal if–then bridges) and original validity counterexamples in the evaluations.

• “With the layout of the San Francisco-Oakland area, a rail line there had a better chance than most,” said rail critic Peter Gordon, a regional planner at USC. “If it doesn’t work there, and I assert it doesn’t, there is no way rail transit will work in a place like Los Angeles.” — Los Angeles Times
• “But if evolution proceeded as a lockstep, then the fossil record should display a pattern of gradual and sequential advance in organization. It does not, and I regard this failure as the most telling argument against an evolutionary ratchet.”—Stephen Gould, Panda’s Thumb (It might help you to know that Gould is a noted professor of paleontology at Harvard. By a “ratchet” and a “lockstep” he means a “gradual, uniform progression.”)
• “If each man had a definite set of rules of conduct by which he regulated his life he would be no better than a machine. But there are no such rules, so men cannot be machines.”—A. M. Turing, Mind (Turing is an expert in artificial intelligence, i.e., what it would take to make a machine think.)
• “ Q : Even so, don’t you think that the use of computers reinforces a child’s problem-solving ability? A: If that were true, then computer professionals would lead better lives than the rest of the population. We know very well that isn’t the case.”—interview with computer expert Joseph Weizenbaum, Le Nouvel Observateur (The argument is in the answer.)
• Pjeter Ivezaj, a U.S. citizen, was sentenced Wednesday to seven years in prison by a panel of judges in Yugoslavia for participating in peaceful anti-Yugoslav activities in this country. Said his brother Frano, 28, “I intend to take this matter to the court of world opinion. If U.S. citizenship has any value, which I believe it does, now is the time for the U.S. government to make a move.”— Detroit Free Press
• Scientists believe that the most likely location of our country’s next severe earthquake is a fault zone that centers on New Madrid, MO. But residents here, where the quake probably will be centered, are unimpressed. “I’m just a non-believer,” said L. H. Rector, publisher of the New Madrid Weekly Record, whose motto is “The only paper in the world that cares about New Madrid.” “It hasn’t been proved that we’re going to have one,” Rector said. “Now, out in California, they can see the fault. It’s been proved. But no one here in New Madrid has seen one fault.”— Los Angeles Times (Provide Rector’s argument with a universal if–then bridge.)
• “The church never wanted disease to be under the control of man. Timothy Dwight, president of Yale College, preached a sermon against vaccination. His idea was that if God had decreed from all eternity that a certain man should die with the smallpox, it was a frightful sin to avoid and annul that decree by the trick of vaccination. Smallpox being regarded as one of the heaviest guns in the arsenal of heaven, to spike it was the height of presumption.”—Robert Ingersoll, Ingersoll, The Immortal Infidel
• The key premise is that a human fetus is a full-fledged, actualized human life. Supposing human embryos are human beings, their innocence is beyond question. So nothing could justify our destroying them except, perhaps, the necessity of saving some other innocent human life.—Roger Wertheimer, “Understanding the Abortion Argument” (Clarify as a complex argument with an if–then bridge in the second inference.)
• “If there be righteousness in the heart, there will be beauty in the character. If there be beauty in the character, there will be harmony in the home. If there be harmony in the home, there will be order in the nation. If there be order in the nation, there will be peace in the world.”—Confucius (Suppose that this is a transitivity of implication argument with an implicit conclusion.)
• “If a man could not have done otherwise than he in fact did, then he is not responsible for his action. But if determinism is true, it is true of every action that the agent could not have done otherwise. Therefore, if determinism is true, no one is ever responsible for what he does.”—Winston Nesbitt and Stewart Candlish, Mind
• Their children, they soon saw, were being presented by EPIC, an organization to help children learn to think about values, with hypothetical situations that called for the students to make choices and decisions. On a spaceship survival trip, an EPIC question asks, “Determine what to take with you. Pretend the ship develops trouble and the load must be lightened. What could you discard?” There was, to a number of parents, something very troubling about these types of questions. The questions seemed to carry with them the presumption that the children were free to reason through to their own answers. If they could do that, it meant that there were no moral absolutes, and nothing was clearly right or wrong, good or bad. This was not the worldview of fundamentalists who believe in the literal word of the Bible. “Once you tell a child that he has to decide upon his own values system, that’s like saying that values are not real, and you can just make them up as you go along,” said Marjorie McNabb, a former Episcopalian who now attends a Baptist church. “Children would be better raised by a street gang than EPIC. At least, they’d learn two values, courage and loyalty. That’s better than no values.”— Los Angeles Times (Look for the actual argument to begin in about the middle, with the words “If they could do that. . . .”)
• In spite of the popularity of the finite-world picture, however, it is open to a devastating objection. In being finite the world must have a limiting boundary, such as Aristotle’s outermost sphere. That is impossible. This objection was put forward by the Greeks, reappeared in the scientific skepticism of the early Renaissance and probably occurs to any schoolchild who thinks about it today. On the basis of the objection, one must conclude that the universe is infinite.—J. J. Callahan, Scientific American (The stylistic variant for the if–then statement is unusual—it is “in being . . . must have . . .”)
• “There is one insuperable obstacle to a belief in ghosts. A ghost never comes naked: he appears either in a winding-sheet or ‘in his habit as he lived.’ To believe in him, then, is to believe that not only have the dead the power to make themselves visible after there is nothing left of them, but that the same power inheres in textile fabrics. Supposing the products of the loom to have this ability, what object would they have in exercising it? And why does not the apparition of a suit of clothes sometimes walk abroad without a ghost in it? These be riddles of significance. They reach away down and get a convulsive grasp on the very taproot of this flourishing faith.”—Ambrose Bierce, Devil’s Dictionary (Treat this as an indirect argument in which the only explicit premise is really the one starting “To believe in him . . .”)
• There was little doubt, then, that if the earth moved through an immovable sea of ether, there would be an ether wind, and if there were an ether wind, the Michelson-Morley apparatus would detect it. In fact, both scientists were confident that they would not only find such a wind, but that they could also determine (by rotating the slab until there was a maximum difference in the time it took light to make the two journeys) the exact direction, at any given moment, of the earth’s path through the ether. Michelson was astounded and disappointed. This time the astonishment was felt by physicists all over the world. Regardless of how Michelson and Morley turned their apparatus, they found no sign of an ether wind! Michelson never dreamed that this ‘failure’ would make the experiment one of the most successful, revolutionary experiments in the history of science. The reason Michelson and Morley were unable to detect an ether wind, Einstein said, is simple: there is no ether wind.—Martin Gardner, Relativity for the Million

