components of hypothesis statement

What Are the Elements of a Good Hypothesis?

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A hypothesis is an educated guess or prediction of what will happen. In science, a hypothesis proposes a relationship between factors called variables. A good hypothesis relates an independent variable and a dependent variable. The effect on the dependent variable depends on or is determined by what happens when you change the independent variable . While you could consider any prediction of an outcome to be a type of hypothesis, a good hypothesis is one you can test using the scientific method. In other words, you want to propose a hypothesis to use as the basis for an experiment.

Cause and Effect or 'If, Then' Relationships

A good experimental hypothesis can be written as an if, then statement to establish cause and effect on the variables. If you make a change to the independent variable, then the dependent variable will respond. Here's an example of a hypothesis:

If you increase the duration of light, (then) corn plants will grow more each day.

The hypothesis establishes two variables, length of light exposure, and the rate of plant growth. An experiment could be designed to test whether the rate of growth depends on the duration of light. The duration of light is the independent variable, which you can control in an experiment . The rate of plant growth is the dependent variable, which you can measure and record as data in an experiment.

Key Points of Hypothesis

When you have an idea for a hypothesis, it may help to write it out in several different ways. Review your choices and select a hypothesis that accurately describes what you are testing.

• Does the hypothesis relate an independent and dependent variable? Can you identify the variables?
• Can you test the hypothesis? In other words, could you design an experiment that would allow you to establish or disprove a relationship between the variables?
• Would your experiment be safe and ethical?
• Is there a simpler or more precise way to state the hypothesis? If so, rewrite it.

What If the Hypothesis Is Incorrect?

It's not wrong or bad if the hypothesis is not supported or is incorrect. Actually, this outcome may tell you more about a relationship between the variables than if the hypothesis is supported. You may intentionally write your hypothesis as a null hypothesis or no-difference hypothesis to establish a relationship between the variables.

For example, the hypothesis:

The rate of corn plant growth does not depend on the duration of light.

This can be tested by exposing corn plants to different length "days" and measuring the rate of plant growth. A statistical test can be applied to measure how well the data support the hypothesis. If the hypothesis is not supported, then you have evidence of a relationship between the variables. It's easier to establish cause and effect by testing whether "no effect" is found. Alternatively, if the null hypothesis is supported, then you have shown the variables are not related. Either way, your experiment is a success.

Need more examples of how to write a hypothesis ? Here you go:

• If you turn out all the lights, you will fall asleep faster. (Think: How would you test it?)
• If you drop different objects, they will fall at the same rate.
• If you eat only fast food, then you will gain weight.
• If you use cruise control, then your car will get better gas mileage.
• If you apply a top coat, then your manicure will last longer.
• If you turn the lights on and off rapidly, then the bulb will burn out faster.
• Null Hypothesis Examples
• Examples of Independent and Dependent Variables
• Difference Between Independent and Dependent Variables
• Null Hypothesis Definition and Examples
• Six Steps of the Scientific Method
• What Is a Hypothesis? (Science)
• Understanding Simple vs Controlled Experiments
• The Role of a Controlled Variable in an Experiment
• How To Design a Science Fair Experiment
• Independent Variable Definition and Examples
• Dependent Variable Definition and Examples
• Scientific Method Flow Chart
• Scientific Method Vocabulary Terms
• Definition of a Hypothesis
• Scientific Variable

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• How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

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

Table of contents

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

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

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

Variables in hypotheses

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

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

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Step 1: ask a question.

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

Step 2: Do some preliminary research

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

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

Step 3: Formulate your hypothesis

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

Step 4: Refine your hypothesis

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

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

Step 5: Phrase your hypothesis in three ways

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

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

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

Step 6. Write a null hypothesis

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

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

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

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

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

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How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

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

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

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

Hypothesis Types

Hypotheses examples.

• Collecting Data

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

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

At a Glance

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

The Hypothesis in the Scientific Method

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

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

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

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

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

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

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

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

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

Elements of a Good Hypothesis

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

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

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

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

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

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

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

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

The Importance of Operational Definitions

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

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

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

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

Replicability

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

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

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

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

Hypothesis Checklist

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

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

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

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

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

A few examples of simple hypotheses:

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

Examples of a complex hypothesis include:

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

Examples of a null hypothesis include:

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

Examples of an alternative hypothesis:

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

Collecting Data on Your Hypothesis

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

Descriptive Research Methods

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

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

Experimental Research Methods

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

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

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

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

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

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

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

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

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

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

How to Write a Hypothesis: A Step-by-Step Guide

Introduction

An overview of the research hypothesis, different types of hypotheses, variables in a hypothesis, how to formulate an effective research hypothesis, designing a study around your hypothesis.

The scientific method can derive and test predictions as hypotheses. Empirical research can then provide support (or lack thereof) for the hypotheses. Even failure to find support for a hypothesis still represents a valuable contribution to scientific knowledge. Let's look more closely at the idea of the hypothesis and the role it plays in research.

As much as the term exists in everyday language, there is a detailed development that informs the word "hypothesis" when applied to research. A good research hypothesis is informed by prior research and guides research design and data analysis , so it is important to understand how a hypothesis is defined and understood by researchers.

What is the simple definition of a hypothesis?

A hypothesis is a testable prediction about an outcome between two or more variables . It functions as a navigational tool in the research process, directing what you aim to predict and how.

What is the hypothesis for in research?

In research, a hypothesis serves as the cornerstone for your empirical study. It not only lays out what you aim to investigate but also provides a structured approach for your data collection and analysis.

Essentially, it bridges the gap between the theoretical and the empirical, guiding your investigation throughout its course.

What is an example of a hypothesis?

If you are studying the relationship between physical exercise and mental health, a suitable hypothesis could be: "Regular physical exercise leads to improved mental well-being among adults."

This statement constitutes a specific and testable hypothesis that directly relates to the variables you are investigating.

What makes a good hypothesis?

A good hypothesis possesses several key characteristics. Firstly, it must be testable, allowing you to analyze data through empirical means, such as observation or experimentation, to assess if there is significant support for the hypothesis. Secondly, a hypothesis should be specific and unambiguous, giving a clear understanding of the expected relationship between variables. Lastly, it should be grounded in existing research or theoretical frameworks , ensuring its relevance and applicability.

Understanding the types of hypotheses can greatly enhance how you construct and work with hypotheses. While all hypotheses serve the essential function of guiding your study, there are varying purposes among the types of hypotheses. In addition, all hypotheses stand in contrast to the null hypothesis, or the assumption that there is no significant relationship between the variables .

Here, we explore various kinds of hypotheses to provide you with the tools needed to craft effective hypotheses for your specific research needs. Bear in mind that many of these hypothesis types may overlap with one another, and the specific type that is typically used will likely depend on the area of research and methodology you are following.

Null hypothesis

The null hypothesis is a statement that there is no effect or relationship between the variables being studied. In statistical terms, it serves as the default assumption that any observed differences are due to random chance.

For example, if you're studying the effect of a drug on blood pressure, the null hypothesis might state that the drug has no effect.

Alternative hypothesis

Contrary to the null hypothesis, the alternative hypothesis suggests that there is a significant relationship or effect between variables.

Using the drug example, the alternative hypothesis would posit that the drug does indeed affect blood pressure. This is what researchers aim to prove.

Simple hypothesis

A simple hypothesis makes a prediction about the relationship between two variables, and only two variables.

For example, "Increased study time results in better exam scores." Here, "study time" and "exam scores" are the only variables involved.

Complex hypothesis

A complex hypothesis, as the name suggests, involves more than two variables. For instance, "Increased study time and access to resources result in better exam scores." Here, "study time," "access to resources," and "exam scores" are all variables.

This hypothesis refers to multiple potential mediating variables. Other hypotheses could also include predictions about variables that moderate the relationship between the independent variable and dependent variable .

Directional hypothesis

A directional hypothesis specifies the direction of the expected relationship between variables. For example, "Eating more fruits and vegetables leads to a decrease in heart disease."

Here, the direction of heart disease is explicitly predicted to decrease, due to effects from eating more fruits and vegetables. All hypotheses typically specify the expected direction of the relationship between the independent and dependent variable, such that researchers can test if this prediction holds in their data analysis .

Statistical hypothesis

A statistical hypothesis is one that is testable through statistical methods, providing a numerical value that can be analyzed. This is commonly seen in quantitative research .

For example, "There is a statistically significant difference in test scores between students who study for one hour and those who study for two."

Empirical hypothesis

An empirical hypothesis is derived from observations and is tested through empirical methods, often through experimentation or survey data . Empirical hypotheses may also be assessed with statistical analyses.

For example, "Regular exercise is correlated with a lower incidence of depression," could be tested through surveys that measure exercise frequency and depression levels.

Causal hypothesis

A causal hypothesis proposes that one variable causes a change in another. This type of hypothesis is often tested through controlled experiments.

For example, "Smoking causes lung cancer," assumes a direct causal relationship.

Associative hypothesis

Unlike causal hypotheses, associative hypotheses suggest a relationship between variables but do not imply causation.

