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How to Formulate a Hypothesis: Example and Explanation

A hypothesis is a smart guess about how things work. It helps scientists figure out what they think will happen in their experiments. Making a good hypothesis is important because it guides the research and helps find answers to questions. In this article, we will learn how to make a strong hypothesis, look at some examples, and understand why they matter.

Key Takeaways

• A hypothesis is an educated guess that can be tested through experiments.
• Good hypotheses are clear, precise, and can be proven wrong.
• There are different types of hypotheses, like simple, complex, null, and alternative.
• Variables play a big role in forming a hypothesis, including independent, dependent, and control variables.
• Testing and refining hypotheses are crucial steps in scientific research.

Understanding the Concept of a Hypothesis

Definition and importance.

A hypothesis is an idea you can test. It's a clear statement predicting the outcome of your study. It's not just a guess ; it should be based on what you already know. A good hypothesis helps you focus your research and guides your experiments.

Role in Scientific Research

In science, a hypothesis is very important. It gives you a starting point for your experiments. You can test it to see if it's true or false. This helps you understand more about the world. A clear, testable hypothesis is key to good research .

Common Misconceptions

Many people think a hypothesis is just a wild guess. This is not true. A hypothesis is based on existing knowledge and theories. Another common mistake is making the hypothesis too broad. A good hypothesis should be specific and testable.

Steps to Formulate a Hypothesis

Formulating a hypothesis is a critical step in the scientific method. It involves several key stages that help ensure your hypothesis is both testable and relevant to your research question. Here are the steps you should follow:

Gathering Observations

Start by collecting as many observations about your topic or problem as possible. These observations will form the foundation of your hypothesis. Good clinical research starts from a plausible hypothesis supported by contemporary scientific knowledge. Look for patterns or trends in the data that might suggest a possible explanation.

Identifying Variables

Next, identify the variables involved in your study. Variables are the elements that you will measure or manipulate in your research. There are typically three types of variables: independent, dependent, and control variables. Understanding these will help you design a more effective experiment.

Developing Possible Explanations

Once you have gathered your observations and identified your variables, the next step is to develop possible explanations for the patterns you have observed. This is where you start to formulate your hypothesis. Think of ways to confirm or disprove each possible explanation through experimentation. This process is known as falsifiability and is crucial for a robust hypothesis.

Characteristics of a Good Hypothesis

Testability and falsifiability.

A good hypothesis must be testable, meaning you can design an experiment to check if it's true or false. Testability is crucial because it allows you to gather evidence to support or refute your hypothesis. Additionally, a hypothesis should be falsifiable, which means there should be a possible outcome that can prove it wrong. This aligns with the falsification principle proposed by Karl Popper, which is fundamental in scientific research.

Clarity and Precision

Your hypothesis should be clear and precise, avoiding any vague language. This clarity helps in demystifying the concept of a thesis statement . A well-defined hypothesis makes it easier to design experiments and interpret results. For example, instead of saying "Plants grow better with more light," you could say, "If plants receive 8 hours of sunlight daily, then they will grow taller than plants that receive 4 hours of sunlight daily."

Relevance to Research Question

A good hypothesis should be directly related to your research question. It should provide a clear direction for your study and help you focus on specific variables. This relevance ensures that your hypothesis is not just a random guess but is grounded in existing knowledge and observations. Hypotheses have strong, arguably foundational, utility as a tool of science . They support the falsification principle, proposed by Karl Popper as fundamental in scientific research.

Types of Hypotheses in Research

When conducting research, it's crucial to understand the different types of hypotheses you might encounter. Each type serves a unique purpose and helps guide your study in specific ways. Knowing these types can enhance the clarity and focus of your research proposal .

Examples of Hypotheses

Simple hypothesis examples.

A simple hypothesis suggests a relationship between two variables: one independent and one dependent. For instance, "If students sleep for at least 8 hours, then their test scores will improve." This type of hypothesis is straightforward and easy to test.

Complex Hypothesis Examples

A complex hypothesis involves more than two variables. An example could be, "If students sleep for at least 8 hours and eat a healthy breakfast, then their test scores and overall well-being will improve." This type of hypothesis examines multiple factors and their combined effects.

Null and Alternative Hypothesis Examples

The null hypothesis states that there is no relationship between the variables. For example, "There is no difference in test scores between students who sleep for 8 hours and those who do not." The alternative hypothesis, on the other hand, suggests a relationship: "Students who sleep for 8 hours will have better test scores than those who do not."

Understanding these examples helps clarify how to structure your own hypotheses. Whether simple or complex, each type plays a crucial role in scientific research.