11.5 Summary of Chapter Eleven

There are three common valid forms of if–then arguments: affirming the antecedent, denying the consequent, and transitivity of implication. There are two common invalid forms: the fallacy of affirming the consequent and the fallacy of denying the antecedent. When an argument takes one of these forms but has both a universal if–then premise and a conclusion about a single instance to which the universal applies, describe it in the same terms but for the addition of the phrase singular. . . .

When paraphrasing, translate variants such as P only if Q and Q assuming P into the standard constant If P then Q.

When judging the truth of if–then premises, concentrate chiefly on the proposed connection—whether causal or broadly logical—between the if-clause and the then-clause. Typically the if-clause is not alone presumed to be sufficient for the then-clause, but to be sufficient only in combination with secondary assumptions that are themselves not in question. The if-clause is the only one mentioned because it is presumed, in this particular context, to be the only factor in doubt. In defending your judgment that an if-then premise is true, point out the truth of the most doubtful secondary assumptions. In defending your judgment that the if–then premise is false, point out the falsity of a secondary assumption. In this way you either reinforce or sever the connection between if-clause and then-clause.

When the if-clause is clearly true and the then-clause is clearly false, you may have the opportunity to effectively show the falsity of the if–then premise without reference to secondary assumptions in two different ways. First, you may provide a truth counterexample, assuming the if–then premise is universal. And second, you may provide an “educated ignorance” defense, which requires that the evidence for the truth of the if-clause and the falsity of the then-clause is strong—much stronger than the evidence for the if–then premise itself.

If–then arguments are frequently enthymematic. When the if–then premise is the implicit statement, be especially attuned to the likely need for a universal if–then bridge.

11.6 Guidelines for Chapter Eleven

• Translate the stylistic variants for the if–then premise into the standard constant.
• When an argument has both a universal premise and a conclusion about a single thing that is encompassed by the universal premise, consider whether it is the singular version of a sentential logical form.
• Defend your judgment that an if–then statement is true by affirming the truth of the most questionable secondary assumptions. Defend your judgment that it is false by showing that a secondary assumption is false.
• Do not defend your judgment of an if–then statement by simply rewording the statement (or, if false, by rewording the denial of the statement).
• When a universal if–then statement is false, try to defend that judgment by providing a truth counterexample.
• It is reasonable to judge an if–then premise false “because some secondary assumption must be mistaken, though I don’t know which one” only if there is very powerful evidence both that the if-clause is true and that the then-clause is false.
• In indirect arguments, be alert for faulty secondary assumptions behind the if–then premise.
• Consider providing a universal if–then bridge when an explicit link between premise and conclusion has not been provided by the arguer.

11.7 Glossary for Chapter Eleven

Affirming the antecedent —valid deductive form, as follows:

Also known as modus ponens, which is Latin for “the method (or mode, from modus ) of affirming (or propounding, from ponens ).”

Antecedent —the if-clause of an if–then statement.

Consequent —the then-clause of an if–then statement.

Denying the consequent —valid deductive form, as follows:

Also known as modus tollens, which is Latin for “the method of denying.”

Educated ignorance defense —defense of your judgment that an if–then premise is false even though you cannot tell which secondary assumption is at fault (thus, it reflects ignorance); it can be a reasonable defense only if your evidence for the truth of the if-clause and for the falsity of the then-clause is especially strong (thus, the defense is educated).

Fallacy of affirming the consequent —invalid deductive form, as follows:

Fallacy of denying the antecedent —invalid deductive form, as follows:

Fallacy of singular affirming the consequent —invalid affirming the consequent in which the if–then premise is universal and the conclusion is about a single instance that is encompassed by the universal term.

Fallacy of singular denying the antecedent —invalid denying the antecedent in which the if–then premise is universal and the conclusion is about a single instance that is encompassed by the universal term.

If–then argument —one of a loosely defined group of deductive arguments that have an if–then statement as a premise. Also known as a conditional argument or hypothetical–syllogism.

If–then statement —a statement in the form of If P then Q. Also known as a conditional.

Secondary assumption —when an if–then statement is asserted, this is an assumption made, often implicit because it is not in doubt, about another factor besides the if-clause that contributes to the truth of the then-clause. Also known as auxiliary hypothesis.

Singular affirming the antecedent —valid affirming the antecedent in which the if–then premise is universal and the conclusion is about a single instance that is encompassed by the universal term.

Singular denying the consequent —valid denying the consequent in which the if–then premise is universal and the conclusion is about a single instance that is encompassed by the universal term.

