what is testing of hypothesis in research

• How it works

"Christmas Offer"

Terms & conditions.

As the Christmas season is upon us, we find ourselves reflecting on the past year and those who we have helped to shape their future. It’s been quite a year for us all! The end of the year brings no greater joy than the opportunity to express to you Christmas greetings and good wishes.

At this special time of year, Research Prospect brings joyful discount of 10% on all its services. May your Christmas and New Year be filled with joy.

We are looking back with appreciation for your loyalty and looking forward to moving into the New Year together.

"Claim this offer"

In unfamiliar and hard times, we have stuck by you. This Christmas, Research Prospect brings you all the joy with exciting discount of 10% on all its services.

Offer valid till 5-1-2024

We love being your partner in success. We know you have been working hard lately, take a break this holiday season to spend time with your loved ones while we make sure you succeed in your academics

Discount code: RP0996Y

Hypothesis Testing – A Complete Guide with Examples

Published by Alvin Nicolas at August 14th, 2021 , Revised On October 26, 2023

In statistics, hypothesis testing is a critical tool. It allows us to make informed decisions about populations based on sample data. Whether you are a researcher trying to prove a scientific point, a marketer analysing A/B test results, or a manufacturer ensuring quality control, hypothesis testing plays a pivotal role. This guide aims to introduce you to the concept and walk you through real-world examples.

What is a Hypothesis and a Hypothesis Testing?

A hypothesis is considered a belief or assumption that has to be accepted, rejected, proved or disproved. In contrast, a research hypothesis is a research question for a researcher that has to be proven correct or incorrect through investigation.

What is Hypothesis Testing?

Hypothesis testing  is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an independent variable to a dependent variable.  

Example: The academic performance of student A is better than student B

Characteristics of the Hypothesis to be Tested

A hypothesis should be:

• Clear and precise
• Capable of being tested
• Able to relate to a variable
• Stated in simple terms
• Consistent with known facts
• Limited in scope and specific
• Tested in a limited timeframe
• Explain the facts in detail

What is a Null Hypothesis and Alternative Hypothesis?

A  null hypothesis  is a hypothesis when there is no significant relationship between the dependent and the participants’ independent  variables . 

In simple words, it’s a hypothesis that has been put forth but hasn’t been proved as yet. A researcher aims to disprove the theory. The abbreviation “Ho” is used to denote a null hypothesis.

If you want to compare two methods and assume that both methods are equally good, this assumption is considered the null hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is similar to the previous model of the car, on average. You can write it as: Ho: there is no difference between the mileage of both vehicles. If your findings don’t support your hypothesis and you get opposite results, this outcome will be considered an alternative hypothesis.

If you assume that one method is better than another method, then it’s considered an alternative hypothesis. The alternative hypothesis is the theory that a researcher seeks to prove and is typically denoted by H1 or HA.

If you support a null hypothesis, it means you’re not supporting the alternative hypothesis. Similarly, if you reject a null hypothesis, it means you are recommending the alternative hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is better than the previous model of the vehicle. You can write it as; Ha: the two vehicles have different mileage. On average/ the fuel consumption of the new vehicle model is better than the previous model.

If a null hypothesis is rejected during the hypothesis test, even if it’s true, then it is considered as a type-I error. On the other hand, if you don’t dismiss a hypothesis, even if it’s false because you could not identify its falseness, it’s considered a type-II error.

Hire an Expert Researcher

Orders completed by our expert writers are

• Formally drafted in academic style
• 100% Plagiarism free & 100% Confidential
• Never resold
• Include unlimited free revisions
• Completed to match exact client requirements

How to Conduct Hypothesis Testing?

Here is a step-by-step guide on how to conduct hypothesis testing.

Step 1: State the Null and Alternative Hypothesis

Once you develop a research hypothesis, it’s important to state it is as a Null hypothesis (Ho) and an Alternative hypothesis (Ha) to test it statistically.

A null hypothesis is a preferred choice as it provides the opportunity to test the theory. In contrast, you can accept the alternative hypothesis when the null hypothesis has been rejected.

Example: You want to identify a relationship between obesity of men and women and the modern living style. You develop a hypothesis that women, on average, gain weight quickly compared to men. Then you write it as: Ho: Women, on average, don’t gain weight quickly compared to men. Ha: Women, on average, gain weight quickly compared to men.

Step 2: Data Collection

Hypothesis testing follows the statistical method, and statistics are all about data. It’s challenging to gather complete information about a specific population you want to study. You need to  gather the data  obtained through a large number of samples from a specific population. 

Example: Suppose you want to test the difference in the rate of obesity between men and women. You should include an equal number of men and women in your sample. Then investigate various aspects such as their lifestyle, eating patterns and profession, and any other variables that may influence average weight. You should also determine your study’s scope, whether it applies to a specific group of population or worldwide population. You can use available information from various places, countries, and regions.

Step 3: Select Appropriate Statistical Test

There are many  types of statistical tests , but we discuss the most two common types below, such as One-sided and two-sided tests.

Note: Your choice of the type of test depends on the purpose of your study 

One-sided Test

In the one-sided test, the values of rejecting a null hypothesis are located in one tail of the probability distribution. The set of values is less or higher than the critical value of the test. It is also called a one-tailed test of significance.

Example: If you want to test that all mangoes in a basket are ripe. You can write it as: Ho: All mangoes in the basket, on average, are ripe. If you find all ripe mangoes in the basket, the null hypothesis you developed will be true.

Two-sided Test

In the two-sided test, the values of rejecting a null hypothesis are located on both tails of the probability distribution. The set of values is less or higher than the first critical value of the test and higher than the second critical value test. It is also called a two-tailed test of significance. 

Example: Nothing can be explicitly said whether all mangoes are ripe in the basket. If you reject the null hypothesis (Ho: All mangoes in the basket, on average, are ripe), then it means all mangoes in the basket are not likely to be ripe. A few mangoes could be raw as well.

Get statistical analysis help at an affordable price

• An expert statistician will complete your work
• Rigorous quality checks
• Confidentiality and reliability
• Any statistical software of your choice
• Free Plagiarism Report

Step 4: Select the Level of Significance

When you reject a null hypothesis, even if it’s true during a statistical hypothesis, it is considered the  significance level . It is the probability of a type one error. The significance should be as minimum as possible to avoid the type-I error, which is considered severe and should be avoided. 

If the significance level is minimum, then it prevents the researchers from false claims. 

The significance level is denoted by  P,  and it has given the value of 0.05 (P=0.05)

If the P-Value is less than 0.05, then the difference will be significant. If the P-value is higher than 0.05, then the difference is non-significant.

Example: Suppose you apply a one-sided test to test whether women gain weight quickly compared to men. You get to know about the average weight between men and women and the factors promoting weight gain.

Step 5: Find out Whether the Null Hypothesis is Rejected or Supported

After conducting a statistical test, you should identify whether your null hypothesis is rejected or accepted based on the test results. It would help if you observed the P-value for this.

Example: If you find the P-value of your test is less than 0.5/5%, then you need to reject your null hypothesis (Ho: Women, on average, don’t gain weight quickly compared to men). On the other hand, if a null hypothesis is rejected, then it means the alternative hypothesis might be true (Ha: Women, on average, gain weight quickly compared to men. If you find your test’s P-value is above 0.5/5%, then it means your null hypothesis is true.

Step 6: Present the Outcomes of your Study

The final step is to present the  outcomes of your study . You need to ensure whether you have met the objectives of your research or not. 

In the discussion section and  conclusion , you can present your findings by using supporting evidence and conclude whether your null hypothesis was rejected or supported.

In the result section, you can summarise your study’s outcomes, including the average difference and P-value of the two groups.

If we talk about the findings, our study your results will be as follows:

Example: In the study of identifying whether women gain weight quickly compared to men, we found the P-value is less than 0.5. Hence, we can reject the null hypothesis (Ho: Women, on average, don’t gain weight quickly than men) and conclude that women may likely gain weight quickly than men.

Did you know in your academic paper you should not mention whether you have accepted or rejected the null hypothesis? 

Always remember that you either conclude to reject Ho in favor of Haor   do not reject Ho . It would help if you never rejected  Ha  or even  accept Ha .

Suppose your null hypothesis is rejected in the hypothesis testing. If you conclude  reject Ho in favor of Haor   do not reject Ho,  then it doesn’t mean that the null hypothesis is true. It only means that there is a lack of evidence against Ho in favour of Ha. If your null hypothesis is not true, then the alternative hypothesis is likely to be true.

Example: We found that the P-value is less than 0.5. Hence, we can conclude reject Ho in favour of Ha (Ho: Women, on average, don’t gain weight quickly than men) reject Ho in favour of Ha. However, rejected in favour of Ha means (Ha: women may likely to gain weight quickly than men)

Frequently Asked Questions

What are the 3 types of hypothesis test.

The 3 types of hypothesis tests are:

• One-Sample Test : Compare sample data to a known population value.
• Two-Sample Test : Compare means between two sample groups.
• ANOVA : Analyze variance among multiple groups to determine significant differences.

What is a hypothesis?

A hypothesis is a proposed explanation or prediction about a phenomenon, often based on observations. It serves as a starting point for research or experimentation, providing a testable statement that can either be supported or refuted through data and analysis. In essence, it’s an educated guess that drives scientific inquiry.

What are null hypothesis?

A null hypothesis (often denoted as H0) suggests that there is no effect or difference in a study or experiment. It represents a default position or status quo. Statistical tests evaluate data to determine if there’s enough evidence to reject this null hypothesis.

What is the probability value?

The probability value, or p-value, is a measure used in statistics to determine the significance of an observed effect. It indicates the probability of obtaining the observed results, or more extreme, if the null hypothesis were true. A small p-value (typically <0.05) suggests evidence against the null hypothesis, warranting its rejection.

What is p value?

The p-value is a fundamental concept in statistical hypothesis testing. It represents the probability of observing a test statistic as extreme, or more so, than the one calculated from sample data, assuming the null hypothesis is true. A low p-value suggests evidence against the null, possibly justifying its rejection.

What is a t test?

A t-test is a statistical test used to compare the means of two groups. It determines if observed differences between the groups are statistically significant or if they likely occurred by chance. Commonly applied in research, there are different t-tests, including independent, paired, and one-sample, tailored to various data scenarios.

When to reject null hypothesis?

Reject the null hypothesis when the test statistic falls into a predefined rejection region or when the p-value is less than the chosen significance level (commonly 0.05). This suggests that the observed data is unlikely under the null hypothesis, indicating evidence for the alternative hypothesis. Always consider the study’s context.

You May Also Like

A meta-analysis is a formal, epidemiological, quantitative study design that uses statistical methods to generalise the findings of the selected independent studies.

Experimental research refers to the experiments conducted in the laboratory or under observation in controlled conditions. Here is all you need to know about experimental research.

A survey includes questions relevant to the research topic. The participants are selected, and the questionnaire is distributed to collect the data.

As Featured On

USEFUL LINKS

LEARNING RESOURCES

COMPANY DETAILS

Splash Sol LLC

• How It Works

• Hypothesis Testing: Definition, Uses, Limitations + Examples

Hypothesis testing is as old as the scientific method and is at the heart of the research process. 

Research exists to validate or disprove assumptions about various phenomena. The process of validation involves testing and it is in this context that we will explore hypothesis testing. 

What is a Hypothesis? 

A hypothesis is a calculated prediction or assumption about a population parameter based on limited evidence. The whole idea behind hypothesis formulation is testing—this means the researcher subjects his or her calculated assumption to a series of evaluations to know whether they are true or false. 

Typically, every research starts with a hypothesis—the investigator makes a claim and experiments to prove that this claim is true or false . For instance, if you predict that students who drink milk before class perform better than those who don’t, then this becomes a hypothesis that can be confirmed or refuted using an experiment.  

Read: What is Empirical Research Study? [Examples & Method]

What are the Types of Hypotheses? 

1. simple hypothesis.

Also known as a basic hypothesis, a simple hypothesis suggests that an independent variable is responsible for a corresponding dependent variable. In other words, an occurrence of the independent variable inevitably leads to an occurrence of the dependent variable. 

Typically, simple hypotheses are considered as generally true, and they establish a causal relationship between two variables. 

Examples of Simple Hypothesis  

• Drinking soda and other sugary drinks can cause obesity. 
• Smoking cigarettes daily leads to lung cancer.