The Role of Variables in Hypothesis Formulation

When formulating a hypothesis, understanding the role of variables is crucial. Variables are the elements that you measure or manipulate in your research . They help you establish relationships and test your predictions effectively.

Testing Your Hypothesis

Designing experiments.

Designing an experiment is a crucial step in testing your hypothesis. A well-designed experiment ensures that you can accurately test your hypothesis and obtain reliable results. Start by defining your independent and dependent variables clearly. Make sure to control other factors that might influence the outcome. This is essential for maintaining the integrity of your experiment. You should also consider the ethical implications of your experiment to ensure it adheres to accepted standards.

Data Collection Methods

Once your experiment is designed, the next step is to collect data. Choose data collection methods that are appropriate for your research question and hypothesis. Common methods include surveys, observations, and experiments. Ensure that your data collection process is systematic and consistent to avoid any biases. Remember, the goal is to gather data that will either support or refute your hypothesis.

Analyzing Results

After collecting your data, the next step is to analyze the results. Use statistical methods to determine whether your data supports your hypothesis. This involves calculating the likelihood that your results are due to chance. If your data does not support your hypothesis, don't be discouraged. Unexpected findings can lead to new questions and further research. Always be open to conducting further experiments to validate and understand your findings.

Common Pitfalls in Hypothesis Formulation

When formulating a hypothesis, it's crucial to avoid common mistakes that can undermine your research. Here are some pitfalls to watch out for:

Overly Broad Hypotheses

One of the most frequent errors is creating a hypothesis that is too broad. A broad hypothesis can be difficult to test and may not provide meaningful results. Narrowing down your hypothesis to a specific aspect of your research question can make it more manageable and testable.

Lack of Testability

A hypothesis must be testable to be valid. If you can't design an experiment to test your hypothesis, it's not useful. Ensure that your hypothesis includes variables that can be measured and tested. This is essential for revolutionizing research: the secrets of effective experimental design .

Ignoring Alternative Explanations

Another common mistake is failing to consider other possible explanations for your observations. When you ignore alternative explanations, you risk missing out on important insights. Always evaluate assumptions, revise methodology, and consider alternative explanations to strengthen your hypothesis.

By being aware of these pitfalls, you can create a more robust and reliable hypothesis for your research.

Refining and Revising Hypotheses

When you conduct research, it’s common to find that your initial hypothesis may not hold true. This is a normal part of the scientific process. If your results do not support your original hypothesis, consider suggesting alternative options for future studies. This can help guide further research and improve understanding of the topic.

To ensure your hypothesis is strong, you can use a checklist to identify any weaknesses. Here are some questions to consider:

• Is the hypothesis clear and specific?
• Can it be tested through experiments?
• Does it relate to the research question?

By answering these questions, you can refine your hypothesis and make it more robust. Additionally, incorporating feedback from peers can provide new insights and help you adjust your hypothesis based on new data.

In summary, refining and revising your hypothesis is essential for advancing your research. It allows you to adapt to new findings and improve the clarity and focus of your work. Remember, the goal is to develop a hypothesis that can lead to meaningful conclusions and further exploration in your field.

In the context of educational research, a recent meta-analysis highlights the importance of understanding the relationship between psychological needs and student well-being. This shows how refining hypotheses can lead to better insights into complex issues. Similarly, a grounded theory study emphasizes the need for thorough reviews to identify key issues in research, which can also inform hypothesis revision.

Case Studies of Hypothesis Formulation

One of the most famous historical examples of hypothesis formulation is Gregor Mendel's work on pea plants. Mendel's hypothesis about inheritance patterns laid the groundwork for modern genetics. He observed the traits of pea plants and formulated hypotheses about how these traits were passed down through generations. His work is a classic example of how careful observation and hypothesis testing can lead to significant scientific breakthroughs.

In contemporary research, hypothesis formulation continues to play a crucial role. For instance, in the field of psychology, researchers often develop hypotheses to understand human behavior. A recent study on the effects of social media on mental health formulated the hypothesis that increased social media use leads to higher levels of anxiety and depression. This hypothesis was tested through surveys and data analysis, providing valuable insights into the relationship between social media and mental health.

From both historical and contemporary examples, several lessons can be learned about effective hypothesis formulation:

• Observation is key : Careful observation of phenomena is the first step in formulating a hypothesis.
• Clarity and precision : A good hypothesis should be clear and precise, making it easier to test.
• Testability: Ensure that your hypothesis can be tested through experiments or data analysis.
• Flexibility: Be prepared to revise your hypothesis based on new data or feedback.