For instance, "People who smoke are more likely to get lung cancer," notes an association but doesn't claim that smoking causes lung cancer directly.

Relational hypothesis

A relational hypothesis explores the relationship between two or more variables but doesn't specify the nature of the relationship.

For example, "There is a relationship between diet and heart health," leaves the nature of the relationship (causal, associative, etc.) open to interpretation.

Logical hypothesis

A logical hypothesis is based on sound reasoning and logical principles. It's often used in theoretical research to explore abstract concepts, rather than being based on empirical data.

For example, "If all men are mortal and Socrates is a man, then Socrates is mortal," employs logical reasoning to make its point.

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In any research hypothesis, variables play a critical role. These are the elements or factors that the researcher manipulates, controls, or measures. Understanding variables is essential for crafting a clear, testable hypothesis and for the stages of research that follow, such as data collection and analysis.

In the realm of hypotheses, there are generally two types of variables to consider: independent and dependent. Independent variables are what you, as the researcher, manipulate or change in your study. It's considered the cause in the relationship you're investigating. For instance, in a study examining the impact of sleep duration on academic performance, the independent variable would be the amount of sleep participants get.

Conversely, the dependent variable is the outcome you measure to gauge the effect of your manipulation. It's the effect in the cause-and-effect relationship. The dependent variable thus refers to the main outcome of interest in your study. In the same sleep study example, the academic performance, perhaps measured by exam scores or GPA, would be the dependent variable.

Beyond these two primary types, you might also encounter control variables. These are variables that could potentially influence the outcome and are therefore kept constant to isolate the relationship between the independent and dependent variables . For example, in the sleep and academic performance study, control variables could include age, diet, or even the subject of study.

By clearly identifying and understanding the roles of these variables in your hypothesis, you set the stage for a methodologically sound research project. It helps you develop focused research questions, design appropriate experiments or observations, and carry out meaningful data analysis . It's a step that lays the groundwork for the success of your entire study.

Crafting a strong, testable hypothesis is crucial for the success of any research project. It sets the stage for everything from your study design to data collection and analysis . Below are some key considerations to keep in mind when formulating your hypothesis:

• Be specific : A vague hypothesis can lead to ambiguous results and interpretations . Clearly define your variables and the expected relationship between them.
• Ensure testability : A good hypothesis should be testable through empirical means, whether by observation , experimentation, or other forms of data analysis.
• Ground in literature : Before creating your hypothesis, consult existing research and theories. This not only helps you identify gaps in current knowledge but also gives you valuable context and credibility for crafting your hypothesis.
• Use simple language : While your hypothesis should be conceptually sound, it doesn't have to be complicated. Aim for clarity and simplicity in your wording.
• State direction, if applicable : If your hypothesis involves a directional outcome (e.g., "increase" or "decrease"), make sure to specify this. You also need to think about how you will measure whether or not the outcome moved in the direction you predicted.
• Keep it focused : One of the common pitfalls in hypothesis formulation is trying to answer too many questions at once. Keep your hypothesis focused on a specific issue or relationship.
• Account for control variables : Identify any variables that could potentially impact the outcome and consider how you will control for them in your study.
• Be ethical : Make sure your hypothesis and the methods for testing it comply with ethical standards , particularly if your research involves human or animal subjects.

Designing your study involves multiple key phases that help ensure the rigor and validity of your research. Here we discuss these crucial components in more detail.

Literature review

Starting with a comprehensive literature review is essential. This step allows you to understand the existing body of knowledge related to your hypothesis and helps you identify gaps that your research could fill. Your research should aim to contribute some novel understanding to existing literature, and your hypotheses can reflect this. A literature review also provides valuable insights into how similar research projects were executed, thereby helping you fine-tune your own approach.

Research methods

Choosing the right research methods is critical. Whether it's a survey, an experiment, or observational study, the methodology should be the most appropriate for testing your hypothesis. Your choice of methods will also depend on whether your research is quantitative, qualitative, or mixed-methods. Make sure the chosen methods align well with the variables you are studying and the type of data you need.

Preliminary research

Before diving into a full-scale study, it’s often beneficial to conduct preliminary research or a pilot study . This allows you to test your research methods on a smaller scale, refine your tools, and identify any potential issues. For instance, a pilot survey can help you determine if your questions are clear and if the survey effectively captures the data you need. This step can save you both time and resources in the long run.

Data analysis

Finally, planning your data analysis in advance is crucial for a successful study. Decide which statistical or analytical tools are most suited for your data type and research questions . For quantitative research, you might opt for t-tests, ANOVA, or regression analyses. For qualitative research , thematic analysis or grounded theory may be more appropriate. This phase is integral for interpreting your results and drawing meaningful conclusions in relation to your research question.

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

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

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

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

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

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

Null Hypothesis

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

Alternative Hypothesis

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

Directional Hypothesis

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

Non-directional Hypothesis

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

Statistical Hypothesis

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

Composite Hypothesis

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

Empirical Hypothesis

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

Simple Hypothesis

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

Complex Hypothesis

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

Applications of Hypothesis

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

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

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

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

Conduct a Literature Review

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

Determine the Variables

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

Formulate the Hypothesis

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

Write the Null Hypothesis

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

Refine the Hypothesis

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

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

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

Purpose of Hypothesis

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

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

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

When to use Hypothesis

Here are some common situations in which hypotheses are used:

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

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

• Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
• Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
• Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
• Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
• Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
• Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
• Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

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

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

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

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Muhammad Hassan

Researcher, Academic Writer, Web developer

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Research Hypothesis In Psychology: Types, & Examples

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

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On This Page:

A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

• A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
• It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
• A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
• Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
• For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
• Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

• Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

• Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
• However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

• Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
• Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
• Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
• Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
• Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

• The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
• The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

• Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
• Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
• Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
• Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
• Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
• Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
• Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
• Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

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Research Paper Guide

How To Write A Hypothesis

Last updated on: Feb 8, 2023

How to Write a Hypothesis - A Step-by-Step Guide

By: Nathan D.

Reviewed By: Rylee W.

Published on: Jul 16, 2019

A hypothesis is generally a statement that a researcher has to test through scientific methods subjectively. Unlike a thesis statement, a hypothesis does not require a researcher to prove it right in any circumstance.

It is a statement that is developed prior to research, experiment, or data collection. In simple words, it is a proposed explanation for any idea, study, or phenomenon.

For  research paper writing , thesis, case studies, or dissertation, you will have to write a hypothesis first. Continue reading the article to learn how to write a good hypothesis effectively.

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What is a Hypothesis?

A hypothesis is a proposed or supposition explanation that a researcher forms based on limited reference about a specific phenomenon. This statement is further investigated to analyze its validity and significance.

A hypothesis statement is an initial point from where an investigation begins. Moreover, it translates the major research question into a prediction.

In professional terms, a hypothesis is an idea whose merit requires evaluation and interpretation. For this purpose, the researcher needs to define the specifics of the hypothesis in operational terms.

It requires a researcher to study in detail whether to approve it or disapprove of it. In this process, the hypothesis either becomes a part of the theory, or a theory itself.

Functions of Hypothesis

Learning the correct writing procedure is not enough if you are not aware of the basic functions that your hypothesis performs. To make your hypothesis stand out, understand the below-given functions

• First and foremost, a hypothesis contributes to making your research, observation, and experiment possible
• This helps in starting the basic investigation about the subject
• It verifies the observation
• It provides the right direction to your inquiries

Components of a Hypothesis

Like other sentences and statements, a hypothesis has major components that play a significant role in making it impactful. It is essential to learn about these parts when you are researching academics.

The following are the different components of the hypothesis:

How to Write a Hypothesis?

Just like every other formal or academic task, writing a hypothesis includes a process. Although there are no set of rules to follow while developing a hypothesis.

However, it is recommended that you follow some steps to ensure a quality statement. These steps will make it easier for you to formulate a strong hypothesis to provide a great direction for your research.

Following is a step-by-step- procedure to write a hypothesis.

1. Develop a Question

When writing a hypothesis, the first thing is to develop a research question that you want to answer in your research. The question that you will formulate should be specific, focused, and researchable within the constraints of your assignment.

2. Conduct a Basic Research

The initial answer to your research question will be spontaneous and based on pre-existing knowledge about the subject. Search for theories and information to form a basic assumption that you will investigate further.

At this stage of creating a hypothesis, a researcher can develop a conceptual framework to identify the variables and their relationship.

3. Develop a Rough Hypothesis

Formulate a rough statement on the available knowledge to provide an idea about what to expect from your research. Brainstorm the answer for this raw question and present it into a clear and concise sentence.

4. Refine the Statement Made

Now that you have a rough statement in hand, it is time to refine and make it a testable hypothesis. There are several ways to shape your hypothesis, but you can arrange your statement keeping in view the parts.

Make sure that your refined statement must contain the following things:

• Relevant variables
• The group being studied
• The predicted result of the research or experiment

5. Phrasing the Hypothesis

The hypothesis can be phrased in three ways. Depending on the requirement of the research and the field type, select a phrasing pattern.