2. Complex Hypothesis

A complex hypothesis is also known as a modal. It accounts for the causal relationship between two independent variables and the resulting dependent variables. This means that the combination of the independent variables leads to the occurrence of the dependent variables . 

Examples of Complex Hypotheses  

• Adults who do not smoke and drink are less likely to develop liver-related conditions.
• Global warming causes icebergs to melt which in turn causes major changes in weather patterns.

3. Null Hypothesis

As the name suggests, a null hypothesis is formed when a researcher suspects that there’s no relationship between the variables in an observation. In this case, the purpose of the research is to approve or disapprove this assumption. 

Examples of Null Hypothesis

• This is no significant change in a student’s performance if they drink coffee or tea before classes. 
• There’s no significant change in the growth of a plant if one uses distilled water only or vitamin-rich water. 

Read: Research Report: Definition, Types + [Writing Guide]

4. Alternative Hypothesis 

To disapprove a null hypothesis, the researcher has to come up with an opposite assumption—this assumption is known as the alternative hypothesis. This means if the null hypothesis says that A is false, the alternative hypothesis assumes that A is true. 

An alternative hypothesis can be directional or non-directional depending on the direction of the difference. A directional alternative hypothesis specifies the direction of the tested relationship, stating that one variable is predicted to be larger or smaller than the null value while a non-directional hypothesis only validates the existence of a difference without stating its direction. 

Examples of Alternative Hypotheses  

• Starting your day with a cup of tea instead of a cup of coffee can make you more alert in the morning. 
• The growth of a plant improves significantly when it receives distilled water instead of vitamin-rich water. 

5. Logical Hypothesis

Logical hypotheses are some of the most common types of calculated assumptions in systematic investigations. It is an attempt to use your reasoning to connect different pieces in research and build a theory using little evidence. In this case, the researcher uses any data available to him, to form a plausible assumption that can be tested. 

Examples of Logical Hypothesis

• Waking up early helps you to have a more productive day. 
• Beings from Mars would not be able to breathe the air in the atmosphere of the Earth. 

6. Empirical Hypothesis  

After forming a logical hypothesis, the next step is to create an empirical or working hypothesis. At this stage, your logical hypothesis undergoes systematic testing to prove or disprove the assumption. An empirical hypothesis is subject to several variables that can trigger changes and lead to specific outcomes. 

Examples of Empirical Testing 

• People who eat more fish run faster than people who eat meat.
• Women taking vitamin E grow hair faster than those taking vitamin K.

7. Statistical Hypothesis

When forming a statistical hypothesis, the researcher examines the portion of a population of interest and makes a calculated assumption based on the data from this sample. A statistical hypothesis is most common with systematic investigations involving a large target audience. Here, it’s impossible to collect responses from every member of the population so you have to depend on data from your sample and extrapolate the results to the wider population. 

Examples of Statistical Hypothesis  

• 45% of students in Louisiana have middle-income parents. 
• 80% of the UK’s population gets a divorce because of irreconcilable differences.

What is Hypothesis Testing? 

Hypothesis testing is an assessment method that allows researchers to determine the plausibility of a hypothesis. It involves testing an assumption about a specific population parameter to know whether it’s true or false. These population parameters include variance, standard deviation, and median. 

Typically, hypothesis testing starts with developing a null hypothesis and then performing several tests that support or reject the null hypothesis. The researcher uses test statistics to compare the association or relationship between two or more variables. 

Explore: Research Bias: Definition, Types + Examples

Researchers also use hypothesis testing to calculate the coefficient of variation and determine if the regression relationship and the correlation coefficient are statistically significant.

How Hypothesis Testing Works

The basis of hypothesis testing is to examine and analyze the null hypothesis and alternative hypothesis to know which one is the most plausible assumption. Since both assumptions are mutually exclusive, only one can be true. In other words, the occurrence of a null hypothesis destroys the chances of the alternative coming to life, and vice-versa. 

Interesting: 21 Chrome Extensions for Academic Researchers in 2021

What Are The Stages of Hypothesis Testing?  

To successfully confirm or refute an assumption, the researcher goes through five (5) stages of hypothesis testing; 

• Determine the null hypothesis
• Specify the alternative hypothesis
• Set the significance level
• Calculate the test statistics and corresponding P-value
• Draw your conclusion
• Determine the Null Hypothesis

Like we mentioned earlier, hypothesis testing starts with creating a null hypothesis which stands as an assumption that a certain statement is false or implausible. For example, the null hypothesis (H0) could suggest that different subgroups in the research population react to a variable in the same way. 

• Specify the Alternative Hypothesis

Once you know the variables for the null hypothesis, the next step is to determine the alternative hypothesis. The alternative hypothesis counters the null assumption by suggesting the statement or assertion is true. Depending on the purpose of your research, the alternative hypothesis can be one-sided or two-sided. 

Using the example we established earlier, the alternative hypothesis may argue that the different sub-groups react differently to the same variable based on several internal and external factors. 

• Set the Significance Level

Many researchers create a 5% allowance for accepting the value of an alternative hypothesis, even if the value is untrue. This means that there is a 0.05 chance that one would go with the value of the alternative hypothesis, despite the truth of the null hypothesis. 

Something to note here is that the smaller the significance level, the greater the burden of proof needed to reject the null hypothesis and support the alternative hypothesis.

Explore: What is Data Interpretation? + [Types, Method & Tools]

• Calculate the Test Statistics and Corresponding P-Value 

Test statistics in hypothesis testing allow you to compare different groups between variables while the p-value accounts for the probability of obtaining sample statistics if your null hypothesis is true. In this case, your test statistics can be the mean, median and similar parameters. 

If your p-value is 0.65, for example, then it means that the variable in your hypothesis will happen 65 in100 times by pure chance. Use this formula to determine the p-value for your data: 

• Draw Your Conclusions

After conducting a series of tests, you should be able to agree or refute the hypothesis based on feedback and insights from your sample data.  

Applications of Hypothesis Testing in Research

Hypothesis testing isn’t only confined to numbers and calculations; it also has several real-life applications in business, manufacturing, advertising, and medicine. 

In a factory or other manufacturing plants, hypothesis testing is an important part of quality and production control before the final products are approved and sent out to the consumer. 

During ideation and strategy development, C-level executives use hypothesis testing to evaluate their theories and assumptions before any form of implementation. For example, they could leverage hypothesis testing to determine whether or not some new advertising campaign, marketing technique, etc. causes increased sales. 

In addition, hypothesis testing is used during clinical trials to prove the efficacy of a drug or new medical method before its approval for widespread human usage. 

What is an Example of Hypothesis Testing?

An employer claims that her workers are of above-average intelligence. She takes a random sample of 20 of them and gets the following results: 

Mean IQ Scores: 110

Standard Deviation: 15 

Mean Population IQ: 100

Step 1: Using the value of the mean population IQ, we establish the null hypothesis as 100.

Step 2: State that the alternative hypothesis is greater than 100.

Step 3: State the alpha level as 0.05 or 5% 

Step 4: Find the rejection region area (given by your alpha level above) from the z-table. An area of .05 is equal to a z-score of 1.645.

Step 5: Calculate the test statistics using this formula

Z = (110–100) ÷ (15÷√20) 

10 ÷ 3.35 = 2.99 

If the value of the test statistics is higher than the value of the rejection region, then you should reject the null hypothesis. If it is less, then you cannot reject the null. 

In this case, 2.99 > 1.645 so we reject the null. 

Importance/Benefits of Hypothesis Testing 

The most significant benefit of hypothesis testing is it allows you to evaluate the strength of your claim or assumption before implementing it in your data set. Also, hypothesis testing is the only valid method to prove that something “is or is not”. Other benefits include: 

• Hypothesis testing provides a reliable framework for making any data decisions for your population of interest. 
• It helps the researcher to successfully extrapolate data from the sample to the larger population. 
• Hypothesis testing allows the researcher to determine whether the data from the sample is statistically significant. 
• Hypothesis testing is one of the most important processes for measuring the validity and reliability of outcomes in any systematic investigation. 
• It helps to provide links to the underlying theory and specific research questions.

Criticism and Limitations of Hypothesis Testing

Several limitations of hypothesis testing can affect the quality of data you get from this process. Some of these limitations include: 

• The interpretation of a p-value for observation depends on the stopping rule and definition of multiple comparisons. This makes it difficult to calculate since the stopping rule is subject to numerous interpretations, plus “multiple comparisons” are unavoidably ambiguous. 
• Conceptual issues often arise in hypothesis testing, especially if the researcher merges Fisher and Neyman-Pearson’s methods which are conceptually distinct. 
• In an attempt to focus on the statistical significance of the data, the researcher might ignore the estimation and confirmation by repeated experiments.
• Hypothesis testing can trigger publication bias, especially when it requires statistical significance as a criterion for publication.
• When used to detect whether a difference exists between groups, hypothesis testing can trigger absurd assumptions that affect the reliability of your observation.

Connect to Formplus, Get Started Now - It's Free!

• alternative hypothesis
• alternative vs null hypothesis
• complex hypothesis
• empirical hypothesis
• hypothesis testing
• logical hypothesis
• simple hypothesis
• statistical hypothesis
• busayo.longe

You may also like:

Internal Validity in Research: Definition, Threats, Examples

In this article, we will discuss the concept of internal validity, some clear examples, its importance, and how to test it.

What is Pure or Basic Research? + [Examples & Method]

Simple guide on pure or basic research, its methods, characteristics, advantages, and examples in science, medicine, education and psychology

Type I vs Type II Errors: Causes, Examples & Prevention

This article will discuss the two different types of errors in hypothesis testing and how you can prevent them from occurring in your research

Alternative vs Null Hypothesis: Pros, Cons, Uses & Examples

We are going to discuss alternative hypotheses and null hypotheses in this post and how they work in research.

Formplus - For Seamless Data Collection

Collect data the right way with a versatile data collection tool. try formplus and transform your work productivity today..

• Python for Data Science
• Data Analysis
• Machine Learning
• Deep Learning
• Deep Learning Interview Questions
• ML Projects
• ML Interview Questions

Understanding Hypothesis Testing

Hypothesis testing is a fundamental statistical method employed in various fields, including data science , machine learning , and statistics , to make informed decisions based on empirical evidence. It involves formulating assumptions about population parameters using sample statistics and rigorously evaluating these assumptions against collected data. At its core, hypothesis testing is a systematic approach that allows researchers to assess the validity of a statistical claim about an unknown population parameter. This article sheds light on the significance of hypothesis testing and the critical steps involved in the process.

Table of Content

What is Hypothesis Testing?

Why do we use hypothesis testing, one-tailed and two-tailed test, what are type 1 and type 2 errors in hypothesis testing, how does hypothesis testing work, real life examples of hypothesis testing, limitations of hypothesis testing.

A hypothesis is an assumption or idea, specifically a statistical claim about an unknown population parameter. For example, a judge assumes a person is innocent and verifies this by reviewing evidence and hearing testimony before reaching a verdict.

Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. 

To test the validity of the claim or assumption about the population parameter:

• A sample is drawn from the population and analyzed.
• The results of the analysis are used to decide whether the claim is true or not.

Example: You say an average height in the class is 30 or a boy is taller than a girl. All of these is an assumption that we are assuming, and we need some statistical way to prove these. We need some mathematical conclusion whatever we are assuming is true.

This structured approach to hypothesis testing in data science , hypothesis testing in machine learning , and hypothesis testing in statistics is crucial for making informed decisions based on data.

• By employing hypothesis testing in data analytics and other fields, practitioners can rigorously evaluate their assumptions and derive meaningful insights from their analyses.
• Understanding hypothesis generation and testing is also essential for effectively implementing statistical hypothesis testing in various applications.

Defining Hypotheses

• Null hypothesis (H 0 ): In statistics, the null hypothesis is a general statement or default position that there is no relationship between two measured cases or no relationship among groups. In other words, it is a basic assumption or made based on the problem knowledge. Example : A company’s mean production is 50 units/per da H 0 : [Tex]\mu [/Tex] = 50.
• Alternative hypothesis (H 1 ): The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis.  Example: A company’s production is not equal to 50 units/per day i.e. H 1 : [Tex]\mu [/Tex] [Tex]\ne [/Tex] 50.