Singular transitivity of implication —valid transitivity of implication in which the if–then premises are universal and the conclusion is about a single instance that is encompassed by the universal term.

Transitivity of implication —valid deductive form, as follows:

It can have any number of if–then premises. It can also have a negative conclusion, as follows:

• ∴ If not R , then not P.

Truth counterexample —strategy for defending your judgment that a universal if–then premise is false, by identifying a single instance in which the if-clause is obviously true and the then-clause is obviously false.

Universal statement —a premise with a term like all, none, anything, or nothing.

• If construction begins before July 4, then the building will be ready to be occupied before snow falls.
• If the building is not ready to be occupied before snow falls, then construction did not begin before July 4.
• The building will not be ready to be occupied before snow falls.
• ∴ Construction did not begin before July 4.
• ∴ If not R then not P.
• If you have studied formal logic, you have learned that you only need to know the truth-values of the antecedent and the consequent to know the truth-value of the if–then statement; you may have memorized truth tables in support of this. But this applies only to a specialized form of the if–then statement called the material, or truth-functional, conditional. This sort of if–then statement is not used in ordinary language. ↵
• For practical purposes, it may be helpful to think of both sorts of connections as ultimately epistemic—that is, as providing in the antecedent a reason for believing the consequent to be true, on the strictly hypothetical assumption that the antecedent is true. ↵
• In formal logic, this sort of argument must produce a logical contradiction. In common usage, however, it only needs to produce something preposterous. ↵

One of a loosely defined group of deductive arguments that have an if–then statement as a premise. Also known as a conditional argument or hypothetical–syllogism.

A statement in the form of If P then Q. Also known as a conditional.

The if-clause of an if–then statement.

The then-clause of an if–then statement.

Valid deductive form, as follows:

1. If P then Q . 2. P ∴ C . Q

1. If P then Q . 2. Not Q. ∴ C . Not P.

Invalid deductive form, as follows:

1. If P then Q . 2. Q ∴ C . P

1. If P then Q . 2. Not P ∴ C . Not Q

1. If P then Q . 2. If Q then R . ∴ C . If P then R.

∴ C . If not R , then not P.

Valid denying the consequent in which the if–then premise is universal and the conclusion is about a single instance that is encompassed by the universal term.

A premise with a term like all, none, anything, or nothing.

Valid affirming the antecedent in which the if–then premise is universal and the conclusion is about a single instance that is encompassed by the universal term.

Valid transitivity of implication in which the if–then premises are universal and the conclusion is about a single instance that is encompassed by the universal term.

Invalid affirming the consequent in which the if–then premise is universal and the conclusion is about a single instance that is encompassed by the universal term.

Invalid denying the antecedent in which the if–then premise is universal and the conclusion is about a single instance that is encompassed by the universal term.

When an if–then statement is asserted, this is an assumption made, often implicit because it is not in doubt, about another factor besides the if-clause that contributes to the truth of the then-clause. Also known as auxiliary hypothesis.

Strategy for defending your judgment that a universal if–then premise is false, by identifying a single instance in which the if-clause is obviously true and the then-clause is obviously false.

Defense of your judgment that an if–then premise is false even though you cannot tell which secondary assumption is at fault (thus, it reflects ignorance); it can be a reasonable defense only if your evidence for the truth of the if-clause and for the falsity of the then-clause is especially strong (thus, the defense is educated).

A Guide to Good Reasoning: Cultivating Intellectual Virtues Copyright © 2020 by David Carl Wilson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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2.11: If Then Statements

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Hypothesis followed by a conclusion in a conditional statement.

Conditional Statements

A conditional statement (also called an if-then statement ) is a statement with a hypothesis followed by a conclusion . The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement. The conclusion is the result of a hypothesis.

If-then statements might not always be written in the “if-then” form. Here are some examples of conditional statements:

• Statement 1: If you work overtime, then you’ll be paid time-and-a-half.
• Statement 2: I’ll wash the car if the weather is nice.
• Statement 3: If 2 divides evenly into \(x\), then \(x\) is an even number.
• Statement 4: I’ll be a millionaire when I win the lottery.
• Statement 5: All equiangular triangles are equilateral.

Statements 1 and 3 are written in the “if-then” form. The hypothesis of Statement 1 is “you work overtime.” The conclusion is “you’ll be paid time-and-a-half.” Statement 2 has the hypothesis after the conclusion. If the word “if” is in the middle of the statement, then the hypothesis is after it. The statement can be rewritten: If the weather is nice, then I will wash the car. Statement 4 uses the word “when” instead of “if” and is like Statement 2. It can be written: If I win the lottery, then I will be a millionaire. Statement 5 “if” and “then” are not there. It can be rewritten: If a triangle is equiangular, then it is equilateral.

What if you were given a statement like "All squares are rectangles"? How could you determine the hypothesis and conclusion of this statement?

Example \(\PageIndex{1}\)

Determine the hypothesis and conclusion: I'll bring an umbrella if it rains.

Hypothesis: "It rains." Conclusion: "I'll bring an umbrella."

Example \(\PageIndex{2}\)

Determine the hypothesis and conclusion: All right angles are \(90^{\circ}\).

Hypothesis: "An angle is right." Conclusion: "It is \(90^{\circ}\)."

Example \(\PageIndex{3}\)

Use the statement: I will graduate when I pass Calculus.

Rewrite in if-then form and determine the hypothesis and conclusion.

This statement can be rewritten as If I pass Calculus, then I will graduate. The hypothesis is “I pass Calculus,” and the conclusion is “I will graduate.”