• To phrase the hypothesis, identify the variables, use a simple prediction pattern of “if...then” form. Present the independent variable first and then the dependent variable in your hypothesis statement.
• When developing a hypothesis for academic research, you can choose correlation and effect phrasing. In this way, you directly present the predicted relationship between the two variables.
• If the statement compares the two groups, the paraphrasing of the hypothesis can be done by stating the expected difference.

6. Write a Null Hypothesis

If your research is based on statistical testing of the hypothesis, you will have to present a null hypothesis. The null hypothesis states that there is no relationship or association between the two variables.

How to Write a Null Hypothesis?

There are two types of hypotheses, the null hypothesis, and the alternative hypothesis. A null hypothesis states that there is no difference between certain characteristics of a population while an alternative hypothesis states otherwise.

So, how does a null hypothesis work? Below is a four-step process to come up with a null hypothesis.

• The analyst will come up with two hypotheses and test them.
• Next, he formulates an analysis plan and decides the ways through which those hypotheses would be analyzed.
• The sample data and hypotheses are evaluated and analyzed.
• The final step is to analyze the acquired results and decide whether the null hypothesis is correct or not.

Other than null analysis, alternative hypotheses are also used. An alternative hypothesis is opposite to the null hypothesis and they are independent of each other.

What kind of Sources should I Add to my Hypothesis

It is important to look for credible and relevant sources of information while writing a hypothesis for your  research proposal . A researcher has to consult these sources to check the reliability and validity of your primary idea.

In case you are wondering what sources will work best for your hypothesis, check out the following:

• Find relevant phenomena that have some resemblance to yours
• Evaluate the studies and observations from the past
• Analyze what the current time has to say about the idea
• Search the competitor’s ideas and opinions
• Analyze scientific theories
• Dig deeper into the patterns that influence people and their thinking

Types of Hypothesis

Depending on the field and  research methods  to collect data, hypotheses can have different types. When writing a research paper, it is essential to know all the types well to form a strong and relevant hypothesis.

Following are the six main types of hypothesis:

• Simple Hypothesis  - A simple hypothesis is a statement that shows a relationship between two variables; an independent and dependent variable. For example, doing exercise can help you lose weight faster. Here doing exercise is an independent variable while losing weight is dependent.
• Complex Hypothesis  - A complex hypothesis presents a relationship between two or more dependent and independent variables. For example, exercising and eating lots of vegetables can reduce weight and other fatal diseases such as heart disease.
• Directional Hypothesis  - A directional hypothesis is a statement that presents the researcher’s commitment to a particular result. Moreover, the relationship between different variables also predicts its nature. For example, people who are sleep-deprived for 24 hours will have more cold symptoms than those who oversleep.
• Non-Directional Hypothesis  - A non-directional hypothesis is used when there is no theory involved. It shows an existing relationship between two variables without highlighting the exact relationship’s nature.
• Null Hypothesis  - A null hypothesis states that there is no relationship between the two variables. Similarly, it also contended that there is not enough information to state the scientific hypothesis. The ‘H0’ symbol denotes this hypothesis.
• Alternative Hypothesis  - It is a statement that the research forms when he disapproves the null hypothesis. As the name suggests, it is an alternative statement to your null hypothesis highlighting the relationship between the variables. It is denoted by ‘H1’.
• Associative and Causal Hypothesis  - In an associative hypothesis, a change in one variable results in a difference in the other variable. On the other hand, the causal hypothesis presents a cause and effect interaction between the two variables.

Characteristics of a Good Hypothesis

Professional writers believe that a hypothesis has certain features that help it become stronger and more effective. These characteristics include:

• To make the hypothesis credible, it should be clear and precise
• If you have chosen a hypothesis type that will state the relationship between the two variables, it should be obvious
• A strong hypothesis is specific and has clear scope for conducting more studies and tests
• The explanation of the hypothesis must be simple. Keep in mind that the simplicity of the hypothesis has nothing to do with its significance

Only a strong hypothesis will motivate the readers to read the entire paper. So make sure that you carefully develop a hypothesis for your research.

Hypothesis Examples

If you are writing a paper for the first time, it is suggested by professionals to go through a few examples. It will help you understand the pattern in which you should be working.

Below-given are examples of how hypotheses are developed for different research experiments.

HOW TO WRITE A HYPOTHESIS FOR RESEARCH PAPER

HOW TO WRITE A HYPOTHESIS FOR SCIENTIFIC RESEARCH

Going through these examples will help you understand better which course of action should be chosen for your research. If it is still difficult for you to look for sources and write a compelling hypothesis, get help from professionals.

5StarEssays.com is a professional ‘ write my essay for me? ’ service that provides different academic writing services. Whether you are looking for an expert to write a compelling essay or any form of paper, we have your back.

Our experts draft all your assignments carefully, ensuring that each part is well-written and structured. Get your assignment today by simply placing your order at the most affordable price.

Frequently Asked Questions

How do you turn a question into a hypothesis.

You can change and transform a question into a hypothesis by changing it into a statement.

Is a hypothesis a prediction?

No, a hypothesis is not a prediction but rather a possibility. The researcher ‘hopes’ to obtain a certain kind of result through the experimentation. This possibility or expected results are the hypothesis.

Can a hypothesis be a question?

No, a hypothesis is and should be a statement and not a question.

Do all research papers have a hypothesis?

No, some research papers are based on exploratory research, which is used to develop the hypothesis. So, such a research paper does not need a hypothesis.

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Nathan completed his Ph.D. in journalism and has been writing articles for well-respected publications for many years now. His work is carefully researched and insightful, showing a true passion for the written word. Nathan's clients appreciate his expertise, deep understanding of the process, and ability to communicate difficult concepts clearly.

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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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How to write an effective hypothesis

Hypothesis validation is the bread and butter of product discovery. Understanding what should be prioritized and why is the most important task of a product manager. It doesn’t matter how well you validate your findings if you’re trying to answer the wrong question.

A question is as good as the answer it can provide. If your hypothesis is well written, but you can’t read its conclusion, it’s a bad hypothesis. Alternatively, if your hypothesis has embedded bias and answers itself, it’s also not going to help you.

There are several different tools available to build hypotheses, and it would be exhaustive to list them all. Apart from being superficial, focusing on the frameworks alone shifts the attention away from the hypothesis itself.

In this article, you will learn what a hypothesis is, the fundamental aspects of a good hypothesis, and what you should expect to get out of one.

The 4 product risks

Mitigating the four product risks is the reason why product managers exist in the first place and it’s where good hypothesis crafting starts.

The four product risks are assessments of everything that could go wrong with your delivery. Our natural thought process is to focus on the happy path at the expense of unknown traps. The risks are a constant reminder that knowing why something won’t work is probably more important than knowing why something might work.

These are the fundamental questions that should fuel your hypothesis creation:

Is it viable for the business?

Is it relevant for the user, can we build it, is it ethical to deliver.

Is this hypothesis the best one to validate now? Is this the most cost-effective initiative we can take? Will this answer help us achieve our goals? How much money can we make from it?

Has the user manifested interest in this solution? Will they be able to use it? Does it solve our users’ challenges? Is it aesthetically pleasing? Is it vital for the user, or just a luxury?

Do we have the resources and know-how to deliver it? Can we scale this solution? How much will it cost? Will it depreciate fast? Is it the best cost-effective solution? Will it deliver on what the user needs?

Is this solution safe both for the user and for the business? Is it inclusive enough? Is there a risk of public opinion whiplash? Is our solution enabling wrongdoers? Are we jeopardizing some to privilege others?

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There is an infinite amount of questions that can surface from these risks, and most of those will be context dependent. Your industry, company, marketplace, team composition, and even the type of product you handle will impose different questions, but the risks remain the same.

How to decide whether your hypothesis is worthy of validation

Assuming you came up with a hefty batch of risks to validate, you must now address them. To address a risk, you could do one of three things: collect concrete evidence that you can mitigate that risk, infer possible ways you can mitigate a risk and, finally, deep dive into that risk because you’re not sure about its repercussions.

This three way road can be illustrated by a CSD matrix :

Certainties

Suppositions.

Everything you’re sure can help you to mitigate whatever risk. An example would be, on the risk “how to build it,” assessing if your engineering team is capable of integrating with a certain API. If your team has made it a thousand times in the past, it’s not something worth validating. You can assume it is true and mark this particular risk as solved.

To put it simply, a supposition is something that you think you know, but you’re not sure. This is the most fertile ground to explore hypotheses, since this is the precise type of answer that needs validation. The most common usage of supposition is addressing the “is it relevant for the user” risk. You presume that clients will enjoy a new feature, but before you talk to them, you can’t say you are sure.

Doubts are different from suppositions because they have no answer whatsoever. A doubt is an open question about a risk which you have no clue on how to solve. A product manager that tries to mitigate the “is it ethical to deliver” risk from an industry that they have absolute no familiarity with is poised to generate a lot of doubts, but no suppositions or certainties. Doubts are not good hypothesis sources, since you have no idea on how to validate it.