Key Terms of Hypothesis Testing

• Level of significance : It refers to the degree of significance in which we accept or reject the null hypothesis. 100% accuracy is not possible for accepting a hypothesis, so we, therefore, select a level of significance that is usually 5%. This is normally denoted with  [Tex]\alpha[/Tex] and generally, it is 0.05 or 5%, which means your output should be 95% confident to give a similar kind of result in each sample.
• P-value: The P value , or calculated probability, is the probability of finding the observed/extreme results when the null hypothesis(H0) of a study-given problem is true. If your P-value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample claims to support the alternative hypothesis.
• Test Statistic: The test statistic is a numerical value calculated from sample data during a hypothesis test, used to determine whether to reject the null hypothesis. It is compared to a critical value or p-value to make decisions about the statistical significance of the observed results.
• Critical value : The critical value in statistics is a threshold or cutoff point used to determine whether to reject the null hypothesis in a hypothesis test.
• Degrees of freedom: Degrees of freedom are associated with the variability or freedom one has in estimating a parameter. The degrees of freedom are related to the sample size and determine the shape.

Hypothesis testing is an important procedure in statistics. Hypothesis testing evaluates two mutually exclusive population statements to determine which statement is most supported by sample data. When we say that the findings are statistically significant, thanks to hypothesis testing.

Understanding hypothesis testing in statistics is essential for data scientists and machine learning practitioners, as it provides a structured framework for statistical hypothesis generation and testing. This methodology can also be applied in hypothesis testing in Python , enabling data analysts to perform robust statistical analyses efficiently. By employing techniques such as multiple hypothesis testing in machine learning , researchers can ensure more reliable results and avoid potential pitfalls associated with drawing conclusions from statistical tests. 

One tailed test focuses on one direction, either greater than or less than a specified value. We use a one-tailed test when there is a clear directional expectation based on prior knowledge or theory. The critical region is located on only one side of the distribution curve. If the sample falls into this critical region, the null hypothesis is rejected in favor of the alternative hypothesis.

One-Tailed Test

There are two types of one-tailed test:

• Left-Tailed (Left-Sided) Test: The alternative hypothesis asserts that the true parameter value is less than the null hypothesis. Example: H 0 ​: [Tex]\mu \geq 50 [/Tex] and H 1 : [Tex]\mu < 50 [/Tex]
• Right-Tailed (Right-Sided) Test : The alternative hypothesis asserts that the true parameter value is greater than the null hypothesis. Example: H 0 : [Tex]\mu \leq50 [/Tex] and H 1 : [Tex]\mu > 50 [/Tex]

Two-Tailed Test

A two-tailed test considers both directions, greater than and less than a specified value.We use a two-tailed test when there is no specific directional expectation, and want to detect any significant difference.

Example: H 0 : [Tex]\mu = [/Tex] 50 and H 1 : [Tex]\mu \neq 50 [/Tex]

To delve deeper into differences into both types of test: Refer to link

In hypothesis testing, Type I and Type II errors are two possible errors that researchers can make when drawing conclusions about a population based on a sample of data. These errors are associated with the decisions made regarding the null hypothesis and the alternative hypothesis.

• Type I error: When we reject the null hypothesis, although that hypothesis was true. Type I error is denoted by alpha( [Tex]\alpha [/Tex] ).
• Type II errors : When we accept the null hypothesis, but it is false. Type II errors are denoted by beta( [Tex]\beta [/Tex] ).

Step 1: Define Null and Alternative Hypothesis

State the null hypothesis ( [Tex]H_0 [/Tex] ), representing no effect, and the alternative hypothesis ( [Tex]H_1 [/Tex] ​), suggesting an effect or difference.

We first identify the problem about which we want to make an assumption keeping in mind that our assumption should be contradictory to one another, assuming Normally distributed data.

Step 2 – Choose significance level

Select a significance level ( [Tex]\alpha [/Tex] ), typically 0.05, to determine the threshold for rejecting the null hypothesis. It provides validity to our hypothesis test, ensuring that we have sufficient data to back up our claims. Usually, we determine our significance level beforehand of the test. The p-value is the criterion used to calculate our significance value.

Step 3 – Collect and Analyze data.

Gather relevant data through observation or experimentation. Analyze the data using appropriate statistical methods to obtain a test statistic.

Step 4-Calculate Test Statistic

The data for the tests are evaluated in this step we look for various scores based on the characteristics of data. The choice of the test statistic depends on the type of hypothesis test being conducted.

There are various hypothesis tests, each appropriate for various goal to calculate our test. This could be a Z-test , Chi-square , T-test , and so on.

• Z-test : If population means and standard deviations are known. Z-statistic is commonly used.
• t-test : If population standard deviations are unknown. and sample size is small than t-test statistic is more appropriate.
• Chi-square test : Chi-square test is used for categorical data or for testing independence in contingency tables
• F-test : F-test is often used in analysis of variance (ANOVA) to compare variances or test the equality of means across multiple groups.

We have a smaller dataset, So, T-test is more appropriate to test our hypothesis.

T-statistic is a measure of the difference between the means of two groups relative to the variability within each group. It is calculated as the difference between the sample means divided by the standard error of the difference. It is also known as the t-value or t-score.

Step 5 – Comparing Test Statistic:

In this stage, we decide where we should accept the null hypothesis or reject the null hypothesis. There are two ways to decide where we should accept or reject the null hypothesis.

Method A: Using Crtical values

Comparing the test statistic and tabulated critical value we have,

• If Test Statistic>Critical Value: Reject the null hypothesis.
• If Test Statistic≤Critical Value: Fail to reject the null hypothesis.

Note: Critical values are predetermined threshold values that are used to make a decision in hypothesis testing. To determine critical values for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Method B: Using P-values

We can also come to an conclusion using the p-value,

• If the p-value is less than or equal to the significance level i.e. ( [Tex]p\leq\alpha [/Tex] ), you reject the null hypothesis. This indicates that the observed results are unlikely to have occurred by chance alone, providing evidence in favor of the alternative hypothesis.
• If the p-value is greater than the significance level i.e. ( [Tex]p\geq \alpha[/Tex] ), you fail to reject the null hypothesis. This suggests that the observed results are consistent with what would be expected under the null hypothesis.

Note : The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed in the sample, assuming the null hypothesis is true. To determine p-value for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Step 7- Interpret the Results

At last, we can conclude our experiment using method A or B.

Calculating test statistic

To validate our hypothesis about a population parameter we use statistical functions . We use the z-score, p-value, and level of significance(alpha) to make evidence for our hypothesis for normally distributed data .

1. Z-statistics:

When population means and standard deviations are known.

[Tex]z = \frac{\bar{x} – \mu}{\frac{\sigma}{\sqrt{n}}}[/Tex]

• [Tex]\bar{x} [/Tex] is the sample mean,
• μ represents the population mean, 
• σ is the standard deviation
• and n is the size of the sample.

2. T-Statistics

T test is used when n<30,

t-statistic calculation is given by:

[Tex]t=\frac{x̄-μ}{s/\sqrt{n}} [/Tex]

• t = t-score,
• x̄ = sample mean
• μ = population mean,
• s = standard deviation of the sample,
• n = sample size

3. Chi-Square Test

Chi-Square Test for Independence categorical Data (Non-normally distributed) using:

[Tex]\chi^2 = \sum \frac{(O_{ij} – E_{ij})^2}{E_{ij}}[/Tex]

• [Tex]O_{ij}[/Tex] is the observed frequency in cell [Tex]{ij} [/Tex]
• i,j are the rows and columns index respectively.
• [Tex]E_{ij}[/Tex] is the expected frequency in cell [Tex]{ij}[/Tex] , calculated as : [Tex]\frac{{\text{{Row total}} \times \text{{Column total}}}}{{\text{{Total observations}}}}[/Tex]

Let’s examine hypothesis testing using two real life situations,

Case A: D oes a New Drug Affect Blood Pressure?

Imagine a pharmaceutical company has developed a new drug that they believe can effectively lower blood pressure in patients with hypertension. Before bringing the drug to market, they need to conduct a study to assess its impact on blood pressure.

• Before Treatment: 120, 122, 118, 130, 125, 128, 115, 121, 123, 119
• After Treatment: 115, 120, 112, 128, 122, 125, 110, 117, 119, 114

Step 1 : Define the Hypothesis

• Null Hypothesis : (H 0 )The new drug has no effect on blood pressure.
• Alternate Hypothesis : (H 1 )The new drug has an effect on blood pressure.

Step 2: Define the Significance level

Let’s consider the Significance level at 0.05, indicating rejection of the null hypothesis.

If the evidence suggests less than a 5% chance of observing the results due to random variation.

Step 3 : Compute the test statistic

Using paired T-test analyze the data to obtain a test statistic and a p-value.

The test statistic (e.g., T-statistic) is calculated based on the differences between blood pressure measurements before and after treatment.

t = m/(s/√n)

• m  = mean of the difference i.e X after, X before
• s  = standard deviation of the difference (d) i.e d i ​= X after, i ​− X before,
• n  = sample size,

then, m= -3.9, s= 1.8 and n= 10

we, calculate the , T-statistic = -9 based on the formula for paired t test

Step 4: Find the p-value

The calculated t-statistic is -9 and degrees of freedom df = 9, you can find the p-value using statistical software or a t-distribution table.

thus, p-value = 8.538051223166285e-06

Step 5: Result

• If the p-value is less than or equal to 0.05, the researchers reject the null hypothesis.
• If the p-value is greater than 0.05, they fail to reject the null hypothesis.

Conclusion: Since the p-value (8.538051223166285e-06) is less than the significance level (0.05), the researchers reject the null hypothesis. There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.

Python Implementation of Case A

Let’s create hypothesis testing with python, where we are testing whether a new drug affects blood pressure. For this example, we will use a paired T-test. We’ll use the scipy.stats library for the T-test.

Scipy is a mathematical library in Python that is mostly used for mathematical equations and computations.

We will implement our first real life problem via python,

T-statistic (from scipy): -9.0 P-value (from scipy): 8.538051223166285e-06 T-statistic (calculated manually): -9.0 Decision: Reject the null hypothesis at alpha=0.05. Conclusion: There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.

In the above example, given the T-statistic of approximately -9 and an extremely small p-value, the results indicate a strong case to reject the null hypothesis at a significance level of 0.05. 

• The results suggest that the new drug, treatment, or intervention has a significant effect on lowering blood pressure.
• The negative T-statistic indicates that the mean blood pressure after treatment is significantly lower than the assumed population mean before treatment.

Case B : Cholesterol level in a population

Data: A sample of 25 individuals is taken, and their cholesterol levels are measured.

Cholesterol Levels (mg/dL): 205, 198, 210, 190, 215, 205, 200, 192, 198, 205, 198, 202, 208, 200, 205, 198, 205, 210, 192, 205, 198, 205, 210, 192, 205.

Populations Mean = 200

Population Standard Deviation (σ): 5 mg/dL(given for this problem)

Step 1: Define the Hypothesis

• Null Hypothesis (H 0 ): The average cholesterol level in a population is 200 mg/dL.
• Alternate Hypothesis (H 1 ): The average cholesterol level in a population is different from 200 mg/dL.

As the direction of deviation is not given , we assume a two-tailed test, and based on a normal distribution table, the critical values for a significance level of 0.05 (two-tailed) can be calculated through the z-table and are approximately -1.96 and 1.96.

The test statistic is calculated by using the z formula Z = [Tex](203.8 – 200) / (5 \div \sqrt{25}) [/Tex] ​ and we get accordingly , Z =2.039999999999992.

Step 4: Result

Since the absolute value of the test statistic (2.04) is greater than the critical value (1.96), we reject the null hypothesis. And conclude that, there is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL

Python Implementation of Case B

Reject the null hypothesis. There is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL.

Although hypothesis testing is a useful technique in data science , it does not offer a comprehensive grasp of the topic being studied.