By understanding these lessons, you can improve your own hypothesis formulation process and contribute to the advancement of scientific knowledge.

In our "Case Studies of Hypothesis Formulation" section, we dive into real-world examples that show how to create strong hypotheses. These case studies are designed to help you understand the process and apply it to your own work. If you're looking for more detailed guidance, visit our website for step-by-step instructions and special offers. Don't miss out on the chance to improve your research skills!

Formulating a hypothesis is a fundamental step in the scientific method that helps guide research and experimentation. By gathering observations, evaluating potential causes, and developing testable statements, researchers can create hypotheses that are both meaningful and falsifiable. This process not only aids in understanding the problem at hand but also in predicting outcomes and drawing conclusions based on empirical evidence. Remember, a well-crafted hypothesis is clear, concise, and provides a direction for future research. With practice and careful consideration, anyone can learn to formulate effective hypotheses that contribute to scientific knowledge.

Frequently Asked Questions

What is a hypothesis.

A hypothesis is an educated guess about how things work. It's a statement that can be tested to see if it's true or false.

Why is a hypothesis important in scientific research?

A hypothesis helps guide your experiments and research. It gives you a clear focus and helps you understand what you're trying to find out.

What are the steps to formulate a good hypothesis?

To create a good hypothesis, start by gathering observations, look for patterns, and identify variables. Then, come up with possible explanations that you can test.

What makes a hypothesis testable?

A testable hypothesis is one that you can prove or disprove through experiments or observations. It should be clear and specific.

Can a hypothesis be proven true?

A hypothesis can be supported by evidence, but it can't be proven true beyond all doubt. New evidence might change our understanding.

What are independent and dependent variables?

Independent variables are the ones you change in an experiment. Dependent variables are the ones you measure to see if they change because of the independent variable.

What is a null hypothesis?

A null hypothesis states that there is no relationship between the variables being studied. It's often used as a starting point for testing.

How can I avoid common pitfalls in hypothesis formulation?

To avoid problems, make sure your hypothesis is specific, testable, and based on observations. Avoid making it too broad or ignoring other possible explanations.

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Hypothesis Testing

Hypothesis testing is a tool for making statistical inferences about the population data. It is an analysis tool that tests assumptions and determines how likely something is within a given standard of accuracy. Hypothesis testing provides a way to verify whether the results of an experiment are valid.

A null hypothesis and an alternative hypothesis are set up before performing the hypothesis testing. This helps to arrive at a conclusion regarding the sample obtained from the population. In this article, we will learn more about hypothesis testing, its types, steps to perform the testing, and associated examples.

What is Hypothesis Testing in Statistics?

Hypothesis testing uses sample data from the population to draw useful conclusions regarding the population probability distribution . It tests an assumption made about the data using different types of hypothesis testing methodologies. The hypothesis testing results in either rejecting or not rejecting the null hypothesis.

Hypothesis Testing Definition

Hypothesis testing can be defined as a statistical tool that is used to identify if the results of an experiment are meaningful or not. It involves setting up a null hypothesis and an alternative hypothesis. These two hypotheses will always be mutually exclusive. This means that if the null hypothesis is true then the alternative hypothesis is false and vice versa. An example of hypothesis testing is setting up a test to check if a new medicine works on a disease in a more efficient manner.

Null Hypothesis

The null hypothesis is a concise mathematical statement that is used to indicate that there is no difference between two possibilities. In other words, there is no difference between certain characteristics of data. This hypothesis assumes that the outcomes of an experiment are based on chance alone. It is denoted as \(H_{0}\). Hypothesis testing is used to conclude if the null hypothesis can be rejected or not. Suppose an experiment is conducted to check if girls are shorter than boys at the age of 5. The null hypothesis will say that they are the same height.

Alternative Hypothesis

The alternative hypothesis is an alternative to the null hypothesis. It is used to show that the observations of an experiment are due to some real effect. It indicates that there is a statistical significance between two possible outcomes and can be denoted as \(H_{1}\) or \(H_{a}\). For the above-mentioned example, the alternative hypothesis would be that girls are shorter than boys at the age of 5.

Hypothesis Testing P Value

In hypothesis testing, the p value is used to indicate whether the results obtained after conducting a test are statistically significant or not. It also indicates the probability of making an error in rejecting or not rejecting the null hypothesis.This value is always a number between 0 and 1. The p value is compared to an alpha level, \(\alpha\) or significance level. The alpha level can be defined as the acceptable risk of incorrectly rejecting the null hypothesis. The alpha level is usually chosen between 1% to 5%.