A hypothesis worth validating comes from a place of uncertainty, not confidence or doubt. If you are sure about a risk mitigation, coming up with a hypothesis to validate it is just a waste of time and resources. Alternatively, trying to come up with a risk assessment for a problem you are clueless about will probably generate hypotheses disconnected with the problem itself.

That said, it’s important to make it clear that suppositions are different from hypotheses. A supposition is merely a mental exercise, creativity executed. A hypothesis is a measurable, cartesian instrument to transform suppositions into certainties, therefore making sure you can mitigate a risk.

How to craft a hypothesis

A good hypothesis comes from a supposed solution to a specific product risk. That alone is good enough to build half of a good hypothesis, but you also need to have measurable confidence.

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You’ll rarely transform a supposition into a certainty without an objective. Returning to the API example we gave when talking about certainties, you know the “can we build it” risk doesn’t need validation because your team has made tens of API integrations before. The “tens” is the quantifiable, measurable indication that gives you the confidence to be sure about mitigating a risk.

What you need from your hypothesis is exactly this quantifiable evidence, the number or hard fact able to give you enough confidence to treat your supposition as a certainty. To achieve that goal, you must come up with a target when creating the hypothesis. A hypothesis without a target can’t be validated, and therefore it’s useless.

Imagine you’re the product manager for an ecommerce app. Your users are predominantly mobile users, and your objective is to increase sales conversions. After some research, you came across the one click check-out experience, made famous by Amazon, but broadly used by ecommerces everywhere.

You know you can build it, but it’s a huge endeavor for your team. You best make sure your bet on one click check-out will work out, otherwise you’ll waste a lot of time and resources on something that won’t be able to influence the sales conversion KPI.

You identify your first risk then: is it valuable to the business?

Literature is abundant on the topic, so you are almost sure that it will bear results, but you’re not sure enough. You only can suppose that implementing the one click functionality will increase sales conversion.

During case study and data exploration, you have reasons to believe that a 30 percent increase of sales conversion is a reasonable target to be achieved. To make sure one click check-out is valuable to the business then, you would have a hypothesis such as this:

We believe that if we implement a one-click checkout on our ecommerce, we can grow our sales conversion by 30 percent

This hypothesis can be played with in all sorts of ways. If you’re trying to improve user-experience, for example, you could make it look something like this:

We believe that if we implement a one-click checkout on our ecommerce, we can reduce the time to conversion by 10 percent

You can also validate different solutions having the same criteria, building an opportunity tree to explore a multitude of hypothesis to find the better one:

We believe that if we implement a user review section on the listing page, we can grow our sales conversion by 30 percent

Sometimes you’re clueless about impact, or maybe any win is a good enough win. In that case, your criteria of validation can be a fact rather than a metric:

We believe that if we implement a one-click checkout on our ecommerce, we can reduce the time to conversion

As long as you are sure of the risk you’re mitigating, the supposition you want to transform into a certainty, and the criteria you’ll use to make that decision, you don’t need to worry so much about “right” or “wrong” when it comes to hypothesis formatting.

That’s why I avoided following up frameworks on this article. You can apply a neat hypothesis design to your product thinking, but if you’re not sure why you’re doing it, you’ll extract nothing out of it.

What comes after a good hypothesis?

The final piece of this puzzle comes after the hypothesis crafting. A hypothesis is only as good as the validation it provides, and that means you have to test it.

If we were to test the first hypothesis we crafted, “we believe that if we implement a one-click checkout on our ecommerce, we can grow our sales conversion by 30 percent,” you could come up with a testing roadmap to build up evidence that would eventually confirm or deny your hypothesis. Some examples of tests are:

A/B testing — Launch a quick and dirty one-click checkout MVP for a controlled group of users and compare their sales conversion rates against a control group. This will provide direct evidence on the effect of the feature on sales conversions

Customer support feedback — Track any inquiries or complaints related to the checkout process. You can use organic user complaints as an indirect measure of latent demand for one-click checkout feature

User survey — Ask why carts were abandoned for a cohort of shoppers that left the checkout step close to completion. Their reasons might indicate the possible success of your hypothesis

Effective hypothesis crafting is at the center of product management. It’s the link between dealing with risks and coming up with solutions that are both viable and valuable. However, it’s important to recognize that the formulation of a hypothesis is just the first step.

The real value of a hypothesis is made possible by rigorous testing. It’s through systematic validation that product managers can transform suppositions into certainties, ensuring the right product decisions are made. Without validation, even the most well-thought-out hypothesis remains unverified.

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8.1: The Elements of Hypothesis Testing

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Learning Objectives

• To understand the logical framework of tests of hypotheses.
• To learn basic terminology connected with hypothesis testing.
• To learn fundamental facts about hypothesis testing.

Types of Hypotheses

A hypothesis about the value of a population parameter is an assertion about its value. As in the introductory example we will be concerned with testing the truth of two competing hypotheses, only one of which can be true.

Definition: null hypothesis and alternative hypothesis

• The null hypothesis , denoted \(H_0\), is the statement about the population parameter that is assumed to be true unless there is convincing evidence to the contrary.
• The alternative hypothesis , denoted \(H_a\), is a statement about the population parameter that is contradictory to the null hypothesis, and is accepted as true only if there is convincing evidence in favor of it.

Definition: statistical procedure

Hypothesis testing is a statistical procedure in which a choice is made between a null hypothesis and an alternative hypothesis based on information in a sample.

The end result of a hypotheses testing procedure is a choice of one of the following two possible conclusions:

• Reject \(H_0\) (and therefore accept \(H_a\)), or
• Fail to reject \(H_0\) (and therefore fail to accept \(H_a\)).

The null hypothesis typically represents the status quo, or what has historically been true. In the example of the respirators, we would believe the claim of the manufacturer unless there is reason not to do so, so the null hypotheses is \(H_0:\mu =75\). The alternative hypothesis in the example is the contradictory statement \(H_a:\mu <75\). The null hypothesis will always be an assertion containing an equals sign, but depending on the situation the alternative hypothesis can have any one of three forms: with the symbol \(<\), as in the example just discussed, with the symbol \(>\), or with the symbol \(\neq\). The following two examples illustrate the latter two cases.

Example \(\PageIndex{1}\)

A publisher of college textbooks claims that the average price of all hardbound college textbooks is \(\$127.50\). A student group believes that the actual mean is higher and wishes to test their belief. State the relevant null and alternative hypotheses.

The default option is to accept the publisher’s claim unless there is compelling evidence to the contrary. Thus the null hypothesis is \(H_0:\mu =127.50\). Since the student group thinks that the average textbook price is greater than the publisher’s figure, the alternative hypothesis in this situation is \(H_a:\mu >127.50\).

Example \(\PageIndex{2}\)

The recipe for a bakery item is designed to result in a product that contains \(8\) grams of fat per serving. The quality control department samples the product periodically to insure that the production process is working as designed. State the relevant null and alternative hypotheses.

The default option is to assume that the product contains the amount of fat it was formulated to contain unless there is compelling evidence to the contrary. Thus the null hypothesis is \(H_0:\mu =8.0\). Since to contain either more fat than desired or to contain less fat than desired are both an indication of a faulty production process, the alternative hypothesis in this situation is that the mean is different from \(8.0\), so \(H_a:\mu \neq 8.0\).

In Example \(\PageIndex{1}\), the textbook example, it might seem more natural that the publisher’s claim be that the average price is at most \(\$127.50\), not exactly \(\$127.50\). If the claim were made this way, then the null hypothesis would be \(H_0:\mu \leq 127.50\), and the value \(\$127.50\) given in the example would be the one that is least favorable to the publisher’s claim, the null hypothesis. It is always true that if the null hypothesis is retained for its least favorable value, then it is retained for every other value.

Thus in order to make the null and alternative hypotheses easy for the student to distinguish, in every example and problem in this text we will always present one of the two competing claims about the value of a parameter with an equality. The claim expressed with an equality is the null hypothesis. This is the same as always stating the null hypothesis in the least favorable light. So in the introductory example about the respirators, we stated the manufacturer’s claim as “the average is \(75\) minutes” instead of the perhaps more natural “the average is at least \(75\) minutes,” essentially reducing the presentation of the null hypothesis to its worst case.

The first step in hypothesis testing is to identify the null and alternative hypotheses.

The Logic of Hypothesis Testing

Although we will study hypothesis testing in situations other than for a single population mean (for example, for a population proportion instead of a mean or in comparing the means of two different populations), in this section the discussion will always be given in terms of a single population mean \(\mu\).

The null hypothesis always has the form \(H_0:\mu =\mu _0\) for a specific number \(\mu _0\) (in the respirator example \(\mu _0=75\), in the textbook example \(\mu _0=127.50\), and in the baked goods example \(\mu _0=8.0\)). Since the null hypothesis is accepted unless there is strong evidence to the contrary, the test procedure is based on the initial assumption that \(H_0\) is true. This point is so important that we will repeat it in a display:

The test procedure is based on the initial assumption that \(H_0\) is true.