• Lack of Comprehensive Insight : Hypothesis testing in data science often focuses on specific hypotheses, which may not fully capture the complexity of the phenomena being studied.
• Dependence on Data Quality : The accuracy of hypothesis testing results relies heavily on the quality of available data. Inaccurate data can lead to incorrect conclusions, particularly in hypothesis testing in machine learning .
• Overlooking Patterns : Sole reliance on hypothesis testing can result in the omission of significant patterns or relationships in the data that are not captured by the tested hypotheses.
• Contextual Limitations : Hypothesis testing in statistics may not reflect the broader context, leading to oversimplification of results.
• Complementary Methods Needed : To gain a more holistic understanding, it’s essential to complement hypothesis testing with other analytical approaches, especially in data analytics and data mining .
• Misinterpretation Risks : Poorly formulated hypotheses or inappropriate statistical methods can lead to misinterpretation, emphasizing the need for careful consideration in hypothesis testing in Python and related analyses.
• Multiple Hypothesis Testing Challenges : Multiple hypothesis testing in machine learning poses additional challenges, as it can increase the likelihood of Type I errors, requiring adjustments to maintain validity.

Hypothesis testing is a cornerstone of statistical analysis , allowing data scientists to navigate uncertainties and draw credible inferences from sample data. By defining null and alternative hypotheses, selecting significance levels, and employing statistical tests, researchers can validate their assumptions effectively.

This article emphasizes the distinction between Type I and Type II errors, highlighting their relevance in hypothesis testing in data science and machine learning . A practical example involving a paired T-test to assess a new drug’s effect on blood pressure underscores the importance of statistical rigor in data-driven decision-making .

Ultimately, understanding hypothesis testing in statistics , alongside its applications in data mining , data analytics , and hypothesis testing in Python , enhances analytical frameworks and supports informed decision-making.

Understanding Hypothesis Testing- FAQs

What is hypothesis testing in data science.

In data science, hypothesis testing is used to validate assumptions or claims about data. It helps data scientists determine whether observed patterns are statistically significant or could have occurred by chance.

How does hypothesis testing work in machine learning?

In machine learning, hypothesis testing helps assess the effectiveness of models. For example, it can be used to compare the performance of different algorithms or to evaluate whether a new feature significantly improves a model’s accuracy.

What is hypothesis testing in ML?

Statistical method to evaluate the performance and validity of machine learning models. Tests specific hypotheses about model behavior, like whether features influence predictions or if a model generalizes well to unseen data.

What is the difference between Pytest and hypothesis in Python?

Pytest purposes general testing framework for Python code while Hypothesis is a Property-based testing framework for Python, focusing on generating test cases based on specified properties of the code.

What is the difference between hypothesis testing and data mining?

Hypothesis testing focuses on evaluating specific claims or hypotheses about a dataset, while data mining involves exploring large datasets to discover patterns, relationships, or insights without predefined hypotheses.

How is hypothesis generation used in business analytics?

In business analytics , hypothesis generation involves formulating assumptions or predictions based on available data. These hypotheses can then be tested using statistical methods to inform decision-making and strategy.

What is the significance level in hypothesis testing?

The significance level, often denoted as alpha (α), is the threshold for deciding whether to reject the null hypothesis. Common significance levels are 0.05, 0.01, and 0.10, indicating the probability of making a Type I error in statistical hypothesis testing .

Similar Reads

• Data Analysis with Python In this article, we will discuss how to do data analysis with Python. We will discuss all sorts of data analysis i.e. analyzing numerical data with NumPy, Tabular data with Pandas, data visualization Matplotlib, and Exploratory data analysis.  Data Analysis With Python Data Analysis is the technique 15+ min read

Introduction to Data Analysis

• What is Data Analysis? Data analysis is an essential aspect of modern decision-making processes across various sectors, including business, healthcare, finance, and academia. As organizations generate massive amounts of data daily, understanding how to extract meaningful insights from this data becomes crucial. In this ar 13 min read
• Data Analytics and its type Data analytics is an important field that involves the process of collecting, processing, and interpreting data to uncover insights and help in making decisions. Data analytics is the practice of examining raw data to identify trends, draw conclusions, and extract meaningful information. This involv 9 min read
• How to Install Numpy on Windows? Python NumPy is a general-purpose array processing package that provides tools for handling n-dimensional arrays. It provides various computing tools such as comprehensive mathematical functions, and linear algebra routines. NumPy provides both the flexibility of Python and the speed of well-optimiz 3 min read
• How to Install Pandas in Python? Pandas in Python is a package that is written for data analysis and manipulation. Pandas offer various operations and data structures to perform numerical data manipulations and time series. Pandas is an open-source library that is built over Numpy libraries. Pandas library is known for its high pro 5 min read
• How to Install Matplotlib on python? Matplotlib is an amazing visualization library in Python for 2D plots of arrays. Matplotlib is a multi-platform data visualization library built on NumPy arrays and designed to work with the broader SciPy stack. In this article, we will look into the various process of installing Matplotlib on Windo 2 min read
• How to Install Python Tensorflow in Windows? Tensorflow is a free and open-source software library used to do computational mathematics to build machine learning models more profoundly deep learning models. It is a product of Google built by Google’s brain team, hence it provides a vast range of operations performance with ease that is compati 3 min read

Data Analysis Libraries

• Pandas Tutorial Pandas is an open-source library that is built on top of NumPy library. Pandas is mainly popular for importing and analyzing data much easier. Pandas is a Python library for data analysis and manipulation, with high-level data structures like Series and DataFrame.Pandas ensures compatibility with nu 5 min read
• NumPy Tutorial - Python Library NumPy is a general-purpose array-processing Python library which provides handy methods/functions for working n-dimensional arrays. NumPy is a short form for "Numerical Python". It provides various computing tools such as comprehensive mathematical functions, and linear algebra routines. NumPy provi 8 min read
• Data Analysis with SciPy Scipy is a Python library useful for solving many mathematical equations and algorithms. It is designed on the top of Numpy library that gives more extension of finding scientific mathematical formulae like Matrix Rank, Inverse, polynomial equations, LU Decomposition, etc. Using its high-level funct 6 min read
• Introduction to TensorFlow TensorFlow is an open-source machine learning library developed by Google. TensorFlow is used to build and train deep learning models as it facilitates the creation of computational graphs and efficient execution on various hardware platforms. The article provides an comprehensive overview of tensor 11 min read

Data Visulization Libraries

• Matplotlib Tutorial Matplotlib is easy to use and an amazing visualizing library in Python. It is built on NumPy arrays and designed to work with the broader SciPy stack and consists of several plots like line, bar, scatter, histogram, etc. In this article, you'll gain a comprehensive understanding of the diverse range 8 min read
• Python Seaborn Tutorial Seaborn is a library mostly used for statistical plotting in Python. It is built on top of Matplotlib and provides beautiful default styles and color palettes to make statistical plots more attractive. In this tutorial, we will learn about Python Seaborn from basics to advance using a huge dataset o 15+ min read
• Plotly tutorial Plotly library in Python is an open-source library that can be used for data visualization and understanding data simply and easily. Plotly supports various types of plots like line charts, scatter plots, histograms, box plots, etc. So you all must be wondering why Plotly is over other visualization 15+ min read
• Introduction to Bokeh in Python Bokeh is a Python interactive data visualization. Unlike Matplotlib and Seaborn, Bokeh renders its plots using HTML and JavaScript. It targets modern web browsers for presentation providing elegant, concise construction of novel graphics with high-performance interactivity. Features of Bokeh: Some o 1 min read

Exploratory Data Analysis (EDA)

• Univariate, Bivariate and Multivariate data and its analysis In this article,we will be discussing univariate, bivariate, and multivariate data and their analysis. Univariate data: Univariate data refers to a type of data in which each observation or data point corresponds to a single variable. In other words, it involves the measurement or observation of a s 5 min read
• Measures of Central Tendency in Statistics Central Tendencies in Statistics are the numerical values that are used to represent mid-value or central value a large collection of numerical data. These obtained numerical values are called central or average values in Statistics. A central or average value of any statistical data or series is th 10 min read
• Measures of Spread - Range, Variance, and Standard Deviation Collecting the data and representing it in form of tables, graphs, and other distributions is essential for us. But, it is also essential that we get a fair idea about how the data is distributed, how scattered it is, and what is the mean of the data. The measures of the mean are not enough to descr 9 min read
• Interquartile Range and Quartile Deviation using NumPy and SciPy In statistical analysis, understanding the spread or variability of a dataset is crucial for gaining insights into its distribution and characteristics. Two common measures used for quantifying this variability are the interquartile range (IQR) and quartile deviation. Quartiles Quartiles are a kind 6 min read
• Anova Formula ANOVA Test, or Analysis of Variance, is a statistical method used to test the differences between means of two or more groups. Developed by Ronald Fisher in the early 20th century, ANOVA helps determine whether there are any statistically significant differences between the means of three or more in 7 min read
• Skewness of Statistical Data Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. In simpler terms, it indicates whether the data is concentrated more on one side of the mean compared to the other side. Why is skewness important?Understanding the skewness of dat 5 min read
• How to Calculate Skewness and Kurtosis in Python? Skewness is a statistical term and it is a way to estimate or measure the shape of a distribution. It is an important statistical methodology that is used to estimate the asymmetrical behavior rather than computing frequency distribution. Skewness can be two types: Symmetrical: A distribution can be 3 min read
• Difference Between Skewness and Kurtosis What is Skewness? Skewness is an important statistical technique that helps to determine the asymmetrical behavior of the frequency distribution, or more precisely, the lack of symmetry of tails both left and right of the frequency curve. A distribution or dataset is symmetric if it looks the same t 4 min read
• Histogram | Meaning, Example, Types and Steps to Draw What is Histogram?A histogram is a graphical representation of the frequency distribution of continuous series using rectangles. The x-axis of the graph represents the class interval, and the y-axis shows the various frequencies corresponding to different class intervals. A histogram is a two-dimens 5 min read
• Interpretations of Histogram Histograms helps visualizing and comprehending the data distribution. The article aims to provide comprehensive overview of histogram and its interpretation. What is Histogram?Histograms are graphical representations of data distributions. They consist of bars, each representing the frequency or cou 7 min read
• Box Plot Box Plot is a graphical method to visualize data distribution for gaining insights and making informed decisions. Box plot is a type of chart that depicts a group of numerical data through their quartiles. In this article, we are going to discuss components of a box plot, how to create a box plot, u 7 min read
• Quantile Quantile plots The quantile-quantile( q-q plot) plot is a graphical method for determining if a dataset follows a certain probability distribution or whether two samples of data came from the same population or not. Q-Q plots are particularly useful for assessing whether a dataset is normally distributed or if it 8 min read
• What is Univariate, Bivariate & Multivariate Analysis in Data Visualisation? Data Visualisation is a graphical representation of information and data. By using different visual elements such as charts, graphs, and maps data visualization tools provide us with an accessible way to find and understand hidden trends and patterns in data. In this article, we are going to see abo 3 min read
• Using pandas crosstab to create a bar plot In this article, we will discuss how to create a bar plot by using pandas crosstab in Python. First Lets us know more about the crosstab, It is a simple cross-tabulation of two or more variables. What is cross-tabulation? It is a simple cross-tabulation that help us to understand the relationship be 3 min read
• Exploring Correlation in Python This article aims to give a better understanding of a very important technique of multivariate exploration. A correlation Matrix is basically a covariance matrix. Also known as the auto-covariance matrix, dispersion matrix, variance matrix, or variance-covariance matrix. It is a matrix in which the 4 min read
• Covariance and Correlation Covariance and correlation are the two key concepts in Statistics that help us analyze the relationship between two variables. Covariance measures how two variables change together, indicating whether they move in the same or opposite directions. In this article, we will learn about the differences 6 min read
• Factor Analysis | Data Analysis Factor analysis is a statistical method used to analyze the relationships among a set of observed variables by explaining the correlations or covariances between them in terms of a smaller number of unobserved variables called factors. Table of Content What is Factor Analysis?What does Factor mean i 13 min read
• Data Mining - Cluster Analysis INTRODUCTION: Cluster analysis, also known as clustering, is a method of data mining that groups similar data points together. The goal of cluster analysis is to divide a dataset into groups (or clusters) such that the data points within each group are more similar to each other than to data points 8 min read
• MANOVA Test in R Programming Multivariate analysis of variance (MANOVA) is simply an ANOVA (Analysis of variance) with several dependent variables. It is a continuation of the ANOVA. In an ANOVA, we test for statistical differences on one continuous dependent variable by an independent grouping variable. The MANOVA continues th 4 min read
• Python - Central Limit Theorem Central Limit Theorem (CLT) is a foundational principle in statistics, and implementing it using Python can significantly enhance data analysis capabilities. Statistics is an important part of data science projects. We use statistical tools whenever we want to make any inference about the population 7 min read
• Probability Distribution Function Probability Distribution refers to the function that gives the probability of all possible values of a random variable.It shows how the probabilities are assigned to the different possible values of the random variable.Common types of probability distributions Include: Binomial Distribution.Bernoull 9 min read
• Probability Density Estimation & Maximum Likelihood Estimation Probability density and maximum likelihood estimation (MLE) are key ideas in statistics that help us make sense of data. Probability Density Function (PDF) tells us how likely different outcomes are for a continuous variable, while Maximum Likelihood Estimation helps us find the best-fitting model f 8 min read
• Exponential Distribution in R Programming - dexp(), pexp(), qexp(), and rexp() Functions The exponential distribution in R Language is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. In R Programming Langu 2 min read
• Mathematics | Probability Distributions Set 4 (Binomial Distribution) The previous articles talked about some of the Continuous Probability Distributions. This article covers one of the distributions which are not continuous but discrete, namely the Binomial Distribution. Introduction - To understand the Binomial distribution, we must first understand what a Bernoulli 5 min read
• Poisson Distribution | Definition, Formula, Table and Examples The Poisson distribution is a type of discrete probability distribution that calculates the likelihood of a certain number of events happening in a fixed time or space, assuming the events occur independently and at a constant rate. It is characterized by a single parameter, λ (lambda), which repres 11 min read
• P-Value: Comprehensive Guide to Understand, Apply, and Interpret A p-value is a statistical metric used to assess a hypothesis by comparing it with observed data. This article delves into the concept of p-value, its calculation, interpretation, and significance. It also explores the factors that influence p-value and highlights its limitations. Table of Content W 12 min read
• Z-Score in Statistics | Definition, Formula, Calculation and Uses Z-Score in statistics is a measurement of how many standard deviations away a data point is from the mean of a distribution. A z-score of 0 indicates that the data point's score is the same as the mean score. A positive z-score indicates that the data point is above average, while a negative z-score 15+ min read
• How to Calculate Point Estimates in R? Point estimation is a technique used to find the estimate or approximate value of population parameters from a given data sample of the population. The point estimate is calculated for the following two measuring parameters: Measuring parameterPopulation ParameterPoint EstimateProportionπp Meanμx̄ T 3 min read
• Confidence Interval In the realm of statistics, precise estimation is paramount to drawing meaningful insights from data. One of the indispensable tools in this pursuit is the confidence interval. Confidence intervals provide a systematic approach to quantifying the uncertainty associated with sample statistics, offeri 12 min read
• Chi-square test in Machine Learning Chi-Square test is a statistical method crucial for analyzing associations in categorical data. Its applications span various fields, aiding researchers in understanding relationships between factors. This article elucidates Chi-Square types, steps for implementation, and its role in feature selecti 11 min read
• Understanding Hypothesis Testing Hypothesis testing is a fundamental statistical method employed in various fields, including data science, machine learning, and statistics, to make informed decisions based on empirical evidence. It involves formulating assumptions about population parameters using sample statistics and rigorously 15+ min read