Example \(\PageIndex{4}\)

Use the statement: All prime numbers are odd.

Rewrite in if-then form, determine the hypothesis and conclusion, and determine whether this is a true statement.

This statement can be rewritten as If a number is prime, then it is odd. The hypothesis is "a number is prime" and the conclusion is "it is odd". This is not a true statement (remember that not all conditional statements will be true!) since 2 is a prime number but it is not odd.

Example \(\PageIndex{5}\)

Determine the hypothesis and conclusion: Sarah will go to the store if Riley does the laundry.

The statement can be rewritten as "If Riley does the laundry then Sarah will go to the store." The hypothesis is "Riley does the laundry" and the conclusion is "Sarah will go to the store."

Determine the hypothesis and the conclusion for each statement.

• If 5 divides evenly into \(x\), then \(x\) ends in 0 or 5.
• If a triangle has three congruent sides, it is an equilateral triangle.
• Three points are coplanar if they all lie in the same plane.
• If \(x=3\), then \(x^2=9\).
• If you take yoga, then you are relaxed.
• All baseball players wear hats.
• I'll learn how to drive when I am 16 years old.
• If you do your homework, then you can watch TV.
• Alternate interior angles are congruent if lines are parallel.
• All kids like ice cream.

Additional Resources

Video: If-Then Statements Principles - Basic

Activities: If-Then Statements Discussion Questions

Study Aids: Conditional Statements Study Guide

Practice: If Then Statements

Real World: If Then Statements

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How to Understand ‘If-Then’ Conditional Statements: A Comprehensive Guide

In math, and even in everyday life, we often say 'if this, then that.' This is the essence of conditional statements. They set up a condition and then describe what happens if that condition is met. For instance, 'If it rains, then the ground gets wet.' These statements are foundational in math, helping us build logical arguments and solve problems. In this guide, we'll dive into the clear-cut world of conditional statements, breaking them down in both simple terms and their mathematical significance.

Step-by-step Guide: Conditional Statements

Defining Conditional Statements: A conditional statement is a logical statement that has two parts: a hypothesis (the ‘if’ part) and a conclusion (the ‘then’ part). Written symbolically, it takes the form: \( \text{If } p, \text{ then } q \) Where \( p \) is the hypothesis and \( q \) is the conclusion.

Truth Values: A conditional statement is either true or false. The only time a conditional statement is false is when the hypothesis is true, but the conclusion is false.

Converse, Inverse, and Contrapositive: 1. Converse: The converse of a conditional statement switches the hypothesis and the conclusion. For the statement “If \( p \), then \( q \)”, the converse is “If \( q \), then \( p \)”.

2. Inverse: The inverse of a conditional statement negates both the hypothesis and the conclusion. For the statement “If \( p \), then \( q \)”, the inverse is “If not \( p \), then not \( q \)”.

3. Contrapositive: The contrapositive of a conditional statement switches and negates both the hypothesis and the conclusion. For the statement “If \( p \), then \( q \)”, the contrapositive is “If not \( q \), then not \( p \)”.

Example 1: Simple Conditional Statement: “If it is raining, then the ground is wet.”

Solution: Hypothesis \(( p )\): It is raining. Conclusion \(( q )\): The ground is wet.

Example 2: Determining Truth Value Statement: “If a shape has four sides, then it is a rectangle.”

Solution: This statement is false because a shape with four sides could be a square, trapezoid, or other quadrilateral, not necessarily a rectangle.

Example 3: Converse, Inverse, and Contrapositive Statement: “If a number is even, then it is divisible by \(2\).”

Solution: Converse: If a number is divisible by \(2\), then it is even. Inverse: If a number is not even, then it is not divisible by \(2\). Contrapositive: If a number is not divisible by \(2\), then it is not even.

Practice Questions:

• Write the converse, inverse, and contrapositive for the statement: “If a bird is a penguin, then it cannot fly.”
• Determine the truth value of the statement: “If a shape has three sides, then it is a triangle.”
• For the statement “If an animal is a cat, then it is a mammal,” which of the following is its converse? a) If an animal is a mammal, then it is a cat. b) If an animal is not a cat, then it is not a mammal. c) If an animal is not a mammal, then it is not a cat.
• Converse: If a bird cannot fly, then it is a penguin. Inverse: If a bird is not a penguin, then it can fly. Contrapositive: If a bird can fly, then it is not a penguin.
• The statement is true. A shape with three sides is defined as a triangle.
• a) If an animal is a mammal, then it is a cat.

by: Effortless Math Team about 7 months ago (category: Articles )

Effortless Math Team

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Algebra I Study Guide A Comprehensive Review and Step-By-Step Guide to Preparing for Algebra I

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Scientific Method: Step 3: HYPOTHESIS

• Step 1: QUESTION
• Step 2: RESEARCH
• Step 3: HYPOTHESIS
• Step 4: EXPERIMENT
• Step 5: DATA
• Step 6: CONCLUSION

Step 3: State your hypothesis

Now it's time to state your hypothesis . The hypothesis is an educated guess as to what will happen during your experiment. 

The hypothesis is often written using the words "IF" and "THEN." For example, " If I do not study, then I will fail the test." The "if' and "then" statements reflect your independent and dependent variables . 

The hypothesis should relate back to your original question and must be testable .

A word about variables...

Your experiment will include variables to measure and to explain any cause and effect. Below you will find some useful links describing the different types of variables.

• "What are independent and dependent variables" NCES
• [VIDEO] Biology: Independent vs. Dependent Variables (Nucleus Medical Media) Video explaining independent and dependent variables, with examples.