Hypothesis Testing Critical region

All sets of values that lead to rejecting the null hypothesis lie in the critical region. Furthermore, the value that separates the critical region from the non-critical region is known as the critical value.

Hypothesis Testing Formula

Depending upon the type of data available and the size, different types of hypothesis testing are used to determine whether the null hypothesis can be rejected or not. The hypothesis testing formula for some important test statistics are given below:

• z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\). \(\overline{x}\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the population standard deviation and n is the size of the sample.
• t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\). s is the sample standard deviation.
• \(\chi ^{2} = \sum \frac{(O_{i}-E_{i})^{2}}{E_{i}}\). \(O_{i}\) is the observed value and \(E_{i}\) is the expected value.

We will learn more about these test statistics in the upcoming section.

Types of Hypothesis Testing

Selecting the correct test for performing hypothesis testing can be confusing. These tests are used to determine a test statistic on the basis of which the null hypothesis can either be rejected or not rejected. Some of the important tests used for hypothesis testing are given below.

Hypothesis Testing Z Test

A z test is a way of hypothesis testing that is used for a large sample size (n ≥ 30). It is used to determine whether there is a difference between the population mean and the sample mean when the population standard deviation is known. It can also be used to compare the mean of two samples. It is used to compute the z test statistic. The formulas are given as follows:

• One sample: z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).
• Two samples: z = \(\frac{(\overline{x_{1}}-\overline{x_{2}})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}\).

Hypothesis Testing t Test

The t test is another method of hypothesis testing that is used for a small sample size (n < 30). It is also used to compare the sample mean and population mean. However, the population standard deviation is not known. Instead, the sample standard deviation is known. The mean of two samples can also be compared using the t test.

• One sample: t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\).
• Two samples: t = \(\frac{(\overline{x_{1}}-\overline{x_{2}})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}\).

Hypothesis Testing Chi Square

The Chi square test is a hypothesis testing method that is used to check whether the variables in a population are independent or not. It is used when the test statistic is chi-squared distributed.

One Tailed Hypothesis Testing

One tailed hypothesis testing is done when the rejection region is only in one direction. It can also be known as directional hypothesis testing because the effects can be tested in one direction only. This type of testing is further classified into the right tailed test and left tailed test.

Right Tailed Hypothesis Testing

The right tail test is also known as the upper tail test. This test is used to check whether the population parameter is greater than some value. The null and alternative hypotheses for this test are given as follows:

\(H_{0}\): The population parameter is ≤ some value

\(H_{1}\): The population parameter is > some value.

If the test statistic has a greater value than the critical value then the null hypothesis is rejected

Left Tailed Hypothesis Testing

The left tail test is also known as the lower tail test. It is used to check whether the population parameter is less than some value. The hypotheses for this hypothesis testing can be written as follows:

\(H_{0}\): The population parameter is ≥ some value

\(H_{1}\): The population parameter is < some value.

The null hypothesis is rejected if the test statistic has a value lesser than the critical value.

Two Tailed Hypothesis Testing

In this hypothesis testing method, the critical region lies on both sides of the sampling distribution. It is also known as a non - directional hypothesis testing method. The two-tailed test is used when it needs to be determined if the population parameter is assumed to be different than some value. The hypotheses can be set up as follows:

\(H_{0}\): the population parameter = some value

\(H_{1}\): the population parameter ≠ some value

The null hypothesis is rejected if the test statistic has a value that is not equal to the critical value.

Hypothesis Testing Steps

Hypothesis testing can be easily performed in five simple steps. The most important step is to correctly set up the hypotheses and identify the right method for hypothesis testing. The basic steps to perform hypothesis testing are as follows:

• Step 1: Set up the null hypothesis by correctly identifying whether it is the left-tailed, right-tailed, or two-tailed hypothesis testing.
• Step 2: Set up the alternative hypothesis.
• Step 3: Choose the correct significance level, \(\alpha\), and find the critical value.
• Step 4: Calculate the correct test statistic (z, t or \(\chi\)) and p-value.
• Step 5: Compare the test statistic with the critical value or compare the p-value with \(\alpha\) to arrive at a conclusion. In other words, decide if the null hypothesis is to be rejected or not.

Hypothesis Testing Example

The best way to solve a problem on hypothesis testing is by applying the 5 steps mentioned in the previous section. Suppose a researcher claims that the mean average weight of men is greater than 100kgs with a standard deviation of 15kgs. 30 men are chosen with an average weight of 112.5 Kgs. Using hypothesis testing, check if there is enough evidence to support the researcher's claim. The confidence interval is given as 95%.