The criterion for judging between \(H_0\) and \(H_a\) based on the sample data is: if the value of \(\overline{X}\) would be highly unlikely to occur if \(H_0\) were true, but favors the truth of \(H_a\), then we reject \(H_0\) in favor of \(H_a\). Otherwise we do not reject \(H_0\).

Supposing for now that \(\overline{X}\) follows a normal distribution, when the null hypothesis is true the density function for the sample mean \(\overline{X}\) must be as in Figure \(\PageIndex{1}\): a bell curve centered at \(\mu _0\). Thus if \(H_0\) is true then \(\overline{X}\) is likely to take a value near \(\mu _0\) and is unlikely to take values far away. Our decision procedure therefore reduces simply to:

• if \(H_a\) has the form \(H_a:\mu <\mu _0\) then reject \(H_0\) if \(\bar{x}\) is far to the left of \(\mu _0\);
• if \(H_a\) has the form \(H_a:\mu >\mu _0\) then reject \(H_0\) if \(\bar{x}\) is far to the right of \(\mu _0\);
• if \(H_a\) has the form \(H_a:\mu \neq \mu _0\) then reject \(H_0\) if \(\bar{x}\) is far away from \(\mu _0\) in either direction.

Think of the respirator example, for which the null hypothesis is \(H_0:\mu =75\), the claim that the average time air is delivered for all respirators is \(75\) minutes. If the sample mean is \(75\) or greater then we certainly would not reject \(H_0\) (since there is no issue with an emergency respirator delivering air even longer than claimed).

If the sample mean is slightly less than \(75\) then we would logically attribute the difference to sampling error and also not reject \(H_0\) either.

Values of the sample mean that are smaller and smaller are less and less likely to come from a population for which the population mean is \(75\). Thus if the sample mean is far less than \(75\), say around \(60\) minutes or less, then we would certainly reject \(H_0\), because we know that it is highly unlikely that the average of a sample would be so low if the population mean were \(75\). This is the rare event criterion for rejection: what we actually observed \((\overline{X}<60)\) would be so rare an event if \(\mu =75\) were true that we regard it as much more likely that the alternative hypothesis \(\mu <75\) holds.

In summary, to decide between \(H_0\) and \(H_a\) in this example we would select a “rejection region” of values sufficiently far to the left of \(75\), based on the rare event criterion, and reject \(H_0\) if the sample mean \(\overline{X}\) lies in the rejection region, but not reject \(H_0\) if it does not.

The Rejection Region

Each different form of the alternative hypothesis Ha has its own kind of rejection region:

• if (as in the respirator example) \(H_a\) has the form \(H_a:\mu <\mu _0\), we reject \(H_0\) if \(\bar{x}\) is far to the left of \(\mu _0\), that is, to the left of some number \(C\), so the rejection region has the form of an interval \((-\infty ,C]\);
• if (as in the textbook example) \(H_a\) has the form \(H_a:\mu >\mu _0\), we reject \(H_0\) if \(\bar{x}\) is far to the right of \(\mu _0\), that is, to the right of some number \(C\), so the rejection region has the form of an interval \([C,\infty )\);
• if (as in the baked good example) \(H_a\) has the form \(H_a:\mu \neq \mu _0\), we reject \(H_0\) if \(\bar{x}\) is far away from \(\mu _0\) in either direction, that is, either to the left of some number \(C\) or to the right of some other number \(C′\), so the rejection region has the form of the union of two intervals \((-\infty ,C]\cup [C',\infty )\).

The key issue in our line of reasoning is the question of how to determine the number \(C\) or numbers \(C\) and \(C′\), called the critical value or critical values of the statistic, that determine the rejection region.

Definition: critical values

The critical value or critical values of a test of hypotheses are the number or numbers that determine the rejection region.

Suppose the rejection region is a single interval, so we need to select a single number \(C\). Here is the procedure for doing so. We select a small probability, denoted \(\alpha\), say \(1\%\), which we take as our definition of “rare event:” an event is “rare” if its probability of occurrence is less than \(\alpha\). (In all the examples and problems in this text the value of \(\alpha\) will be given already.) The probability that \(\overline{X}\) takes a value in an interval is the area under its density curve and above that interval, so as shown in Figure \(\PageIndex{2}\) (drawn under the assumption that \(H_0\) is true, so that the curve centers at \(\mu _0\)) the critical value \(C\) is the value of \(\overline{X}\) that cuts off a tail area \(\alpha\) in the probability density curve of \(\overline{X}\). When the rejection region is in two pieces, that is, composed of two intervals, the total area above both of them must be \(\alpha\), so the area above each one is \(\alpha /2\), as also shown in Figure \(\PageIndex{2}\).

The number \(\alpha\) is the total area of a tail or a pair of tails.

Example \(\PageIndex{3}\)

In the context of Example \(\PageIndex{2}\), suppose that it is known that the population is normally distributed with standard deviation \(\alpha =0.15\) gram, and suppose that the test of hypotheses \(H_0:\mu =8.0\) versus \(H_a:\mu \neq 8.0\) will be performed with a sample of size \(5\). Construct the rejection region for the test for the choice \(\alpha =0.10\). Explain the decision procedure and interpret it.

If \(H_0\) is true then the sample mean \(\overline{X}\) is normally distributed with mean and standard deviation

\[\begin{align} \mu _{\overline{X}} &=\mu \nonumber \\[5pt] &=8.0 \nonumber \end{align} \nonumber \]

\[\begin{align} \sigma _{\overline{X}}&=\dfrac{\sigma}{\sqrt{n}} \nonumber \\[5pt] &= \dfrac{0.15}{\sqrt{5}} \nonumber\\[5pt] &=0.067 \nonumber \end{align} \nonumber \]

Since \(H_a\) contains the \(\neq\) symbol the rejection region will be in two pieces, each one corresponding to a tail of area \(\alpha /2=0.10/2=0.05\). From Figure 7.1.6, \(z_{0.05}=1.645\), so \(C\) and \(C′\) are \(1.645\) standard deviations of \(\overline{X}\) to the right and left of its mean \(8.0\):

\[C=8.0-(1.645)(0.067) = 7.89 \; \; \text{and}\; \; C'=8.0 + (1.645)(0.067) = 8.11 \nonumber \]

The result is shown in Figure \(\PageIndex{3}\). α = 0.1

The decision procedure is: take a sample of size \(5\) and compute the sample mean \(\bar{x}\). If \(\bar{x}\) is either \(7.89\) grams or less or \(8.11\) grams or more then reject the hypothesis that the average amount of fat in all servings of the product is \(8.0\) grams in favor of the alternative that it is different from \(8.0\) grams. Otherwise do not reject the hypothesis that the average amount is \(8.0\) grams.

The reasoning is that if the true average amount of fat per serving were \(8.0\) grams then there would be less than a \(10\%\) chance that a sample of size \(5\) would produce a mean of either \(7.89\) grams or less or \(8.11\) grams or more. Hence if that happened it would be more likely that the value \(8.0\) is incorrect (always assuming that the population standard deviation is \(0.15\) gram).

Because the rejection regions are computed based on areas in tails of distributions, as shown in Figure \(\PageIndex{2}\), hypothesis tests are classified according to the form of the alternative hypothesis in the following way.

Definitions: Test classifications

• If \(H_a\) has the form \(\mu \neq \mu _0\) the test is called a two-tailed test .
• If \(H_a\) has the form \(\mu < \mu _0\) the test is called a left-tailed test .
• If \(H_a\) has the form \(\mu > \mu _0\)the test is called a right-tailed test .

Each of the last two forms is also called a one-tailed test .

Two Types of Errors

The format of the testing procedure in general terms is to take a sample and use the information it contains to come to a decision about the two hypotheses. As stated before our decision will always be either

• reject the null hypothesis \(H_0\) in favor of the alternative \(H_a\) presented, or
• do not reject the null hypothesis \(H_0\) in favor of the alternative \(H_0\) presented.

There are four possible outcomes of hypothesis testing procedure, as shown in the following table:

As the table shows, there are two ways to be right and two ways to be wrong. Typically to reject \(H_0\) when it is actually true is a more serious error than to fail to reject it when it is false, so the former error is labeled “ Type I ” and the latter error “ Type II ”.

Definition: Type I and Type II errors

In a test of hypotheses:

• A Type I error is the decision to reject \(H_0\) when it is in fact true.
• A Type II error is the decision not to reject \(H_0\) when it is in fact not true.

Unless we perform a census we do not have certain knowledge, so we do not know whether our decision matches the true state of nature or if we have made an error. We reject \(H_0\) if what we observe would be a “rare” event if \(H_0\) were true. But rare events are not impossible: they occur with probability \(\alpha\). Thus when \(H_0\) is true, a rare event will be observed in the proportion \(\alpha\) of repeated similar tests, and \(H_0\) will be erroneously rejected in those tests. Thus \(\alpha\) is the probability that in following the testing procedure to decide between \(H_0\) and \(H_a\) we will make a Type I error.

Definition: level of significance

The number \(\alpha\) that is used to determine the rejection region is called the level of significance of the test. It is the probability that the test procedure will result in a Type I error .