Resource Links

• What is and How to Write a Good Hypothesis in Research? (Elsevier)
• Hypothesis brochure from Penn State/Berks

• << Previous: Step 2: RESEARCH
• Next: Step 4: EXPERIMENT >>
• Last Updated: May 9, 2024 10:59 AM
• URL: https://harford.libguides.com/scientific_method

an Excelsior University site

Formulating Strong Hypotheses

When you write your hypothesis statement, you want to do more than simply wager a guess. To make sure you generate a solid hypothesis, first ask yourself these questions:

• What is the connection between your hypothesis and your research topic?
• Is your hypothesis testable?
• What potential explanations or justifications of the hypothesis could you explore?
• What are the counter-arguments to your hypothesis?
• Does your hypothesis include an independent as well as a dependent variable?

Exploring these questions will help you make sure that your hypothesis is solid and, if not, where its weaknesses lie. It is important to go through these steps first so that you know you are well-positioned to conduct your research.

A testable hypothesis is not a simple statement. It is rather an informed, predictive statement that provides a clear introduction to a study, its goals, and the possible outcomes. There are some important things to consider when building a compelling, testable hypothesis.

• Make sure that the hypothesis clearly defines the topic and the focus of the study.
• Follow this template: If a specific action is taken, then a certain outcome is expected.
• In the example, the independent variable is whether people in the study wear masks.
• The dependent variable is how many cases of virus emerge among the group studied.
• You can’t prove that wearing a mask has prevented you from being infected by a virus, but you can measure over time whether mask-wearing is associated with lower cases of virus in a specific population.

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“If-then”: Using Conditional Sentences in Academic Writing

Conditional sentences are statements of an “if-then” or “unless-then” situation (although “then” is not used), or a probability. These sentences present situations and their possible outcomes. Conditional sentences are often used to discuss the results of the research studies or are part of a research hypothesis statement.

Conditional sentences are perfectly acceptable and, in many cases, necessary to state and test a condition and its outcome. Most authors of the scientific papers will use these sentences in their abstracts to discuss the reasons to conduct their study. So, it is important to frame them correctly.

One way of writing conditional sentences correctly is using Trinka – world’s first AI-powered grammar checker and language enhancement tool custom designed for academic writing. Its smart features help you in incorporating all the requirements of academic writing such as formal tone, consistency, style guide preferences and much more! Moreover, Trinka corrects advance grammar errors unique to technical writing which includes conditional sentences, too.

Types of Conditional Sentences

Conditional sentences are constructed using two clauses—the if (or unless ) clause and the main clause. There are five types of conditional sentences. It is important to understand each because each conveys a different meaning . Some conditional sentences refer to the general truths and others to hypothetical situations.

• Zero conditional sentences refer to the general truth about a situation. These sentences state that one condition always results in the same outcome. For example:

If I don’t turn on my air conditioner, my house is hot.

Note that the both clauses are in the present tense.

• First conditional sentences present a situation in which a future outcome is not ensured. For example:

If you eat your broccoli, you will feel great.

Note that the present tense is used in the if clause and the future tense in the main clause.

• Second conditional sentences express if clauses and results that are extremely unlikely, such as those we “wish for.” For example:

If I had control over the food sources, I would end world hunger.

Note the use of the simple past tense in the if clause and the verb (i.e., would, could, should) in the main clause.

• Third conditional sentences are a bit different. They suggest that the result would be different had the past been different. For example:

If you had told me you were hungry, I would have bought food for you.

Note that the conditions did not happen. The past perfect tense (had + past participle form of the verb) is used in the if clause and the verb (would) plus “have” plus the past participle of the verb was used in the main clause.

• Mixed type conditional sentences refer to something in the past but continuing into the present; however, the past condition and the results are not real. For example,

If I had learned to ride sooner, I would be a top rodeo star by now.

Note that the past perfect verb is used in the if clause and the present conditional verb is used in the main clause.

Punctuating these conditional sentences is simple. Use a comma to separate the if clause from the main clause when the if clause comes first. Again, Trinka can help you in the punctuating the sentences correctly, within minutes!

Some Exceptions to the Rules

For example, in the following sentence, we use the simple future verb in the if clause:

If turmeric will ease my arthritis pain, I will take some every day.

Note that the action in the if clause hasn’t happened yet, but will happen after the action in the main clause is taken.

The use of were to in the if clause is another exception. This phrase is used to emphasize the importance of the result of something that might happen. For example:

If she were to fall on that arm again, she would have to have surgery.

The action in the main clause is emphasized by were to in the if clause.

Importance to Researchers

In your research, you are most likely going to either perform your own experiments or use the results of others’ experiments to conduct a meta-analysis. Whichever the case, you will need to report your findings and assessments . In doing so, there will be situations in which the results of your study or even future studies are based on certain conditions. Your conclusions are based on evidence, data, or theory. You might present your conclusions as likelihoods that something has already happened, is currently happening, or will happen at some point. This is where conditional sentence is a great help.

Writing conditional sentences might appear to be a difficult thing to do, but with practice and good understanding of the above mentioned rules, you can perfect it. Alternatively, you can check out Trinka ! Its robust AI facilitates you in integrating all the conventions and language requirements of academic writing. Along with, conditional sentences Trinka can also assist you in logic, syntax, technical spellings and much more!

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What is a scientific hypothesis?

It's the initial building block in the scientific method.

Hypothesis basics

What makes a hypothesis testable.

• Types of hypotheses
• Hypothesis versus theory

Additional resources

Bibliography.