Step 1: This is an example of a right-tailed test. Set up the null hypothesis as \(H_{0}\): \(\mu\) = 100.

Step 2: The alternative hypothesis is given by \(H_{1}\): \(\mu\) > 100.

Step 3: As this is a one-tailed test, \(\alpha\) = 100% - 95% = 5%. This can be used to determine the critical value.

1 - \(\alpha\) = 1 - 0.05 = 0.95

0.95 gives the required area under the curve. Now using a normal distribution table, the area 0.95 is at z = 1.645. A similar process can be followed for a t-test. The only additional requirement is to calculate the degrees of freedom given by n - 1.

Step 4: Calculate the z test statistic. This is because the sample size is 30. Furthermore, the sample and population means are known along with the standard deviation.

z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).

\(\mu\) = 100, \(\overline{x}\) = 112.5, n = 30, \(\sigma\) = 15

z = \(\frac{112.5-100}{\frac{15}{\sqrt{30}}}\) = 4.56

Step 5: Conclusion. As 4.56 > 1.645 thus, the null hypothesis can be rejected.

Hypothesis Testing and Confidence Intervals

Confidence intervals form an important part of hypothesis testing. This is because the alpha level can be determined from a given confidence interval. Suppose a confidence interval is given as 95%. Subtract the confidence interval from 100%. This gives 100 - 95 = 5% or 0.05. This is the alpha value of a one-tailed hypothesis testing. To obtain the alpha value for a two-tailed hypothesis testing, divide this value by 2. This gives 0.05 / 2 = 0.025.

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Important Notes on Hypothesis Testing

• Hypothesis testing is a technique that is used to verify whether the results of an experiment are statistically significant.
• It involves the setting up of a null hypothesis and an alternate hypothesis.
• There are three types of tests that can be conducted under hypothesis testing - z test, t test, and chi square test.
• Hypothesis testing can be classified as right tail, left tail, and two tail tests.

Examples on Hypothesis Testing

• Example 1: The average weight of a dumbbell in a gym is 90lbs. However, a physical trainer believes that the average weight might be higher. A random sample of 5 dumbbells with an average weight of 110lbs and a standard deviation of 18lbs. Using hypothesis testing check if the physical trainer's claim can be supported for a 95% confidence level. Solution: As the sample size is lesser than 30, the t-test is used. \(H_{0}\): \(\mu\) = 90, \(H_{1}\): \(\mu\) > 90 \(\overline{x}\) = 110, \(\mu\) = 90, n = 5, s = 18. \(\alpha\) = 0.05 Using the t-distribution table, the critical value is 2.132 t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\) t = 2.484 As 2.484 > 2.132, the null hypothesis is rejected. Answer: The average weight of the dumbbells may be greater than 90lbs
• Example 2: The average score on a test is 80 with a standard deviation of 10. With a new teaching curriculum introduced it is believed that this score will change. On random testing, the score of 38 students, the mean was found to be 88. With a 0.05 significance level, is there any evidence to support this claim? Solution: This is an example of two-tail hypothesis testing. The z test will be used. \(H_{0}\): \(\mu\) = 80, \(H_{1}\): \(\mu\) ≠ 80 \(\overline{x}\) = 88, \(\mu\) = 80, n = 36, \(\sigma\) = 10. \(\alpha\) = 0.05 / 2 = 0.025 The critical value using the normal distribution table is 1.96 z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\) z = \(\frac{88-80}{\frac{10}{\sqrt{36}}}\) = 4.8 As 4.8 > 1.96, the null hypothesis is rejected. Answer: There is a difference in the scores after the new curriculum was introduced.
• Example 3: The average score of a class is 90. However, a teacher believes that the average score might be lower. The scores of 6 students were randomly measured. The mean was 82 with a standard deviation of 18. With a 0.05 significance level use hypothesis testing to check if this claim is true. Solution: The t test will be used. \(H_{0}\): \(\mu\) = 90, \(H_{1}\): \(\mu\) < 90 \(\overline{x}\) = 110, \(\mu\) = 90, n = 6, s = 18 The critical value from the t table is -2.015 t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\) t = \(\frac{82-90}{\frac{18}{\sqrt{6}}}\) t = -1.088 As -1.088 > -2.015, we fail to reject the null hypothesis. Answer: There is not enough evidence to support the claim.

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FAQs on Hypothesis Testing

What is hypothesis testing.

Hypothesis testing in statistics is a tool that is used to make inferences about the population data. It is also used to check if the results of an experiment are valid.