Data Preprocessing

• ML | Data Preprocessing in Python In order to derive knowledge and insights from data, the area of data science integrates statistical analysis, machine learning, and computer programming. It entails gathering, purifying, and converting unstructured data into a form that can be analysed and visualised. Data scientists process and an 7 min read
• ML | Overview of Data Cleaning Data cleaning is one of the important parts of machine learning. It plays a significant part in building a model. In this article, we'll understand Data cleaning, its significance and Python implementation. What is Data Cleaning?Data cleaning is a crucial step in the machine learning (ML) pipeline, 15 min read
• ML | Handling Missing Values Missing values are a common issue in machine learning. This occurs when a particular variable lacks data points, resulting in incomplete information and potentially harming the accuracy and dependability of your models. It is essential to address missing values efficiently to ensure strong and impar 12 min read
• Detect and Remove the Outliers using Python Outliers, deviating significantly from the norm, can distort measures of central tendency and affect statistical analyses. The piece explores common causes of outliers, from errors to intentional introduction, and highlights their relevance in outlier mining during data analysis. The article delves 10 min read

Data Transformation

• Data Normalization Machine Learning Normalization is an essential step in the preprocessing of data for machine learning models, and it is a feature scaling technique. Normalization is especially crucial for data manipulation, scaling down, or up the range of data before it is utilized for subsequent stages in the fields of soft compu 9 min read
• Sampling distribution Using Python There are different types of distributions that we study in statistics like normal/gaussian distribution, exponential distribution, binomial distribution, and many others. We will study one such distribution today which is Sampling Distribution. Let's say we have some data then if we sample some fin 3 min read

Time Series Data Analysis

• Data Mining - Time-Series, Symbolic and Biological Sequences Data Data mining refers to extracting or mining knowledge from large amounts of data. In other words, Data mining is the science, art, and technology of discovering large and complex bodies of data in order to discover useful patterns. Theoreticians and practitioners are continually seeking improved tech 3 min read
• Basic DateTime Operations in Python Python has an in-built module named DateTime to deal with dates and times in numerous ways. In this article, we are going to see basic DateTime operations in Python. There are six main object classes with their respective components in the datetime module mentioned below: datetime.datedatetime.timed 12 min read
• Time Series Analysis & Visualization in Python Every dataset has distinct qualities that function as essential aspects in the field of data analytics, providing insightful information about the underlying data. Time series data is one kind of dataset that is especially important. This article delves into the complexities of time series datasets, 11 min read
• How to deal with missing values in a Timeseries in Python? It is common to come across missing values when working with real-world data. Time series data is different from traditional machine learning datasets because it is collected under varying conditions over time. As a result, different mechanisms can be responsible for missing records at different tim 10 min read
• How to calculate MOVING AVERAGE in a Pandas DataFrame? Calculating the moving average in a Pandas DataFrame is used for smoothing time series data and identifying trends. The moving average, also known as the rolling mean, helps reduce noise and highlight significant patterns by averaging data points over a specific window. In Pandas, this can be achiev 7 min read
• What is a trend in time series? Time series data is a sequence of data points that measure some variable over ordered period of time. It is the fastest-growing category of databases as it is widely used in a variety of industries to understand and forecast data patterns. So while preparing this time series data for modeling it's i 3 min read
• How to Perform an Augmented Dickey-Fuller Test in R Augmented Dickey-Fuller Test: It is a common test in statistics and is used to check whether a given time series is at rest. A given time series can be called stationary or at rest if it doesn't have any trend and depicts a constant variance over time and follows autocorrelation structure over a per 3 min read
• AutoCorrelation Autocorrelation is a fundamental concept in time series analysis. Autocorrelation is a statistical concept that assesses the degree of correlation between the values of variable at different time points. The article aims to discuss the fundamentals and working of Autocorrelation. Table of Content Wh 10 min read

Case Studies and Projects

• Top 8 Free Dataset Sources to Use for Data Science Projects Did you think data is only for big companies and corporations to analyze and obtain business insights? No, data is also fun! There is nothing more interesting than analyzing a data set to find the correlations between the data and obtain unique insights. It’s almost like a mystery game where the dat 7 min read
• Step by Step Predictive Analysis - Machine Learning Predictive analytics involves certain manipulations on data from existing data sets with the goal of identifying some new trends and patterns. These trends and patterns are then used to predict future outcomes and trends. By performing predictive analysis, we can predict future trends and performanc 3 min read
• 6 Tips for Creating Effective Data Visualizations The reality of things has completely changed, making data visualization a necessary aspect when you intend to make any decision that impacts your business growth. Data is no longer for data professionals; it now serves as the center of all decisions you make on your daily operations. It's vital to e 6 min read
• Data Science
• data-science

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

An official website of the United States government

The .gov means it's official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you're on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings
• Browse Titles

NCBI Bookshelf. A service of the National Library of Medicine, National Institutes of Health.

StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-.

StatPearls [Internet].

Hypothesis testing, p values, confidence intervals, and significance.

Jacob Shreffler ; Martin R. Huecker .

Affiliations

Last Update: March 13, 2023 .

• Definition/Introduction

Medical providers often rely on evidence-based medicine to guide decision-making in practice. Often a research hypothesis is tested with results provided, typically with p values, confidence intervals, or both. Additionally, statistical or research significance is estimated or determined by the investigators. Unfortunately, healthcare providers may have different comfort levels in interpreting these findings, which may affect the adequate application of the data.

• Issues of Concern

Without a foundational understanding of hypothesis testing, p values, confidence intervals, and the difference between statistical and clinical significance, it may affect healthcare providers' ability to make clinical decisions without relying purely on the research investigators deemed level of significance. Therefore, an overview of these concepts is provided to allow medical professionals to use their expertise to determine if results are reported sufficiently and if the study outcomes are clinically appropriate to be applied in healthcare practice.

Hypothesis Testing

Investigators conducting studies need research questions and hypotheses to guide analyses. Starting with broad research questions (RQs), investigators then identify a gap in current clinical practice or research. Any research problem or statement is grounded in a better understanding of relationships between two or more variables. For this article, we will use the following research question example:

Research Question: Is Drug 23 an effective treatment for Disease A?

Research questions do not directly imply specific guesses or predictions; we must formulate research hypotheses. A hypothesis is a predetermined declaration regarding the research question in which the investigator(s) makes a precise, educated guess about a study outcome. This is sometimes called the alternative hypothesis and ultimately allows the researcher to take a stance based on experience or insight from medical literature. An example of a hypothesis is below.

Research Hypothesis: Drug 23 will significantly reduce symptoms associated with Disease A compared to Drug 22.

The null hypothesis states that there is no statistical difference between groups based on the stated research hypothesis.

Researchers should be aware of journal recommendations when considering how to report p values, and manuscripts should remain internally consistent.

Regarding p values, as the number of individuals enrolled in a study (the sample size) increases, the likelihood of finding a statistically significant effect increases. With very large sample sizes, the p-value can be very low significant differences in the reduction of symptoms for Disease A between Drug 23 and Drug 22. The null hypothesis is deemed true until a study presents significant data to support rejecting the null hypothesis. Based on the results, the investigators will either reject the null hypothesis (if they found significant differences or associations) or fail to reject the null hypothesis (they could not provide proof that there were significant differences or associations).

To test a hypothesis, researchers obtain data on a representative sample to determine whether to reject or fail to reject a null hypothesis. In most research studies, it is not feasible to obtain data for an entire population. Using a sampling procedure allows for statistical inference, though this involves a certain possibility of error. [1]  When determining whether to reject or fail to reject the null hypothesis, mistakes can be made: Type I and Type II errors. Though it is impossible to ensure that these errors have not occurred, researchers should limit the possibilities of these faults. [2]

Significance

Significance is a term to describe the substantive importance of medical research. Statistical significance is the likelihood of results due to chance. [3]  Healthcare providers should always delineate statistical significance from clinical significance, a common error when reviewing biomedical research. [4]  When conceptualizing findings reported as either significant or not significant, healthcare providers should not simply accept researchers' results or conclusions without considering the clinical significance. Healthcare professionals should consider the clinical importance of findings and understand both p values and confidence intervals so they do not have to rely on the researchers to determine the level of significance. [5]  One criterion often used to determine statistical significance is the utilization of p values.

P values are used in research to determine whether the sample estimate is significantly different from a hypothesized value. The p-value is the probability that the observed effect within the study would have occurred by chance if, in reality, there was no true effect. Conventionally, data yielding a p<0.05 or p<0.01 is considered statistically significant. While some have debated that the 0.05 level should be lowered, it is still universally practiced. [6]  Hypothesis testing allows us to determine the size of the effect.

An example of findings reported with p values are below:

Statement: Drug 23 reduced patients' symptoms compared to Drug 22. Patients who received Drug 23 (n=100) were 2.1 times less likely than patients who received Drug 22 (n = 100) to experience symptoms of Disease A, p<0.05.

Statement:Individuals who were prescribed Drug 23 experienced fewer symptoms (M = 1.3, SD = 0.7) compared to individuals who were prescribed Drug 22 (M = 5.3, SD = 1.9). This finding was statistically significant, p= 0.02.