A scientific hypothesis is a tentative, testable explanation for a phenomenon in the natural world. It's the initial building block in the scientific method . Many describe it as an "educated guess" based on prior knowledge and observation. While this is true, a hypothesis is more informed than a guess. While an "educated guess" suggests a random prediction based on a person's expertise, developing a hypothesis requires active observation and background research. 

The basic idea of a hypothesis is that there is no predetermined outcome. For a solution to be termed a scientific hypothesis, it has to be an idea that can be supported or refuted through carefully crafted experimentation or observation. This concept, called falsifiability and testability, was advanced in the mid-20th century by Austrian-British philosopher Karl Popper in his famous book "The Logic of Scientific Discovery" (Routledge, 1959).

A key function of a hypothesis is to derive predictions about the results of future experiments and then perform those experiments to see whether they support the predictions.

A hypothesis is usually written in the form of an if-then statement, which gives a possibility (if) and explains what may happen because of the possibility (then). The statement could also include "may," according to California State University, Bakersfield .

Here are some examples of hypothesis statements:

• If garlic repels fleas, then a dog that is given garlic every day will not get fleas.
• If sugar causes cavities, then people who eat a lot of candy may be more prone to cavities.
• If ultraviolet light can damage the eyes, then maybe this light can cause blindness.

A useful hypothesis should be testable and falsifiable. That means that it should be possible to prove it wrong. A theory that can't be proved wrong is nonscientific, according to Karl Popper's 1963 book " Conjectures and Refutations ."

An example of an untestable statement is, "Dogs are better than cats." That's because the definition of "better" is vague and subjective. However, an untestable statement can be reworded to make it testable. For example, the previous statement could be changed to this: "Owning a dog is associated with higher levels of physical fitness than owning a cat." With this statement, the researcher can take measures of physical fitness from dog and cat owners and compare the two.

Types of scientific hypotheses

In an experiment, researchers generally state their hypotheses in two ways. The null hypothesis predicts that there will be no relationship between the variables tested, or no difference between the experimental groups. The alternative hypothesis predicts the opposite: that there will be a difference between the experimental groups. This is usually the hypothesis scientists are most interested in, according to the University of Miami .

For example, a null hypothesis might state, "There will be no difference in the rate of muscle growth between people who take a protein supplement and people who don't." The alternative hypothesis would state, "There will be a difference in the rate of muscle growth between people who take a protein supplement and people who don't."

If the results of the experiment show a relationship between the variables, then the null hypothesis has been rejected in favor of the alternative hypothesis, according to the book " Research Methods in Psychology " (​​BCcampus, 2015). 

There are other ways to describe an alternative hypothesis. The alternative hypothesis above does not specify a direction of the effect, only that there will be a difference between the two groups. That type of prediction is called a two-tailed hypothesis. If a hypothesis specifies a certain direction — for example, that people who take a protein supplement will gain more muscle than people who don't — it is called a one-tailed hypothesis, according to William M. K. Trochim , a professor of Policy Analysis and Management at Cornell University.

Sometimes, errors take place during an experiment. These errors can happen in one of two ways. A type I error is when the null hypothesis is rejected when it is true. This is also known as a false positive. A type II error occurs when the null hypothesis is not rejected when it is false. This is also known as a false negative, according to the University of California, Berkeley . 

A hypothesis can be rejected or modified, but it can never be proved correct 100% of the time. For example, a scientist can form a hypothesis stating that if a certain type of tomato has a gene for red pigment, that type of tomato will be red. During research, the scientist then finds that each tomato of this type is red. Though the findings confirm the hypothesis, there may be a tomato of that type somewhere in the world that isn't red. Thus, the hypothesis is true, but it may not be true 100% of the time.

Scientific theory vs. scientific hypothesis

The best hypotheses are simple. They deal with a relatively narrow set of phenomena. But theories are broader; they generally combine multiple hypotheses into a general explanation for a wide range of phenomena, according to the University of California, Berkeley . For example, a hypothesis might state, "If animals adapt to suit their environments, then birds that live on islands with lots of seeds to eat will have differently shaped beaks than birds that live on islands with lots of insects to eat." After testing many hypotheses like these, Charles Darwin formulated an overarching theory: the theory of evolution by natural selection.

"Theories are the ways that we make sense of what we observe in the natural world," Tanner said. "Theories are structures of ideas that explain and interpret facts." 

• Read more about writing a hypothesis, from the American Medical Writers Association.
• Find out why a hypothesis isn't always necessary in science, from The American Biology Teacher.
• Learn about null and alternative hypotheses, from Prof. Essa on YouTube .

Encyclopedia Britannica. Scientific Hypothesis. Jan. 13, 2022. https://www.britannica.com/science/scientific-hypothesis

Karl Popper, "The Logic of Scientific Discovery," Routledge, 1959.

California State University, Bakersfield, "Formatting a testable hypothesis." https://www.csub.edu/~ddodenhoff/Bio100/Bio100sp04/formattingahypothesis.htm  

Karl Popper, "Conjectures and Refutations," Routledge, 1963.

Price, P., Jhangiani, R., & Chiang, I., "Research Methods of Psychology — 2nd Canadian Edition," BCcampus, 2015.‌

University of Miami, "The Scientific Method" http://www.bio.miami.edu/dana/161/evolution/161app1_scimethod.pdf  

William M.K. Trochim, "Research Methods Knowledge Base," https://conjointly.com/kb/hypotheses-explained/  

University of California, Berkeley, "Multiple Hypothesis Testing and False Discovery Rate" https://www.stat.berkeley.edu/~hhuang/STAT141/Lecture-FDR.pdf  

University of California, Berkeley, "Science at multiple levels" https://undsci.berkeley.edu/article/0_0_0/howscienceworks_19

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Sat / act prep online guides and tips, what is a hypothesis and how do i write one.