The probability of making a Type II error is too complicated to discuss in a beginning text, so we will say no more about it than this: for a fixed sample size, choosing \(alpha\) smaller in order to reduce the chance of making a Type I error has the effect of increasing the chance of making a Type II error . The only way to simultaneously reduce the chances of making either kind of error is to increase the sample size.

Standardizing the Test Statistic

Hypotheses testing will be considered in a number of contexts, and great unification as well as simplification results when the relevant sample statistic is standardized by subtracting its mean from it and then dividing by its standard deviation. The resulting statistic is called a standardized test statistic . In every situation treated in this and the following two chapters the standardized test statistic will have either the standard normal distribution or Student’s \(t\)-distribution.

Definition: hypothesis test

A standardized test statistic for a hypothesis test is the statistic that is formed by subtracting from the statistic of interest its mean and dividing by its standard deviation.

For example, reviewing Example \(\PageIndex{3}\), if instead of working with the sample mean \(\overline{X}\) we instead work with the test statistic

\[\frac{\overline{X}-8.0}{0.067} \nonumber \]

then the distribution involved is standard normal and the critical values are just \(\pm z_{0.05}\). The extra work that was done to find that \(C=7.89\) and \(C′=8.11\) is eliminated. In every hypothesis test in this book the standardized test statistic will be governed by either the standard normal distribution or Student’s \(t\)-distribution. Information about rejection regions is summarized in the following tables:

Every instance of hypothesis testing discussed in this and the following two chapters will have a rejection region like one of the six forms tabulated in the tables above.

No matter what the context a test of hypotheses can always be performed by applying the following systematic procedure, which will be illustrated in the examples in the succeeding sections.

Systematic Hypothesis Testing Procedure: Critical Value Approach

• Identify the null and alternative hypotheses.
• Identify the relevant test statistic and its distribution.
• Compute from the data the value of the test statistic.
• Construct the rejection region.
• Compare the value computed in Step 3 to the rejection region constructed in Step 4 and make a decision. Formulate the decision in the context of the problem, if applicable.

The procedure that we have outlined in this section is called the “Critical Value Approach” to hypothesis testing to distinguish it from an alternative but equivalent approach that will be introduced at the end of Section 8.3.

Key Takeaway

• A test of hypotheses is a statistical process for deciding between two competing assertions about a population parameter.
• The testing procedure is formalized in a five-step procedure.

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The 5 Components of a Good Hypothesis

November 12, 2014 by Teresa Torres

Update: I’ve since revised this hypothesis format. You can find the most current version in this article:

• How to Improve Your Experiment Design (And Build Trust in Your Product Experiments)

“My hypothesis is …”

These words are becoming more common everyday. Product teams are starting to talk like scientists. Are you?

The internet industry is going through a mindset shift. Instead of assuming we have all the right answers, we are starting to acknowledge that building products is hard. We are accepting the reality that our ideas are going to fail more often than they are going to succeed.

Rather than waiting to find out which ideas are which after engineers build them, smart product teams are starting to integrate experimentation into their product discovery process. They are asking themselves, how can we test this idea before we invest in it?

This process starts with formulating a good hypothesis.

These Are Not the Hypotheses You Are Looking For

When we are new to hypothesis testing, we tend to start with hypotheses like these:

• Fixing the hard-to-use comment form will increase user engagement.
• A redesign will improve site usability.
• Reducing prices will make customers happy.

There’s only one problem. These aren’t testable hypotheses. They aren’t specific enough.

A good hypothesis can be clearly refuted or supported by an experiment. – Tweet This

To make sure that your hypotheses can be supported or refuted by an experiment, you will want to include each of these elements:

• the change that you are testing
• what impact we expect the change to have
• who you expect it to impact
• by how much
• after how long

The Change:  This is the change that you are introducing to your product. You are testing a new design, you are adding new copy to a landing page, or you are rolling out a new feature.

Be sure to get specific. Fixing a hard-to-use comment form is not specific enough. How will you fix it? Some solutions might work. Others might not. Each is a hypothesis in its own right.

Design changes can be particularly challenging. Your hypothesis should cover a specific design not the idea of a redesign.

In other words, use this:

• This specific design will increase conversions.
• Redesigning the landing page will increase conversions.

The former can be supported or refuted by an experiment. The latter can encompass dozens of design solutions, where some might work and others might not.

The Expected Impact:  The expected impact should clearly define what you expect to see as a result of making the change.

How will you know if your change is successful? Will it reduce response times, increase conversions, or grow your audience?

The expected impact needs to be specific and measurable. – Tweet This

You might hypothesize that your new design will increase usability. This isn’t specific enough.

You need to define how you will measure an increase in usability. Will it reduce the time to complete some action? Will it increase customer satisfaction? Will it reduce bounce rates?

There are dozens of ways that you might measure an increase in usability. In order for this to be a testable hypothesis, you need to define which metric you expect to be affected by this change.

Who Will Be Impacted: The third component of a good hypothesis is who will be impacted by this change. Too often, we assume everyone. But this is rarely the case.

I was recently working with a product manager who was testing a sign up form popup upon exiting a page.

I’m sure you’ve seen these before. You are reading a blog post and just as you are about to navigate away, you get a popup that asks, “Would you like to subscribe to our newsletter?”

She A/B tested this change by showing it to half of her population, leaving the rest as her control group. But there was a problem.

Some of her visitors were already subscribers. They don’t need to subscribe again. For this population, the answer to this popup will always be no.

Rather than testing with her whole population, she should be testing with just the people who are not currently subscribers.

This isn’t easy to do. And it might not sound like it’s worth the effort, but it’s the only way to get good results.

Suppose she has 100 visitors. Fifty see the popup and fifty don’t. If 45 of the people who see the popup are already subscribers and as a result they all say no, and of the five remaining visitors only 1 says yes, it’s going to look like her conversion rate is 1 out of 50, or 2%. However, if she limits her test to just the people who haven’t subscribed, her conversion rate is 1 out of 5, or 20%. This is a huge difference.

Who you test with is often the most important factor for getting clean results. – Tweet This

By how much: The fourth component builds on the expected impact. You need to define how much of an impact you expect your change to have.

For example, if you are hypothesizing that your change will increase conversion rates, then you need to estimate by how much, as in the change will increase conversion rate from x% to y%, where x is your current conversion rate and y is your expected conversion rate after making the change.

This can be hard to do and is often a guess. However, you still want to do it. It serves two purposes.

First, it helps you draw a line in the sand. This number should determine in black and white terms whether or not your hypothesis passes or fails and should dictate how you act on the results.

Suppose you hypothesize that the change will improve conversion rates by 10%, then if your change results in a 9% increase, your hypothesis fails.

This might seem extreme, but it’s a critical step in making sure that you don’t succumb to your own biases down the road.

It’s very easy after the fact to determine that 9% is good enough. Or that 2% is good enough. Or that -2% is okay, because you like the change. Without a line in the sand, you are setting yourself up to ignore your data.

The second reason why you need to define by how much is so that you can calculate for how long to run your test.

After how long:  Too many teams run their tests for an arbitrary amount of time or stop the results when one version is winning.

This is a problem. It opens you up to false positives and releasing changes that don’t actually have an impact.

If you hypothesize the expected impact ahead of time than you can use a duration calculator to determine for how long to run the test.

Finally, you want to add the duration of the test to your hypothesis. This will help to ensure that everyone knows that your results aren’t valid until the duration has passed.

If your traffic is sporadic, “how long” doesn’t have to be defined in time. It can also be defined in page views or sign ups or after a specific number of any event.

Putting It All Together

Use the following examples as templates for your own hypotheses:

• Design x [the change] will increase conversions [the impact] for search campaign traffic [the who] by 10% [the how much] after 7 days [the how long].
• Reducing the sign up steps from 3 to 1 will increase signs up by 25% for new visitors after 1,000 visits to the sign up page.
• This subject line will increase open rates for daily digest subscribers by 15% after 3 days.

After you write a hypothesis, break it down into its five components to make sure that you haven’t forgotten anything.

• Change: this subject line
• Impact: will increase open rates
• Who: for daily digest subscribers
• By how much: by 15%
• After how long: After 3 days

And then ask yourself:

• Is your expected impact specific and measurable?
• Can you clearly explain why the change will drive the expected impact?
• Are you testing with the right population?
• Did you estimate your how much based on a baseline and / or comparable changes? (more on this in a future post)
• Did you calculate the duration using a duration calculator?

It’s easy to give lip service to experimentation and hypothesis testing. But if you want to get the most out of your efforts, make sure you are starting with a good hypothesis.

Did you learn something new reading this article? Keep learning. Subscribe to the Product Talk mailing list to get the next article in this series delivered to your inbox.

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May 21, 2017 at 2:11 am

Interesting article, I am thinking about making forming a hypothesis around my product, if certain customers will find a proposed value useful. Can you kindly let me know if I’m on the right track.