For either statement, if the threshold had been set at 0.05, the null hypothesis (that there was no relationship) should be rejected, and we should conclude significant differences. Noticeably, as can be seen in the two statements above, some researchers will report findings with < or > and others will provide an exact p-value (0.000001) but never zero [6] . When examining research, readers should understand how p values are reported. The best practice is to report all p values for all variables within a study design, rather than only providing p values for variables with significant findings. [7]  The inclusion of all p values provides evidence for study validity and limits suspicion for selective reporting/data mining.  

While researchers have historically used p values, experts who find p values problematic encourage the use of confidence intervals. [8] . P-values alone do not allow us to understand the size or the extent of the differences or associations. [3]  In March 2016, the American Statistical Association (ASA) released a statement on p values, noting that scientific decision-making and conclusions should not be based on a fixed p-value threshold (e.g., 0.05). They recommend focusing on the significance of results in the context of study design, quality of measurements, and validity of data. Ultimately, the ASA statement noted that in isolation, a p-value does not provide strong evidence. [9]

When conceptualizing clinical work, healthcare professionals should consider p values with a concurrent appraisal study design validity. For example, a p-value from a double-blinded randomized clinical trial (designed to minimize bias) should be weighted higher than one from a retrospective observational study [7] . The p-value debate has smoldered since the 1950s [10] , and replacement with confidence intervals has been suggested since the 1980s. [11]

Confidence Intervals

A confidence interval provides a range of values within given confidence (e.g., 95%), including the accurate value of the statistical constraint within a targeted population. [12]  Most research uses a 95% CI, but investigators can set any level (e.g., 90% CI, 99% CI). [13]  A CI provides a range with the lower bound and upper bound limits of a difference or association that would be plausible for a population. [14]  Therefore, a CI of 95% indicates that if a study were to be carried out 100 times, the range would contain the true value in 95, [15]  confidence intervals provide more evidence regarding the precision of an estimate compared to p-values. [6]

In consideration of the similar research example provided above, one could make the following statement with 95% CI:

Statement: Individuals who were prescribed Drug 23 had no symptoms after three days, which was significantly faster than those prescribed Drug 22; there was a mean difference between the two groups of days to the recovery of 4.2 days (95% CI: 1.9 – 7.8).

It is important to note that the width of the CI is affected by the standard error and the sample size; reducing a study sample number will result in less precision of the CI (increase the width). [14]  A larger width indicates a smaller sample size or a larger variability. [16]  A researcher would want to increase the precision of the CI. For example, a 95% CI of 1.43 – 1.47 is much more precise than the one provided in the example above. In research and clinical practice, CIs provide valuable information on whether the interval includes or excludes any clinically significant values. [14]

Null values are sometimes used for differences with CI (zero for differential comparisons and 1 for ratios). However, CIs provide more information than that. [15]  Consider this example: A hospital implements a new protocol that reduced wait time for patients in the emergency department by an average of 25 minutes (95% CI: -2.5 – 41 minutes). Because the range crosses zero, implementing this protocol in different populations could result in longer wait times; however, the range is much higher on the positive side. Thus, while the p-value used to detect statistical significance for this may result in "not significant" findings, individuals should examine this range, consider the study design, and weigh whether or not it is still worth piloting in their workplace.

Similarly to p-values, 95% CIs cannot control for researchers' errors (e.g., study bias or improper data analysis). [14]  In consideration of whether to report p-values or CIs, researchers should examine journal preferences. When in doubt, reporting both may be beneficial. [13]  An example is below:

Reporting both: Individuals who were prescribed Drug 23 had no symptoms after three days, which was significantly faster than those prescribed Drug 22, p = 0.009. There was a mean difference between the two groups of days to the recovery of 4.2 days (95% CI: 1.9 – 7.8).

• Clinical Significance

Recall that clinical significance and statistical significance are two different concepts. Healthcare providers should remember that a study with statistically significant differences and large sample size may be of no interest to clinicians, whereas a study with smaller sample size and statistically non-significant results could impact clinical practice. [14]  Additionally, as previously mentioned, a non-significant finding may reflect the study design itself rather than relationships between variables.

Healthcare providers using evidence-based medicine to inform practice should use clinical judgment to determine the practical importance of studies through careful evaluation of the design, sample size, power, likelihood of type I and type II errors, data analysis, and reporting of statistical findings (p values, 95% CI or both). [4]  Interestingly, some experts have called for "statistically significant" or "not significant" to be excluded from work as statistical significance never has and will never be equivalent to clinical significance. [17]

The decision on what is clinically significant can be challenging, depending on the providers' experience and especially the severity of the disease. Providers should use their knowledge and experiences to determine the meaningfulness of study results and make inferences based not only on significant or insignificant results by researchers but through their understanding of study limitations and practical implications.

• Nursing, Allied Health, and Interprofessional Team Interventions

All physicians, nurses, pharmacists, and other healthcare professionals should strive to understand the concepts in this chapter. These individuals should maintain the ability to review and incorporate new literature for evidence-based and safe care. 

• Review Questions
• Access free multiple choice questions on this topic.
• Comment on this article.

Disclosure: Jacob Shreffler declares no relevant financial relationships with ineligible companies.

Disclosure: Martin Huecker declares no relevant financial relationships with ineligible companies.

This book is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ), which permits others to distribute the work, provided that the article is not altered or used commercially. You are not required to obtain permission to distribute this article, provided that you credit the author and journal.

• Cite this Page Shreffler J, Huecker MR. Hypothesis Testing, P Values, Confidence Intervals, and Significance. [Updated 2023 Mar 13]. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-.

In this Page

Bulk download.

• Bulk download StatPearls data from FTP

Related information

• PMC PubMed Central citations
• PubMed Links to PubMed

Similar articles in PubMed

• The reporting of p values, confidence intervals and statistical significance in Preventive Veterinary Medicine (1997-2017). [PeerJ. 2021] The reporting of p values, confidence intervals and statistical significance in Preventive Veterinary Medicine (1997-2017). Messam LLM, Weng HY, Rosenberger NWY, Tan ZH, Payet SDM, Santbakshsing M. PeerJ. 2021; 9:e12453. Epub 2021 Nov 24.
• Review Clinical versus statistical significance: interpreting P values and confidence intervals related to measures of association to guide decision making. [J Pharm Pract. 2010] Review Clinical versus statistical significance: interpreting P values and confidence intervals related to measures of association to guide decision making. Ferrill MJ, Brown DA, Kyle JA. J Pharm Pract. 2010 Aug; 23(4):344-51. Epub 2010 Apr 13.
• Interpreting "statistical hypothesis testing" results in clinical research. [J Ayurveda Integr Med. 2012] Interpreting "statistical hypothesis testing" results in clinical research. Sarmukaddam SB. J Ayurveda Integr Med. 2012 Apr; 3(2):65-9.
• Confidence intervals in procedural dermatology: an intuitive approach to interpreting data. [Dermatol Surg. 2005] Confidence intervals in procedural dermatology: an intuitive approach to interpreting data. Alam M, Barzilai DA, Wrone DA. Dermatol Surg. 2005 Apr; 31(4):462-6.
• Review Is statistical significance testing useful in interpreting data? [Reprod Toxicol. 1993] Review Is statistical significance testing useful in interpreting data? Savitz DA. Reprod Toxicol. 1993; 7(2):95-100.

Recent Activity

• Hypothesis Testing, P Values, Confidence Intervals, and Significance - StatPearl... Hypothesis Testing, P Values, Confidence Intervals, and Significance - StatPearls

Your browsing activity is empty.

Activity recording is turned off.

Turn recording back on

Connect with NLM

National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894

Web Policies FOIA HHS Vulnerability Disclosure

Help Accessibility Careers

An official website of the United States government

Official websites use .gov A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS A lock ( Lock Locked padlock icon ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

• Publications
• Account settings
• Advanced Search
• Journal List

Hypothesis tests

• Author information
• Article notes
• Copyright and License information

Accepted 2019 Mar 28; Issue date 2019 Jul.

Key points.

Hypothesis tests are used to assess whether a difference between two samples represents a real difference between the populations from which the samples were taken.

A null hypothesis of ‘no difference’ is taken as a starting point, and we calculate the probability that both sets of data came from the same population. This probability is expressed as a p -value.

When the null hypothesis is false, p- values tend to be small. When the null hypothesis is true, any p- value is equally likely.

Learning objectives.

By reading this article, you should be able to:

Explain why hypothesis testing is used.

Use a table to determine which hypothesis test should be used for a particular situation.

Interpret a p- value.

A hypothesis test is a procedure used in statistics to assess whether a particular viewpoint is likely to be true. They follow a strict protocol, and they generate a ‘ p- value’, on the basis of which a decision is made about the truth of the hypothesis under investigation. All of the routine statistical ‘tests’ used in research— t- tests, χ 2 tests, Mann–Whitney tests, etc.—are all hypothesis tests, and in spite of their differences they are all used in essentially the same way. But why do we use them at all?

Comparing the heights of two individuals is easy: we can measure their height in a standardised way and compare them. When we want to compare the heights of two small well-defined groups (for example two groups of children), we need to use a summary statistic that we can calculate for each group. Such summaries (means, medians, etc.) form the basis of descriptive statistics, and are well described elsewhere. 1 However, a problem arises when we try to compare very large groups or populations: it may be impractical or even impossible to take a measurement from everyone in the population, and by the time you do so, the population itself will have changed. A similar problem arises when we try to describe the effects of drugs—for example by how much on average does a particular vasopressor increase MAP?

To solve this problem, we use random samples to estimate values for populations. By convention, the values we calculate from samples are referred to as statistics and denoted by Latin letters ( x ¯ for sample mean; SD for sample standard deviation) while the unknown population values are called parameters , and denoted by Greek letters (μ for population mean, σ for population standard deviation).

Inferential statistics describes the methods we use to estimate population parameters from random samples; how we can quantify the level of inaccuracy in a sample statistic; and how we can go on to use these estimates to compare populations.

Sampling error

There are many reasons why a sample may give an inaccurate picture of the population it represents: it may be biased, it may not be big enough, and it may not be truly random. However, even if we have been careful to avoid these pitfalls, there is an inherent difference between the sample and the population at large. To illustrate this, let us imagine that the actual average height of males in London is 174 cm. If I were to sample 100 male Londoners and take a mean of their heights, I would be very unlikely to get exactly 174 cm. Furthermore, if somebody else were to perform the same exercise, it would be unlikely that they would get the same answer as I did. The sample mean is different each time it is taken, and the way it differs from the actual mean of the population is described by the standard error of the mean (standard error, or SEM ). The standard error is larger if there is a lot of variation in the population, and becomes smaller as the sample size increases. It is calculated thus:

where SD is the sample standard deviation, and n is the sample size.

As errors are normally distributed, we can use this to estimate a 95% confidence interval on our sample mean as follows:

We can interpret this as meaning ‘We are 95% confident that the actual mean is within this range.’

Some confusion arises at this point between the SD and the standard error. The SD is a measure of variation in the sample. The range x ¯ ± ( 1.96 × SD ) will normally contain 95% of all your data. It can be used to illustrate the spread of the data and shows what values are likely. In contrast, standard error tells you about the precision of the mean and is used to calculate confidence intervals.

One straightforward way to compare two samples is to use confidence intervals. If we calculate the mean height of two groups and find that the 95% confidence intervals do not overlap, this can be taken as evidence of a difference between the two means. This method of statistical inference is reasonably intuitive and can be used in many situations. 2 Many journals, however, prefer to report inferential statistics using p -values.

Inference testing using a null hypothesis

In 1925, the British statistician R.A. Fisher described a technique for comparing groups using a null hypothesis , a method which has dominated statistical comparison ever since. The technique itself is rather straightforward, but often gets lost in the mechanics of how it is done. To illustrate, imagine we want to compare the HR of two different groups of people. We take a random sample from each group, which we call our data. Then:

Assume that both samples came from the same group. This is our ‘null hypothesis’.

Calculate the probability that an experiment would give us these data, assuming that the null hypothesis is true. We express this probability as a p- value, a number between 0 and 1, where 0 is ‘impossible’ and 1 is ‘certain’.

If the probability of the data is low, we reject the null hypothesis and conclude that there must be a difference between the two groups.