What is the z Test in Hypothesis Testing?

The z test in hypothesis testing is used to find the z test statistic for normally distributed data . The z test is used when the standard deviation of the population is known and the sample size is greater than or equal to 30.

What is the t Test in Hypothesis Testing?

The t test in hypothesis testing is used when the data follows a student t distribution . It is used when the sample size is less than 30 and standard deviation of the population is not known.

What is the formula for z test in Hypothesis Testing?

The formula for a one sample z test in hypothesis testing is z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\) and for two samples is z = \(\frac{(\overline{x_{1}}-\overline{x_{2}})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}\).

What is the p Value in Hypothesis Testing?

The p value helps to determine if the test results are statistically significant or not. In hypothesis testing, the null hypothesis can either be rejected or not rejected based on the comparison between the p value and the alpha level.

What is One Tail Hypothesis Testing?

When the rejection region is only on one side of the distribution curve then it is known as one tail hypothesis testing. The right tail test and the left tail test are two types of directional hypothesis testing.

What is the Alpha Level in Two Tail Hypothesis Testing?

To get the alpha level in a two tail hypothesis testing divide \(\alpha\) by 2. This is done as there are two rejection regions in the curve.

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Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

• State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a  or H 1 ).
• Collect data in a way designed to test the hypothesis.
• Perform an appropriate statistical test .
• Decide whether to reject or fail to reject your null hypothesis.
• Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Table of contents

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

• H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

• an estimate of the difference in average height between the two groups.
• a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

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The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

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

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• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

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 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).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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Statistics By Jim

Making statistics intuitive

Hypothesis Testing: Uses, Steps & Example

By Jim Frost 4 Comments

What is Hypothesis Testing?

Hypothesis testing in statistics uses sample data to infer the properties of a whole population . These tests determine whether a random sample provides sufficient evidence to conclude an effect or relationship exists in the population. Researchers use them to help separate genuine population-level effects from false effects that random chance can create in samples. These methods are also known as significance testing.

For example, researchers are testing a new medication to see if it lowers blood pressure. They compare a group taking the drug to a control group taking a placebo. If their hypothesis test results are statistically significant, the medication’s effect of lowering blood pressure likely exists in the broader population, not just the sample studied.

Using Hypothesis Tests

A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement the sample data best supports. These two statements are called the null hypothesis and the alternative hypothesis . The following are typical examples:

• Null Hypothesis : The effect does not exist in the population.
• Alternative Hypothesis : The effect does exist in the population.

Hypothesis testing accounts for the inherent uncertainty of using a sample to draw conclusions about a population, which reduces the chances of false discoveries. These procedures determine whether the sample data are sufficiently inconsistent with the null hypothesis that you can reject it. If you can reject the null, your data favor the alternative statement that an effect exists in the population.

Statistical significance in hypothesis testing indicates that an effect you see in sample data also likely exists in the population after accounting for random sampling error , variability, and sample size. Your results are statistically significant when the p-value is less than your significance level or, equivalently, when your confidence interval excludes the null hypothesis value.

Conversely, non-significant results indicate that despite an apparent sample effect, you can’t be sure it exists in the population. It could be chance variation in the sample and not a genuine effect.

Learn more about Failing to Reject the Null .

5 Steps of Significance Testing

Hypothesis testing involves five key steps, each critical to validating a research hypothesis using statistical methods:

• Formulate the Hypotheses : Write your research hypotheses as a null hypothesis (H 0 ) and an alternative hypothesis (H A ).
• Data Collection : Gather data specifically aimed at testing the hypothesis.
• Conduct A Test : Use a suitable statistical test to analyze your data.
• Make a Decision : Based on the statistical test results, decide whether to reject the null hypothesis or fail to reject it.
• Report the Results : Summarize and present the outcomes in your report’s results and discussion sections.

While the specifics of these steps can vary depending on the research context and the data type, the fundamental process of hypothesis testing remains consistent across different studies.

Let’s work through these steps in an example!

Hypothesis Testing Example

Researchers want to determine if a new educational program improves student performance on standardized tests. They randomly assign 30 students to a control group , which follows the standard curriculum, and another 30 students to a treatment group, which participates in the new educational program. After a semester, they compare the test scores of both groups.

Download the CSV data file to perform the hypothesis testing yourself: Hypothesis_Testing .

The researchers write their hypotheses. These statements apply to the population, so they use the mu (μ) symbol for the population mean parameter .