“Certain customer segment (AAA) will find value in feature (XXX), to tackle their pain point ”

Change: using a feature (XXX)/ product Impact: will reduce monetary costs/ help solve a problem Who: for certain customers segment (AAA) By how much: by 5% After how long: 10 days

April 4, 2020 at 12:33 pm

Hi! Could you throw a little light on this: “Suppose you hypothesize that the change will improve conversion rates by 10%, then if your change results in a 9% increase, your hypothesis fails.”

I understood the rationale behind having a number x (10% in this case) associated with “by how much”, but could you explain with an example of how to ballpark a figure like this?

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8.1 The Elements of Hypothesis Testing

Learning objectives.

• To understand the logical framework of tests of hypotheses.
• To learn basic terminology connected with hypothesis testing.
• To learn fundamental facts about hypothesis testing.

Types of Hypotheses

A hypothesis about the value of a population parameter is an assertion about its value. As in the introductory example we will be concerned with testing the truth of two competing hypotheses, only one of which can be true.

The null hypothesis The statement that is assumed to be true unless there is convincing evidence to the contrary. , denoted H 0 , is the statement about the population parameter that is assumed to be true unless there is convincing evidence to the contrary .

The alternative hypothesis A statement that is accepted as true only if there is convincing evidence in favor of it. , denoted H a , is a statement about the population parameter that is contradictory to the null hypothesis, and is accepted as true only if there is convincing evidence in favor of it.

Hypothesis testing A statistical procedure in which a choice is made between a null hypothesis and a specific alternative hypothesis based on information in a sample. is a statistical procedure in which a choice is made between a null hypothesis and an alternative hypothesis based on information in a sample.

The end result of a hypotheses testing procedure is a choice of one of the following two possible conclusions:

• Reject H 0 (and therefore accept H a ), or
• Fail to reject H 0 (and therefore fail to accept H a ).

The null hypothesis typically represents the status quo, or what has historically been true. In the example of the respirators, we would believe the claim of the manufacturer unless there is reason not to do so, so the null hypotheses is H 0 : μ = 75 . The alternative hypothesis in the example is the contradictory statement H a : μ < 75 . The null hypothesis will always be an assertion containing an equals sign, but depending on the situation the alternative hypothesis can have any one of three forms: with the symbol “<,” as in the example just discussed, with the symbol “>,” or with the symbol “≠” The following two examples illustrate the latter two cases.

A publisher of college textbooks claims that the average price of all hardbound college textbooks is $127.50. A student group believes that the actual mean is higher and wishes to test their belief. State the relevant null and alternative hypotheses.

The default option is to accept the publisher’s claim unless there is compelling evidence to the contrary. Thus the null hypothesis is H 0 : μ = 127.50 . Since the student group thinks that the average textbook price is greater than the publisher’s figure, the alternative hypothesis in this situation is H a : μ > 127.50 .

The recipe for a bakery item is designed to result in a product that contains 8 grams of fat per serving. The quality control department samples the product periodically to insure that the production process is working as designed. State the relevant null and alternative hypotheses.

The default option is to assume that the product contains the amount of fat it was formulated to contain unless there is compelling evidence to the contrary. Thus the null hypothesis is H 0 : μ = 8.0 . Since to contain either more fat than desired or to contain less fat than desired are both an indication of a faulty production process, the alternative hypothesis in this situation is that the mean is different from 8.0, so H a : μ ≠ 8.0 .

In Note 8.8 "Example 1" , the textbook example, it might seem more natural that the publisher’s claim be that the average price is at most $127.50, not exactly $127.50. If the claim were made this way, then the null hypothesis would be H 0 : μ ≤ 127.50 , and the value $127.50 given in the example would be the one that is least favorable to the publisher’s claim, the null hypothesis. It is always true that if the null hypothesis is retained for its least favorable value, then it is retained for every other value.

Thus in order to make the null and alternative hypotheses easy for the student to distinguish, in every example and problem in this text we will always present one of the two competing claims about the value of a parameter with an equality. The claim expressed with an equality is the null hypothesis. This is the same as always stating the null hypothesis in the least favorable light. So in the introductory example about the respirators, we stated the manufacturer’s claim as “the average is 75 minutes” instead of the perhaps more natural “the average is at least 75 minutes,” essentially reducing the presentation of the null hypothesis to its worst case.

The first step in hypothesis testing is to identify the null and alternative hypotheses.

The Logic of Hypothesis Testing

Although we will study hypothesis testing in situations other than for a single population mean (for example, for a population proportion instead of a mean or in comparing the means of two different populations), in this section the discussion will always be given in terms of a single population mean μ .

The null hypothesis always has the form H 0 : μ = μ 0 for a specific number μ 0 (in the respirator example μ 0 = 75 , in the textbook example μ 0 = 127.50 , and in the baked goods example μ 0 = 8.0 ). Since the null hypothesis is accepted unless there is strong evidence to the contrary, the test procedure is based on the initial assumption that H 0 is true. This point is so important that we will repeat it in a display:

The test procedure is based on the initial assumption that H 0 is true.

The criterion for judging between H 0 and H a based on the sample data is: if the value of X - would be highly unlikely to occur if H 0 were true, but favors the truth of H a , then we reject H 0 in favor of H a . Otherwise we do not reject H 0 .

Supposing for now that X - follows a normal distribution, when the null hypothesis is true the density function for the sample mean X - must be as in Figure 8.1 "The Density Curve for " : a bell curve centered at μ 0 . Thus if H 0 is true then X - is likely to take a value near μ 0 and is unlikely to take values far away. Our decision procedure therefore reduces simply to:

• if H a has the form H a : μ < μ 0 then reject H 0 if x - is far to the left of μ 0 ;
• if H a has the form H a : μ > μ 0 then reject H 0 if x - is far to the right of μ 0 ;
• if H a has the form H a : μ ≠ μ 0 then reject H 0 if x - is far away from μ 0 in either direction.

Figure 8.1 The Density Curve for X - if H 0 Is True

Think of the respirator example, for which the null hypothesis is H 0 : μ = 75 , the claim that the average time air is delivered for all respirators is 75 minutes. If the sample mean is 75 or greater then we certainly would not reject H 0 (since there is no issue with an emergency respirator delivering air even longer than claimed).

If the sample mean is slightly less than 75 then we would logically attribute the difference to sampling error and also not reject H 0 either.

Values of the sample mean that are smaller and smaller are less and less likely to come from a population for which the population mean is 75. Thus if the sample mean is far less than 75, say around 60 minutes or less, then we would certainly reject H 0 , because we know that it is highly unlikely that the average of a sample would be so low if the population mean were 75. This is the rare event criterion for rejection: what we actually observed ( X - < 60 ) would be so rare an event if μ = 75 were true that we regard it as much more likely that the alternative hypothesis μ < 75 holds.

In summary, to decide between H 0 and H a in this example we would select a “ rejection region An interval or union of intervals such that the null hypothesis is rejected if and only if the statistic of interest lies in this region. ” of values sufficiently far to the left of 75, based on the rare event criterion, and reject H 0 if the sample mean X - lies in the rejection region, but not reject H 0 if it does not.

The Rejection Region

Each different form of the alternative hypothesis H a has its own kind of rejection region:

• if (as in the respirator example) H a has the form H a : μ < μ 0 , we reject H 0 if x - is far to the left of μ 0 , that is, to the left of some number C , so the rejection region has the form of an interval (−∞, C ];
• if (as in the textbook example) H a has the form H a : μ > μ 0 , we reject H 0 if x - is far to the right of μ 0 , that is, to the right of some number C , so the rejection region has the form of an interval [ C ,∞);
• if (as in the baked good example) H a has the form H a : μ ≠ μ 0 , we reject H 0 if x - is far away from μ 0 in either direction, that is, either to the left of some number C or to the right of some other number C ′, so the rejection region has the form of the union of two intervals (−∞, C ]∪[ C ′,∞).

The key issue in our line of reasoning is the question of how to determine the number C or numbers C and C ′, called the critical value or critical values of the statistic, that determine the rejection region.

The critical value The number or one of a pair of numbers that determines the rejection region. or critical values of a test of hypotheses are the number or numbers that determine the rejection region.

Suppose the rejection region is a single interval, so we need to select a single number C . Here is the procedure for doing so. We select a small probability, denoted α , say 1%, which we take as our definition of “rare event:” an event is “rare” if its probability of occurrence is less than α . (In all the examples and problems in this text the value of α will be given already.) The probability that X - takes a value in an interval is the area under its density curve and above that interval, so as shown in Figure 8.2 (drawn under the assumption that H 0 is true, so that the curve centers at μ 0 ) the critical value C is the value of X - that cuts off a tail area α in the probability density curve of X - . When the rejection region is in two pieces, that is, composed of two intervals, the total area above both of them must be α , so the area above each one is α ∕ 2 , as also shown in Figure 8.2 .

The number α is the total area of a tail or a pair of tails.

In the context of Note 8.9 "Example 2" , suppose that it is known that the population is normally distributed with standard deviation σ = 0.15 gram, and suppose that the test of hypotheses H 0 : μ = 8.0 versus H a : μ ≠ 8.0 will be performed with a sample of size 5. Construct the rejection region for the test for the choice α = 0.10 . Explain the decision procedure and interpret it.