Formally, we can define a p- value as ‘the probability of finding the observed result or a more extreme result, if the null hypothesis were true.’ Standard practice is to set a cut-off at p <0.05 (this cut-off is termed the alpha value). If the null hypothesis were true, a result such as this would only occur 5% of the time or less; this in turn would indicate that the null hypothesis itself is unlikely. Fisher described the process as follows: ‘Set a low standard of significance at the 5 per cent point, and ignore entirely all results which fail to reach this level. A scientific fact should be regarded as experimentally established only if a properly designed experiment rarely fails to give this level of significance.’ 3 This probably remains the most succinct description of the procedure.

A question which often arises at this point is ‘Why do we use a null hypothesis?’ The simple answer is that it is easy: we can readily describe what we would expect of our data under a null hypothesis, we know how data would behave, and we can readily work out the probability of getting the result that we did. It therefore makes a very simple starting point for our probability assessment. All probabilities require a set of starting conditions, in much the same way that measuring the distance to London needs a starting point. The null hypothesis can be thought of as an easy place to put the start of your ruler.

If a null hypothesis is rejected, an alternate hypothesis must be adopted in its place. The null and alternate hypotheses must be mutually exclusive, but must also between them describe all situations. If a null hypothesis is ‘no difference exists’ then the alternate should be simply ‘a difference exists’.

Hypothesis testing in practice

The components of a hypothesis test can be readily described using the acronym GOST: identify the Groups you wish to compare; define the Outcome to be measured; collect and Summarise the data; then evaluate the likelihood of the null hypothesis, using a Test statistic .

When considering groups, think first about how many. Is there just one group being compared against an audit standard, or are you comparing one group with another? Some studies may wish to compare more than two groups. Another situation may involve a single group measured at different points in time, for example before or after a particular treatment. In this situation each participant is compared with themselves, and this is often referred to as a ‘paired’ or a ‘repeated measures’ design. It is possible to combine these types of groups—for example a researcher may measure arterial BP on a number of different occasions in five different groups of patients. Such studies can be difficult, both to analyse and interpret.

In other studies we may want to see how a continuous variable (such as age or height) affects the outcomes. These techniques involve regression analysis, and are beyond the scope of this article.

The outcome measures are the data being collected. This may be a continuous measure, such as temperature or BMI, or it may be a categorical measure, such as ASA status or surgical specialty. Often, inexperienced researchers will strive to collect lots of outcome measures in an attempt to find something that differs between the groups of interest; if this is done, a ‘primary outcome measure’ should be identified before the research begins. In addition, the results of any hypothesis tests will need to be corrected for multiple measures.

The summary and the test statistic will be defined by the type of data that have been collected. The test statistic is calculated then transformed into a p- value using tables or software. It is worth looking at two common tests in a little more detail: the χ 2 test, and the t -test.

Categorical data: the χ 2 test

The χ 2 test of independence is a test for comparing categorical outcomes in two or more groups. For example, a number of trials have compared surgical site infections in patients who have been given different concentrations of oxygen perioperatively. In the PROXI trial, 4 685 patients received oxygen 80%, and 701 patients received oxygen 30%. In the 80% group there were 131 infections, while in the 30% group there were 141 infections. In this study, the groups were oxygen 80% and oxygen 30%, and the outcome measure was the presence of a surgical site infection.

The summary is a table ( Table 1 ), and the hypothesis test compares this table (the ‘observed’ table) with the table that would be expected if the proportion of infections in each group was the same (the ‘expected’ table). The test statistic is χ 2 , from which a p- value is calculated. In this instance the p -value is 0.64, which means that results like this would occur 64% of the time if the null hypothesis were true. We thus have no evidence to reject the null hypothesis; the observed difference probably results from sampling variation rather than from an inherent difference between the two groups.

Summary of the results of the PROXI trial. Figures are numbers of patients.

Continuous data: the t- test

The t- test is a statistical method for comparing means, and is one of the most widely used hypothesis tests. Imagine a study where we try to see if there is a difference in the onset time of a new neuromuscular blocking agent compared with suxamethonium. We could enlist 100 volunteers, give them a general anaesthetic, and randomise 50 of them to receive the new drug and 50 of them to receive suxamethonium. We then time how long it takes (in seconds) to have ideal intubation conditions, as measured by a quantitative nerve stimulator. Our data are therefore a list of times. In this case, the groups are ‘new drug’ and suxamethonium, and the outcome is time, measured in seconds. This can be summarised by using means; the hypothesis test will compare the means of the two groups, using a p- value calculated from a ‘ t statistic’. Hopefully it is becoming obvious at this point that the test statistic is usually identified by a letter, and this letter is often cited in the name of the test.

The t -test comes in a number of guises, depending on the comparison being made. A single sample can be compared with a standard (Is the BMI of school leavers in this town different from the national average?); two samples can be compared with each other, as in the example above; or the same study subjects can be measured at two different times. The latter case is referred to as a paired t- test, because each participant provides a pair of measurements—such as in a pre- or postintervention study.

A large number of methods for testing hypotheses exist; the commonest ones and their uses are described in Table 2 . In each case, the test can be described by detailing the groups being compared ( Table 2 , columns) the outcome measures (rows), the summary, and the test statistic. The decision to use a particular test or method should be made during the planning stages of a trial or experiment. At this stage, an estimate needs to be made of how many test subjects will be needed. Such calculations are described in detail elsewhere. 5

The principle types of hypothesis test. Tests comparing more than two samples can indicate that one group differs from the others, but will not identify which. Subsequent ‘post hoc’ testing is required if a difference is found.

Controversies surrounding hypothesis testing

Although hypothesis tests have been the basis of modern science since the middle of the 20th century, they have been plagued by misconceptions from the outset; this has led to what has been described as a crisis in science in the last few years: some journals have gone so far as to ban p -value s outright. 6 This is not because of any flaw in the concept of a p -value, but because of a lack of understanding of what they mean.

Possibly the most pervasive misunderstanding is the belief that the p- value is the chance that the null hypothesis is true, or that the p- value represents the frequency with which you will be wrong if you reject the null hypothesis (i.e. claim to have found a difference). This interpretation has frequently made it into the literature, and is a very easy trap to fall into when discussing hypothesis tests. To avoid this, it is important to remember that the p- value is telling us something about our sample , not about the null hypothesis. Put in simple terms, we would like to know the probability that the null hypothesis is true, given our data. The p- value tells us the probability of getting these data if the null hypothesis were true, which is not the same thing. This fallacy is referred to as ‘flipping the conditional’; the probability of an outcome under certain conditions is not the same as the probability of those conditions given that the outcome has happened.

A useful example is to imagine a magic trick in which you select a card from a normal deck of 52 cards, and the performer reveals your chosen card in a surprising manner. If the performer were relying purely on chance, this would only happen on average once in every 52 attempts. On the basis of this, we conclude that it is unlikely that the magician is simply relying on chance. Although simple, we have just performed an entire hypothesis test. We have declared a null hypothesis (the performer was relying on chance); we have even calculated a p -value (1 in 52, ≈0.02); and on the basis of this low p- value we have rejected our null hypothesis. We would, however, be wrong to suggest that there is a probability of 0.02 that the performer is relying on chance—that is not what our figure of 0.02 is telling us.

To explore this further we can create two populations, and watch what happens when we use simulation to take repeated samples to compare these populations. Computers allow us to do this repeatedly, and to see what p- value s are generated (see Supplementary online material). 7 Fig 1 illustrates the results of 100,000 simulated t -tests, generated in two set of circumstances. In Fig 1 a , we have a situation in which there is a difference between the two populations. The p- value s cluster below the 0.05 cut-off, although there is a small proportion with p >0.05. Interestingly, the proportion of comparisons where p <0.05 is 0.8 or 80%, which is the power of the study (the sample size was specifically calculated to give a power of 80%).

The p- value s generated when 100,000 t -tests are used to compare two samples taken from defined populations. ( a ) The populations have a difference and the p- value s are mostly significant. ( b ) The samples were taken from the same population (i.e. the null hypothesis is true) and the p- value s are distributed uniformly.

Figure 1 b depicts the situation where repeated samples are taken from the same parent population (i.e. the null hypothesis is true). Somewhat surprisingly, all p- value s occur with equal frequency, with p <0.05 occurring exactly 5% of the time. Thus, when the null hypothesis is true, a type I error will occur with a frequency equal to the alpha significance cut-off.

Figure 1 highlights the underlying problem: when presented with a p -value <0.05, is it possible with no further information, to determine whether you are looking at something from Fig 1 a or Fig 1 b ?

Finally, it cannot be stressed enough that although hypothesis testing identifies whether or not a difference is likely, it is up to us as clinicians to decide whether or not a statistically significant difference is also significant clinically.

Hypothesis testing: what next?

As mentioned above, some have suggested moving away from p -values, but it is not entirely clear what we should use instead. Some sources have advocated focussing more on effect size; however, without a measure of significance we have merely returned to our original problem: how do we know that our difference is not just a result of sampling variation?

One solution is to use Bayesian statistics. Up until very recently, these techniques have been considered both too difficult and not sufficiently rigorous. However, recent advances in computing have led to the development of Bayesian equivalents of a number of standard hypothesis tests. 8 These generate a ‘Bayes Factor’ (BF), which tells us how more (or less) likely the alternative hypothesis is after our experiment. A BF of 1.0 indicates that the likelihood of the alternate hypothesis has not changed. A BF of 10 indicates that the alternate hypothesis is 10 times more likely than we originally thought. A number of classifications for BF exist; greater than 10 can be considered ‘strong evidence’, while BF greater than 100 can be classed as ‘decisive’.

Figures such as the BF can be quoted in conjunction with the traditional p- value, but it remains to be seen whether they will become mainstream.

Declaration of interest

The author declares that they have no conflict of interest.

The associated MCQs (to support CME/CPD activity) will be accessible at www.bjaed.org/cme/home by subscribers to BJA Education .

Jason Walker FRCA FRSS BSc (Hons) Math Stat is a consultant anaesthetist at Ysbyty Gwynedd Hospital, Bangor, Wales, and an honorary senior lecturer at Bangor University. He is vice chair of his local research ethics committee, and an examiner for the Primary FRCA.

Matrix codes: 1A03, 2A04, 3J03

Supplementary data to this article can be found online at https://doi.org/10.1016/j.bjae.2019.03.006 .

Supplementary material

The following is the Supplementary data to this article:

• 1. McCluskey A., Lalkhen A.G. Statistics II: central tendency and spread of data. CEACCP. 2007;7:127–130. [ Google Scholar ]
• 2. Altman D.G., Machin D., Bryant T.N., Gardner M.J. 2nd Edn. BMJ Books; London: 2000. Statistics with confidence. [ Google Scholar ]
• 3. Fisher R.A. The arrangement of field experiments. J Min Agric Gr Br. 1926;33:503–513. [ Google Scholar ]
• 4. Meyhoff C.S., Wetterslev J., Jorgensen L.N. Effect of high perioperative oxygen fraction on surgical site infection and pulmonary complications after abdominal surgery: the PROXI randomized clinical trial. JAMA. 2009;302:1543–1550. doi: 10.1001/jama.2009.1452. [ DOI ] [ PubMed ] [ Google Scholar ]
• 5. Columb M.O., Atkinson M.S. Statistical analysis: sample size and power estimations. BJA Educ. 2016;16:159–161. [ Google Scholar ]
• 6. Trafimow D., Marks M. Editorial. Basic Appl Soc Psych. 2015;37:1–2. [ Google Scholar ]
• 7. Colquhoun D. An investigation of the false discovery rate and the misinterpretation of p-values. R Soc Open Sci. 2014;1:140216. doi: 10.1098/rsos.140216. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ]
• 8. Ly A., Verhagen J., Wagenmakers E. Harold Jeffreys’s default Bayes factor hypothesis tests: explanation, extension, and application in psychology. J Math Psychol. 2016;72:19–32. [ Google Scholar ]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

• View on publisher site
• PDF (344.3 KB)
• Collections

Similar articles

Cited by other articles, links to ncbi databases.

• Download .nbib .nbib
• Format: AMA APA MLA NLM

Add to Collections

Hypothesis Testing: Understanding the Basics, Types, and Importance

Hypothesis testing is a statistical method used to determine whether a hypothesis about a population parameter is true or not. This technique helps researchers and decision-makers make informed decisions based on evidence rather than guesses. Hypothesis testing is an essential tool in scientific research, social sciences, and business analysis. In this article, we will delve deeper into the basics of hypothesis testing, types of hypotheses, significance level, p-values, and the importance of hypothesis testing.