General Education

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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What Are Examples of a Hypothesis?

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A hypothesis is an explanation for a set of observations. Here are examples of a scientific hypothesis.

Although you could state a scientific hypothesis in various ways, most hypotheses are either "If, then" statements or forms of the null hypothesis . The null hypothesis is sometimes called the "no difference" hypothesis. The null hypothesis is good for experimentation because it's simple to disprove. If you disprove a null hypothesis, that is evidence for a relationship between the variables you are examining.

Examples of Null Hypotheses

• Hyperactivity is unrelated to eating sugar.
• All daisies have the same number of petals.
• The number of pets in a household is unrelated to the number of people living in it.
• A person's preference for a shirt is unrelated to its color.

Examples of If, Then Hypotheses

• If you get at least 6 hours of sleep, you will do better on tests than if you get less sleep.
• If you drop a ball, it will fall toward the ground.
• If you drink coffee before going to bed, then it will take longer to fall asleep.
• If you cover a wound with a bandage, then it will heal with less scarring.

Improving a Hypothesis to Make It Testable

You may wish to revise your first hypothesis in order to make it easier to design an experiment to test. For example, let's say you have a bad breakout the morning after eating a lot of greasy food. You may wonder if there is a correlation between eating greasy food and getting pimples. You propose the hypothesis:

Eating greasy food causes pimples.

Next, you need to design an experiment to test this hypothesis. Let's say you decide to eat greasy food every day for a week and record the effect on your face. Then, as a control, you'll avoid greasy food for the next week and see what happens. Now, this is not a good experiment because it does not take into account other factors such as hormone levels, stress, sun exposure, exercise, or any number of other variables that might conceivably affect your skin.

The problem is that you cannot assign cause to your effect . If you eat french fries for a week and suffer a breakout, can you definitely say it was the grease in the food that caused it? Maybe it was the salt. Maybe it was the potato. Maybe it was unrelated to diet. You can't prove your hypothesis. It's much easier to disprove a hypothesis.

So, let's restate the hypothesis to make it easier to evaluate the data:

Getting pimples is unaffected by eating greasy food.

So, if you eat fatty food every day for a week and suffer breakouts and then don't break out the week that you avoid greasy food, you can be pretty sure something is up. Can you disprove the hypothesis? Probably not, since it is so hard to assign cause and effect. However, you can make a strong case that there is some relationship between diet and acne.

If your skin stays clear for the entire test, you may decide to accept your hypothesis . Again, you didn't prove or disprove anything, which is fine

• Null Hypothesis Definition and Examples
• What Is a Hypothesis? (Science)
• What Are the Elements of a Good Hypothesis?
• Understanding Simple vs Controlled Experiments
• What Is a Testable Hypothesis?
• What 'Fail to Reject' Means in a Hypothesis Test
• Null Hypothesis Examples
• How To Design a Science Fair Experiment
• Scientific Method Vocabulary Terms
• Scientific Hypothesis Examples
• Six Steps of the Scientific Method
• An Example of a Hypothesis Test
• Definition of a Hypothesis
• Scientific Method Flow Chart
• Null Hypothesis and Alternative Hypothesis

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If-then statement

• Logical correct I
• Logical correct II

When we previously discussed inductive reasoning we based our reasoning on examples and on data from earlier events. If we instead use facts, rules and definitions then it's called deductive reasoning.

We will explain this by using an example.

If you get good grades then you will get into a good college.

The part after the "if": you get good grades - is called a hypotheses and the part after the "then" - you will get into a good college - is called a conclusion.

Hypotheses followed by a conclusion is called an If-then statement or a conditional statement.

This is noted as

$$p \to q$$

This is read - if p then q.

A conditional statement is false if hypothesis is true and the conclusion is false. The example above would be false if it said "if you get good grades then you will not get into a good college".

If we re-arrange a conditional statement or change parts of it then we have what is called a related conditional.

Our conditional statement is: if a population consists of 50% men then 50% of the population must be women.

If we exchange the position of the hypothesis and the conclusion we get a converse statemen t: if a population consists of 50% women then 50% of the population must be men.

$$q\rightarrow p$$

If both statements are true or if both statements are false then the converse is true. A conditional and its converse do not mean the same thing

If we negate both the hypothesis and the conclusion we get a inverse statemen t: if a population do not consist of 50% men then the population do not consist of 50% women.

$$\sim p\rightarrow \: \sim q$$

The inverse is not true juest because the conditional is true. The inverse always has the same truth value as the converse.

We could also negate a converse statement, this is called a contrapositive statemen t:  if a population do not consist of 50% women then the population do not consist of 50% men.

$$\sim q\rightarrow \: \sim p$$

The contrapositive does always have the same truth value as the conditional. If the conditional is true then the contrapositive is true.

A pattern of reaoning is a true assumption if it always lead to a true conclusion. The most common patterns of reasoning are detachment and syllogism.

If we turn of the water in the shower, then the water will stop pouring.

If we call the first part p and the second part q then we know that p results in q. This means that if p is true then q will also be true. This is called the law of detachment and is noted:

$$\left [ (p \to q)\wedge p \right ] \to q$$

The law of syllogism tells us that if p → q and q → r then p → r is also true.