• Null Hypothesis (H 0 ) : The population means of the test scores for the two groups are equal (μ 1 = μ 2 ).
• Alternative Hypothesis (H A ) : The population means of the test scores for the two groups are unequal (μ 1 ≠ μ 2 ).

Choosing the correct hypothesis test depends on attributes such as data type and number of groups. Because they’re using continuous data and comparing two means, the researchers use a 2-sample t-test .

Here are the results.

The treatment group’s mean is 58.70, compared to the control group’s mean of 48.12. The mean difference is 10.67 points. Use the test’s p-value and significance level to determine whether this difference is likely a product of random fluctuation in the sample or a genuine population effect.

Because the p-value (0.000) is less than the standard significance level of 0.05, the results are statistically significant, and we can reject the null hypothesis. The sample data provides sufficient evidence to conclude that the new program’s effect exists in the population.

Limitations

Hypothesis testing improves your effectiveness in making data-driven decisions. However, it is not 100% accurate because random samples occasionally produce fluky results. Hypothesis tests have two types of errors, both relating to drawing incorrect conclusions.

• Type I error: The test rejects a true null hypothesis—a false positive.
• Type II error: The test fails to reject a false null hypothesis—a false negative.

Learn more about Type I and Type II Errors .

Our exploration of hypothesis testing using a practical example of an educational program reveals its powerful ability to guide decisions based on statistical evidence. Whether you’re a student, researcher, or professional, understanding and applying these procedures can open new doors to discovering insights and making informed decisions. Let this tool empower your analytical endeavors as you navigate through the vast seas of data.

Learn more about the Hypothesis Tests for Various Data Types .

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Reader Interactions

June 10, 2024 at 10:51 am

Thank you, Jim, for another helpful article; timely too since I have started reading your new book on hypothesis testing and, now that we are at the end of the school year, my district is asking me to perform a number of evaluations on instructional programs. This is where my question/concern comes in. You mention that hypothesis testing is all about testing samples. However, I use all the students in my district when I make these comparisons. Since I am using the entire “population” in my evaluations (I don’t select a sample of third grade students, for example, but I use all 700 third graders), am I somehow misusing the tests? Or can I rest assured that my district’s student population is only a sample of the universal population of students?

June 10, 2024 at 1:50 pm

I hope you are finding the book helpful!

Yes, the purpose of hypothesis testing is to infer the properties of a population while accounting for random sampling error.

In your case, it comes down to how you want to use the results. Who do you want the results to apply to?

If you’re summarizing the sample, looking for trends and patterns, or evaluating those students and don’t plan to apply those results to other students, you don’t need hypothesis testing because there is no sampling error. They are the population and you can just use descriptive statistics. In this case, you’d only need to focus on the practical significance of the effect sizes.

On the other hand, if you want to apply the results from this group to other students, you’ll need hypothesis testing. However, there is the complicating issue of what population your sample of students represent. I’m sure your district has its own unique characteristics, demographics, etc. Your district’s students probably don’t adequately represent a universal population. At the very least, you’d need to recognize any special attributes of your district and how they could bias the results when trying to apply them outside the district. Or they might apply to similar districts in your region.

However, I’d imagine your 3rd graders probably adequately represent future classes of 3rd graders in your district. You need to be alert to changing demographics. At least in the short run I’d imagine they’d be representative of future classes.

Think about how these results will be used. Do they just apply to the students you measured? Then you don’t need hypothesis tests. However, if the results are being used to infer things about other students outside of the sample, you’ll need hypothesis testing along with considering how well your students represent the other students and how they differ.

I hope that helps!

June 10, 2024 at 3:21 pm

Thank you so much, Jim, for the suggestions in terms of what I need to think about and consider! You are always so clear in your explanations!!!!

June 10, 2024 at 3:22 pm

You’re very welcome! Best of luck with your evaluations!

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A Beginner's Guide to Hypothesis Testing: Key Concepts and Applications

• September 27, 2024

In our everyday lives, we often encounter statements and claims that we can't instantly verify. 

Have you ever questioned how to determine which statements are factual or validate them with certainty? 

Fortunately, there's a systematic way to find answers: Hypothesis Testing.

Hypothesis Testing is a fundamental concept in analytics and statistics, yet it remains a mystery to many. This method helps us understand and validate data and supports decision-making in various fields. 

Are you curious about how it works and why it's so crucial? 

Let's understand the hypothesis testing basics and explore its applications together.

What is hypothesis testing in statistics?

Hypothesis evaluation is a statistical method used to determine whether there is enough evidence in a sample of data to support a particular assumption. 