If H 0 is true then the sample mean X - is normally distributed with mean and standard deviation

Since H a contains the ≠ symbol the rejection region will be in two pieces, each one corresponding to a tail of area α ∕ 2 = 0.10 ∕ 2 = 0.05 . From Figure 12.3 "Critical Values of " , z 0.05 = 1.645 , so C and C ′ are 1.645 standard deviations of X - to the right and left of its mean 8.0:

The result is shown in Figure 8.3 "Rejection Region for the Choice " .

Figure 8.3 Rejection Region for the Choice α = 0.10

The decision procedure is: take a sample of size 5 and compute the sample mean x - . If x - is either 7.89 grams or less or 8.11 grams or more then reject the hypothesis that the average amount of fat in all servings of the product is 8.0 grams in favor of the alternative that it is different from 8.0 grams. Otherwise do not reject the hypothesis that the average amount is 8.0 grams.

The reasoning is that if the true average amount of fat per serving were 8.0 grams then there would be less than a 10% chance that a sample of size 5 would produce a mean of either 7.89 grams or less or 8.11 grams or more. Hence if that happened it would be more likely that the value 8.0 is incorrect (always assuming that the population standard deviation is 0.15 gram).

Because the rejection regions are computed based on areas in tails of distributions, as shown in Figure 8.2 , hypothesis tests are classified according to the form of the alternative hypothesis in the following way.

If H a has the form μ ≠ μ 0 the test is called a two-tailed test .

If H a has the form μ < μ 0 the test is called a left-tailed test .

If H a has the form μ > μ 0 the test is called a right-tailed test .

Each of the last two forms is also called a one-tailed test .

Two Types of Errors

The format of the testing procedure in general terms is to take a sample and use the information it contains to come to a decision about the two hypotheses. As stated before our decision will always be either

• reject the null hypothesis H 0 in favor of the alternative H a presented, or
• do not reject the null hypothesis H 0 in favor of the alternative H a presented.

There are four possible outcomes of hypothesis testing procedure, as shown in the following table:

As the table shows, there are two ways to be right and two ways to be wrong. Typically to reject H 0 when it is actually true is a more serious error than to fail to reject it when it is false, so the former error is labeled “Type I” and the latter error “Type II.”

In a test of hypotheses, a Type I error Rejection of a true null hypothesis. is the decision to reject H 0 when it is in fact true. A Type II error Failure to reject a false null hypothesis. is the decision not to reject H 0 when it is in fact not true.

Unless we perform a census we do not have certain knowledge, so we do not know whether our decision matches the true state of nature or if we have made an error. We reject H 0 if what we observe would be a “rare” event if H 0 were true. But rare events are not impossible: they occur with probability α . Thus when H 0 is true, a rare event will be observed in the proportion α of repeated similar tests, and H 0 will be erroneously rejected in those tests. Thus α is the probability that in following the testing procedure to decide between H 0 and H a we will make a Type I error.

The number α that is used to determine the rejection region is called the level of significance of the test The probability α that defines an event as “rare;” the probability that the test procedure will lead to a Type I error. . It is the probability that the test procedure will result in a Type I error.

The probability of making a Type II error is too complicated to discuss in a beginning text, so we will say no more about it than this: for a fixed sample size, choosing α smaller in order to reduce the chance of making a Type I error has the effect of increasing the chance of making a Type II error. The only way to simultaneously reduce the chances of making either kind of error is to increase the sample size.

Standardizing the Test Statistic

Hypotheses testing will be considered in a number of contexts, and great unification as well as simplification results when the relevant sample statistic is standardized by subtracting its mean from it and then dividing by its standard deviation. The resulting statistic is called a standardized test statistic . In every situation treated in this and the following two chapters the standardized test statistic will have either the standard normal distribution or Student’s t -distribution.

A standardized test statistic The standardized statistic used in performing the test. for a hypothesis test is the statistic that is formed by subtracting from the statistic of interest its mean and dividing by its standard deviation.

For example, reviewing Note 8.14 "Example 3" , if instead of working with the sample mean X - we instead work with the test statistic

then the distribution involved is standard normal and the critical values are just ± z 0.05 . The extra work that was done to find that C = 7.89 and C ′ = 8.11 is eliminated. In every hypothesis test in this book the standardized test statistic will be governed by either the standard normal distribution or Student’s t -distribution. Information about rejection regions is summarized in the following tables:

Every instance of hypothesis testing discussed in this and the following two chapters will have a rejection region like one of the six forms tabulated in the tables above.

No matter what the context a test of hypotheses can always be performed by applying the following systematic procedure, which will be illustrated in the examples in the succeeding sections.

Systematic Hypothesis Testing Procedure: Critical Value Approach

• Identify the null and alternative hypotheses.
• Identify the relevant test statistic and its distribution.
• Compute from the data the value of the test statistic.
• Construct the rejection region.
• Compare the value computed in Step 3 to the rejection region constructed in Step 4 and make a decision. Formulate the decision in the context of the problem, if applicable.

The procedure that we have outlined in this section is called the “Critical Value Approach” to hypothesis testing to distinguish it from an alternative but equivalent approach that will be introduced at the end of Section 8.3 "The Observed Significance of a Test" .

Key Takeaways

• A test of hypotheses is a statistical process for deciding between two competing assertions about a population parameter.
• The testing procedure is formalized in a five-step procedure.

State the null and alternative hypotheses for each of the following situations. (That is, identify the correct number μ 0 and write H 0 : μ = μ 0 and the appropriate analogous expression for H a .)

• The average July temperature in a region historically has been 74.5°F. Perhaps it is higher now.
• The average weight of a female airline passenger with luggage was 145 pounds ten years ago. The FAA believes it to be higher now.
• The average stipend for doctoral students in a particular discipline at a state university is $14,756. The department chairman believes that the national average is higher.
• The average room rate in hotels in a certain region is $82.53. A travel agent believes that the average in a particular resort area is different.
• The average farm size in a predominately rural state was 69.4 acres. The secretary of agriculture of that state asserts that it is less today.
• The average time workers spent commuting to work in Verona five years ago was 38.2 minutes. The Verona Chamber of Commerce asserts that the average is less now.
• The mean salary for all men in a certain profession is $58,291. A special interest group thinks that the mean salary for women in the same profession is different.
• The accepted figure for the caffeine content of an 8-ounce cup of coffee is 133 mg. A dietitian believes that the average for coffee served in a local restaurants is higher.
• The average yield per acre for all types of corn in a recent year was 161.9 bushels. An economist believes that the average yield per acre is different this year.
• An industry association asserts that the average age of all self-described fly fishermen is 42.8 years. A sociologist suspects that it is higher.

Describe the two types of errors that can be made in a test of hypotheses.

Under what circumstance is a test of hypotheses certain to yield a correct decision?

• H 0 : μ = 74.5 vs. H a : μ > 74.5
• H 0 : μ = 145 vs. H a : μ > 145
• H 0 : μ = 14756 vs. H a : μ > 14756
• H 0 : μ = 82.53 vs. H a : μ ≠ 82.53
• H 0 : μ = 69.4 vs. H a : μ < 69.4

A Type I error is made when a true H 0 is rejected. A Type II error is made when a false H 0 is not rejected.

• Learning Modules
• About the Project
• Project Resources

Functional Behavior Assessment

• Overview of Functional Behavior Assessment
• Step 1 Planning
• Step 2.1 Collect baseline data using direct and indirect assessment methods
• Step 2.2 Gather observation-based data on the occurrence of the interfering behavior
• Step 2.3a Identify variables of the behavior

Step 2.3b Create a hypothesis statement for the purpose of the behavior

• Step 2.3c Test the hypothesis (behavior) statement
• Step 2.4 Develop a behavior intervention plan (BIP)
• Practice Scenarios: Implementing FBA
• Knowledge Check
• Step 3 Monitoring Progress
• Module Resources

Create a hypothesis (behavior) statement

A hypothesis statement should be based upon the assessment results and describes the best guess of the purpose of the behavior in sufficient detail. That is, what is the behavior trying to tell us? Analyzing assessment data helps  team members  identify patterns or behaviors across time and settings. Often times, patterns of behavior and the possible reasons for the behaviors will be obvious; however, at other times, the behavior patterns may be subtle and difficult to identify. When this occurs, additional data might need to be gathered to guide the development of a behavior statement. 

Team members develop a behavior statement for the interfering behavior that includes:

• the setting events, immediate antecedents, and immediate consequences that surround the interfering behavior
• a restatement and refinement of the description of the interfering behavior that is occurring
• the purpose the behavior serves (i.e., get/obtain, escape/avoid)

Example hypothesis (behavior) statement:

“Tino falls onto the floor, screaming and crying, when asked to clean up his toys, and he is then taken to his room where his mom rocks him on the rocking chair to calm him down.”

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This project is a program of the Frank Porter Graham Child Development Institute at University of North Carolina at Chapel Hill .