This is noted:

$$\left [ (p \to q)\wedge (q \to r ) \right ] \to (p \to r)$$

If the following statements are true:

If we turn of the water (p), then the water will stop pouring (q). If the water stops pouring (q) then we don't get wet any more (r).

Then the law of syllogism tells us that if we turn of the water (p) then we don't get wet (r) must be true.

Video lesson

Write a converse, inverse and contrapositive to the conditional

"If you eat a whole pint of ice cream, then you won't be hungry"

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Hypothesis Maker Online

Looking for a hypothesis maker? This online tool for students will help you formulate a beautiful hypothesis quickly, efficiently, and for free.

Are you looking for an effective hypothesis maker online? Worry no more; try our online tool for students and formulate your hypothesis within no time.

• 🔎 How to Use the Tool?
• ⚗️ What Is a Hypothesis in Science?

👍 What Does a Good Hypothesis Mean?

• 🧭 Steps to Making a Good Hypothesis

🔗 References

📄 hypothesis maker: how to use it.

Our hypothesis maker is a simple and efficient tool you can access online for free.

If you want to create a research hypothesis quickly, you should fill out the research details in the given fields on the hypothesis generator.

Below are the fields you should complete to generate your hypothesis:

• Who or what is your research based on? For instance, the subject can be research group 1.
• What does the subject (research group 1) do?
• What does the subject affect? - This shows the predicted outcome, which is the object.
• Who or what will be compared with research group 1? (research group 2).

Once you fill the in the fields, you can click the ‘Make a hypothesis’ tab and get your results.

⚗️ What Is a Hypothesis in the Scientific Method?

A hypothesis is a statement describing an expectation or prediction of your research through observation.

It is similar to academic speculation and reasoning that discloses the outcome of your scientific test . An effective hypothesis, therefore, should be crafted carefully and with precision.

A good hypothesis should have dependent and independent variables . These variables are the elements you will test in your research method – it can be a concept, an event, or an object as long as it is observable.

You can observe the dependent variables while the independent variables keep changing during the experiment.

In a nutshell, a hypothesis directs and organizes the research methods you will use, forming a large section of research paper writing.

Hypothesis vs. Theory

A hypothesis is a realistic expectation that researchers make before any investigation. It is formulated and tested to prove whether the statement is true. A theory, on the other hand, is a factual principle supported by evidence. Thus, a theory is more fact-backed compared to a hypothesis.

Another difference is that a hypothesis is presented as a single statement , while a theory can be an assortment of things . Hypotheses are based on future possibilities toward a specific projection, but the results are uncertain. Theories are verified with undisputable results because of proper substantiation.

When it comes to data, a hypothesis relies on limited information , while a theory is established on an extensive data set tested on various conditions.

You should observe the stated assumption to prove its accuracy.

Since hypotheses have observable variables, their outcome is usually based on a specific occurrence. Conversely, theories are grounded on a general principle involving multiple experiments and research tests.

This general principle can apply to many specific cases.

The primary purpose of formulating a hypothesis is to present a tentative prediction for researchers to explore further through tests and observations. Theories, in their turn, aim to explain plausible occurrences in the form of a scientific study.

It would help to rely on several criteria to establish a good hypothesis. Below are the parameters you should use to analyze the quality of your hypothesis.

🧭 6 Steps to Making a Good Hypothesis

Writing a hypothesis becomes way simpler if you follow a tried-and-tested algorithm. Let’s explore how you can formulate a good hypothesis in a few steps:

Step #1: Ask Questions

The first step in hypothesis creation is asking real questions about the surrounding reality.

Why do things happen as they do? What are the causes of some occurrences?

Your curiosity will trigger great questions that you can use to formulate a stellar hypothesis. So, ensure you pick a research topic of interest to scrutinize the world’s phenomena, processes, and events.

Step #2: Do Initial Research

Carry out preliminary research and gather essential background information about your topic of choice.

The extent of the information you collect will depend on what you want to prove.

Your initial research can be complete with a few academic books or a simple Internet search for quick answers with relevant statistics.

Still, keep in mind that in this phase, it is too early to prove or disapprove of your hypothesis.

Step #3: Identify Your Variables

Now that you have a basic understanding of the topic, choose the dependent and independent variables.

Take note that independent variables are the ones you can’t control, so understand the limitations of your test before settling on a final hypothesis.

Step #4: Formulate Your Hypothesis

You can write your hypothesis as an ‘if – then’ expression . Presenting any hypothesis in this format is reliable since it describes the cause-and-effect you want to test.

For instance: If I study every day, then I will get good grades.

Step #5: Gather Relevant Data

Once you have identified your variables and formulated the hypothesis, you can start the experiment. Remember, the conclusion you make will be a proof or rebuttal of your initial assumption.

So, gather relevant information, whether for a simple or statistical hypothesis, because you need to back your statement.

Step #6: Record Your Findings

Finally, write down your conclusions in a research paper .

Outline in detail whether the test has proved or disproved your hypothesis.

Edit and proofread your work, using a plagiarism checker to ensure the authenticity of your text.

We hope that the above tips will be useful for you. Note that if you need to conduct business analysis, you can use the free templates we’ve prepared: SWOT , PESTLE , VRIO , SOAR , and Porter’s 5 Forces .

❓ Hypothesis Formulator FAQ

Updated: Oct 25th, 2023

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Use our hypothesis maker whenever you need to formulate a hypothesis for your study. We offer a very simple tool where you just need to provide basic info about your variables, subjects, and predicted outcomes. The rest is on us. Get a perfect hypothesis in no time!