A statistical hypothesis test generally involves calculating a test statistic. The decision is then made by either comparing the test statistic to a crucial value or assessing the p-value derived from the test statistic.

The P-value in Hypothesis Testing

P-value helps determine whether to accept or reject the null hypothesis (H₀) during hypothesis testing.

Two types of errors in this process are:

• Type I error (α):

This happens when the null hypothesis is incorrectly rejected, meaning we think there's an effect or difference when there isn't.

It is denoted by α (significance level).

• Type II error (β)

This occurs when the null hypothesis gets incorrectly accepted, meaning we fail to detect an effect or difference that exists.

It is denoted by β (power level).

• Type I error: Rejecting something that's true.
• Type II error: Accepting something that's false.

Here's a simplified breakdown of the key components of hypothesis testing :

• Null Hypothesis (H₀): The default assumption that there's no significant effect or difference
• Alternative Hypothesis (H₁): The statement that challenges the null hypothesis, suggesting a significant effect
• P-Value : This tells you how likely it is that your results happened by chance. 
• Significance Level (α): Typically set at 0.05, this is the threshold used to conclude whether to reject the null hypothesis.

This process is often used in financial analysis to test the effectiveness of trading strategies, assess portfolio performance, or predict market trends.

Statistical Hypothesis Testing for Beginners: A Step-by-Step Guide

Applying hypothesis testing in finance requires a clear understanding of the steps involved. 

Here's a practical approach for beginners:

STEP 1: Define the Hypothesis

Start by formulating your null and alternative hypotheses. For example, you might hypothesise that a certain stock's returns outperform the market average.

STEP 2: Collect Data

Gather relevant financial data from reliable sources, ensuring that your sample size is appropriate to draw meaningful conclusions.

STEP 3: Choose the Right Test

Select a one-tailed or two-tailed test depending on the data type and your hypothesis. Two-tailed tests are commonly used for financial analysis to assess whether a parameter differs in either direction.

STEP 4: Calculate the Test Statistic

Use statistical software or a financial calculator to compute your test statistic and compare it to the critical value.

STEP 5: Interpret the Results

Based on the p-value, decide whether to reject or fail to reject the null hypothesis. If the p-value is below the significance level, it indicates that the null hypothesis is unlikely, and you may accept the alternative hypothesis.

Here's a quick reference table to help with your decisions:

  Real-Life Applications of Hypothesis Testing in Finance

The concept of hypothesis testing basics might sound theoretical, but its real-world applications are vast in the financial sector. 

Here's how professionals use it:

• Investment Portfolio Performance : Analysts often use statistical hypothesis testing for beginners to determine whether one investment portfolio performs better than another.
• Risk Assessment: Statistical testing helps evaluate market risk by testing assumptions about asset price movements and volatility.
• Forecasting Market Trends : Predicting future market trends using past data can be tricky, but research testing allows professionals to make more informed predictions by validating their assumptions.

Common Pitfalls to Avoid in Hypothesis Testing

Even seasoned professionals sometimes need to correct their theory testing analysis.

Here are some common mistakes you'll want to avoid:

Misinterpreting P-Values

A common misunderstanding is that a low p-value proves that the alternative hypothesis is correct. It just means there's strong evidence against the null hypothesis.

Ignoring Sample Size

Small sample sizes can also lead to misleading results, so ensuring that your data set is large enough to provide reliable insights is crucial.

Overfitting the Model

This happens when you tailor your hypothesis too closely to the sample data, resulting in a model that only holds up under different conditions.

By being aware of these pitfalls, you'll be better positioned to conduct accurate hypothesis tests in any financial scenario.

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Achieve a prestigious qualification in investment management and thrive in a competitive industry. Imarticus, a leading learning partner approved by the CFA Institute, offers the best CFA course . Benefit from Comprehensive Learning with top-tier materials from Kaplan Schweser, including books, study notes, and mock exams. 

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Q: What is hypothesis testing in finance?

A: This is a statistical method used in finance to validate assumptions or hypotheses about financial data, such as testing the performance of investment strategies.

Q: What are the types of hypothesis testing?

A: The two primary types are one-tailed and two-tailed tests. You can use one-tailed tests to assess a specific direction of effect, while you can use two-tailed tests to determine if there is any significant difference, regardless of the direction.

Q: What is a p-value in hypothesis testing?

A: A p-value indicates the probability that your observed results occurred by chance. A lower p-value suggests stronger evidence against the null hypothesis.

Q: Why is sample size important in hypothesis testing?

A: A larger sample size increases the reliability of results, reducing the risk of errors and providing more accurate conclusions in hypothesis testing.

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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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