• Introduction

What is a hypothesis?

What is hypothesis testing, types of hypotheses, null hypothesis, alternative hypothesis, one-tailed and two-tailed tests, significance level and p-values, avoiding type i and type ii errors, making informed decisions, testing business strategies, a/b testing, formulating the null and alternative hypotheses, selecting the appropriate test, setting the level of significance, calculating the p-value, making a decision, common misconceptions about hypothesis testing, understanding hypothesis testing.

A hypothesis is an assumption or a proposition made about a population parameter. It is a statement that can be tested and either supported or refuted. For example, a hypothesis could be that a new medication reduces the severity of symptoms in patients with a particular disease.

Hypothesis testing is a statistical method that helps to determine whether a hypothesis is true or not. It is a procedure that involves collecting and analyzing data to evaluate the probability of the null hypothesis being true. The null hypothesis is the hypothesis that there is no significant difference between a sample and the population.

In hypothesis testing, there are two types of hypotheses: null and alternative.

The null hypothesis, denoted by H0, is a statement of no effect, no relationship, or no difference between the sample and the population. It is assumed to be true until there is sufficient evidence to reject it. For example, the null hypothesis could be that there is no significant difference in the blood pressure of patients who received the medication and those who received a placebo.

The alternative hypothesis, denoted by H1, is a statement of an effect, relationship, or difference between the sample and the population. It is the opposite of the null hypothesis. For example, the alternative hypothesis could be that the medication reduces the blood pressure of patients compared to those who received a placebo.

There are two types of alternative hypotheses: one-tailed and two-tailed. A one-tailed test is used when there is a directional hypothesis. For example, the hypothesis could be that the medication reduces blood pressure. A two-tailed test is used when there is a non-directional hypothesis. For example, the hypothesis could be that there is a significant difference in blood pressure between patients who received the medication and those who received a placebo.

The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is true. It is set at the beginning of the test, usually at 5% or 1%. The p-value is the probability of obtaining a test statistic as extreme as

or more extreme than the observed one, assuming that the null hypothesis is true. If the p-value is less than the significance level, we reject the null hypothesis.

Importance of Hypothesis Testing

Hypothesis testing helps to avoid Type I and Type II errors. Type I error occurs when we reject the null hypothesis when it is actually true. Type II error occurs when we fail to reject the null hypothesis when it is actually false. By setting a significance level and calculating the p-value, we can control the probability of making these errors.

Hypothesis testing helps researchers and decision-makers make informed decisions based on evidence. For example, a medical researcher can use hypothesis testing to determine the effectiveness of a new drug. A business analyst can use hypothesis testing to evaluate the performance of a marketing campaign. By testing hypotheses, decision-makers can avoid making decisions based on guesses or assumptions.

Hypothesis testing is widely used in business analysis to test strategies and make data-driven decisions. For example, a business owner can use hypothesis testing to determine whether a new product will be profitable. By conducting A/B testing, businesses can compare the performance of two versions of a product and make data-driven decisions.

Examples of Hypothesis Testing

• A/B testing is a popular technique used in online marketing and web design. It involves comparing two versions of a webpage or an advertisement to determine which one performs better. By conducting A/B testing, businesses can optimize their websites and advertisements to increase conversions and sales.

A t-test is used to compare the means of two samples. It is commonly used in medical research, social sciences, and business analysis. For example, a researcher can use a t-test to determine whether there is a significant difference in the cholesterol levels of patients who received a new drug and those who received a placebo.

Analysis of Variance (ANOVA) is a statistical technique used to compare the means of more than two samples. It is commonly used in medical research, social sciences, and business analysis. For example, a business owner can use ANOVA to determine whether there is a significant difference in the sales performance of three different stores.

Steps in Hypothesis Testing

The first step in hypothesis testing is to formulate the null and alternative hypotheses. The null hypothesis is the hypothesis that there is no significant difference between the sample and the population, while the alternative hypothesis is the opposite.

The second step is to select the appropriate test based on the type of data and the research question. There are different types of tests for different types of data, such as t-test for continuous data and chi-square test for categorical data.

The third step is to set the level of significance, which is usually 5% or 1%. The significance level represents the probability of rejecting the null hypothesis when it is actually true.

The fourth step is to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as or more extreme than the observed one, assuming that the null hypothesis is true.

The final step is to make a decision based on the p-value and the significance level. If the p-value is less than the significance level, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

There are several common misconceptions about hypothesis testing. One of the most common misconceptions is that rejecting the null hypothesis means that the alternative hypothesis is true. However

this is not necessarily the case. Rejecting the null hypothesis only means that there is evidence against it, but it does not prove that the alternative hypothesis is true. Another common misconception is that hypothesis testing can prove causality. However, hypothesis testing can only provide evidence for or against a hypothesis, and causality can only be inferred from a well-designed experiment.

Hypothesis testing is an important statistical technique used to test hypotheses and make informed decisions based on evidence. It helps to avoid Type I and Type II errors, and it is widely used in medical research, social sciences, and business analysis. By following the steps in hypothesis testing and avoiding common misconceptions, researchers and decision-makers can make data-driven decisions and avoid making decisions based on guesses or assumptions.

• What is the difference between Type I and Type II errors in hypothesis testing?
• Type I error occurs when we reject the null hypothesis when it is actually true, while Type II error occurs when we fail to reject the null hypothesis when it is actually false.
• How do you select the appropriate test in hypothesis testing?
• The appropriate test is selected based on the type of data and the research question. There are different types of tests for different types of data, such as t-test for continuous data and chi-square test for categorical data.
• Can hypothesis testing prove causality?
• No, hypothesis testing can only provide evidence for or against a hypothesis, and causality can only be inferred from a well-designed experiment.
• Why is hypothesis testing important in business analysis?
• Hypothesis testing is important in business analysis because it helps businesses make data-driven decisions and avoid making decisions based on guesses or assumptions. By testing hypotheses, businesses can evaluate the effectiveness of their strategies and optimize their performance.
• What is A/B testing?

If you want to learn more about statistical analysis, including central tendency measures, check out our  comprehensive statistical course . Our course provides a hands-on learning experience that covers all the essential statistical concepts and tools, empowering you to analyze complex data with confidence. With practical examples and interactive exercises, you’ll gain the skills you need to succeed in your statistical analysis endeavors. Enroll now and take your statistical knowledge to the next level!

If you’re looking to jumpstart your career as a data analyst, consider enrolling in our comprehensive  Data Analyst Bootcamp with Internship program . Our program provides you with the skills and experience necessary to succeed in today’s data-driven world. You’ll learn the fundamentals of statistical analysis, as well as how to use tools such as SQL, Python, Excel, and PowerBI to analyze and visualize data. But that’s not all – our program also includes a 3-month internship with us where you can showcase your Capstone Project.

2 Responses

This is a great and comprehensive article on hypothesis testing, covering everything from the basics to practical examples. I particularly appreciate the section on common misconceptions, as it’s important to understand what hypothesis testing can and cannot do. Overall, a valuable resource for anyone looking to understand this statistical technique.

Thanks, Ana Carol for your Kind words, Yes these topics are very important to know in Artificial intelligence.

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Hypothesis Testing for Research – Complete Guide With Example

Published 16 October, 2023

Hypothesis testing is a statistical technique used for deciding whether to reject the null hypothesis. Hypothesis testing helps researchers know whether or not they are on the correct path for their research project and can save them from time wasted pursuing wrong leads. Before starting any type of hypothesis test, it is vital that you have an idea of what your variable will be and how to measure it accurately. This post will cover some of the most common types of hypothesis tests and provide examples, as well as discuss what they are designed to test.

What is a hypothesis in research?

Hypothesis in research is basically a statement that helps you to define the relationship between different types of variables for your study. You can consider the hypothesis as the expectation about the things that can happen during research. The main objective of including hypotheses in research is to get the answer to research questions .

For example, while watering a plant you expect that if you will give more amount of water and sunlight to the plant, it would grow big soon.

What are the different types of hypothesis?

There are different types of hypothesis but here, we will discuss mainly two types of hypothesis, these are :

Null hypothesis: It is a hypothesis, where you can not expect variations. The null hypothesis states that there is no relationship between the dependent and independent variables. For instance, there is no significant relationship between compensation policy and employee satisfaction. In research null hypothesis is denoted as H0. Alternative hypothesis: In the Alternative hypothesis, variations are expected. This is something that a researcher aims to indirectly verify by stating their assumption, which states that there exists a significant linkage between population parameters. For instance, there is a significant relationship between companies’ compensation policy and employee satisfaction. It denoted as H a  or H 1.

What is hypothesis testing?

Hypothesis testing is basically a statistical procedure that is researcher performs with the purpose of determining whether there are chances of a specific hypothesis to be true. In simple words, by using the statistics you can tests whether your prediction about the population parameters is correct or not.

Or we can say, Hypothesis testing is a research method that uses statistical tools to prove or disprove a theory. The hypothesis is an idea about what might be true, and the goal of hypothesis testing is to provide evidence for or against that idea.

What are the uses of hypothesis testing?

• You can use hypothesis testing for making assumptions about the outcome of the hypothesis on sample information that you have gathered from a large population.
• Students can utilize it for analyzing the strong proof which you have collected from the sample.
• Hypothesis testing provides the structure for making various assumptions about the population.

How to conduct hypothesis testing?

The test procedure or the rule is based upon a test statistic and a rejection region. The process of testing the hypothesis consists of the following steps:

Step 1 – Specification of hypothesis

It is the first step in hypothesis testing where you need to clearly define the null and alternative hypotheses . While stating the hypothesis you need to make sure that it is mutually exclusive which means that if one statement is true then the other should be false. While defining the variables you need to confirm that the statement representing the relationship between two or more variables.

Step 2 – Selection of significance level

This is a stage where you need to set the significance level. The significance level (denoted by the Greek letter alpha— a) is generally set at 0.05. This means that there is a 5% chance that you will accept your alternative hypothesis when your null hypothesis is actually true. The smaller the significance level, the greater the burden of proof needed to reject the null hypothesis, or in other words, to support the alternative hypothesis.

Step 3 – Collection of information

It is a stage where you will require accumulating all the facts about the research topic. The process of making statistical inferences should be done in a way that is designed to test your hypothesis. If you do not design the sampling methods and data collection appropriately, then it will make no sense for you to try drawing conclusions about any population at all!

Step 4 – Determination of critical values

This is a phase where you need to determine P-value. It is basically a value that the researcher utilizes for determining statistical importance in hypothesis tests. Determination of P-value is important as it will help you in evaluating the extent up to which the hypothesis statement given by you is true. It will also help you in analyzing the extent up to which the facts which you have gathered are compatible with the null hypothesis.

There are basically two types of P-value these are :

• High: High P-value indicates that the facts which you have collected are highly compatible with the null hypothesis.
• Low: It is the P-value that represents that the information which the researcher has to accumulate is not at all compatible with the null hypothesis .

Comparison of critical value and making a judgment: Here, you need to make a comparison between P values, and on the basis of the same you need to make a decision.

Step 5 – Drawing a conclusion

With the conclusion stage, we either accept or reject the null hypothesis. The decision is based on computed values of the test statistics and whether it lies in the acceptance region or rejection region respectively. If the computed value of the test statistic falls in the acceptance region (it means the computed value is less than the critical value), the null hypothesis is accepted. On the contrary, if the computed value of the test statistic is greater than the critical value, the computed value of the statistic falls in the rejection region, and the null hypothesis is rejected.

Hypothesis Testing Example

A manager in pipe manufacturing needs to ensure that the diameters of pipes manufactured by the machine are 5 cm. Then you as a manager is needed to undergo the following phases of the hypothesis test these are:

• Establishment for criteria: At this stage, you as a manager will need to design the hypothesis. The null hypothesis here could be every pipe has a diameter of 5 cm. AS manager needs to confirm that every pipe should be diameter 5 cm then he can make a selection from an alternative hypothesis which could be The population mean is fewer than the target, the mean of the population which manager has select is greater in comparison to the target. A third alternative hypothesis could be men population is completely different from the target.  In such a case, the manager can select two side alternative hypotheses. An alternative hypothesis which manager could select is the mean population of all pipes is not 5 cm.
• Selection of significance level: At this stage, you can select the most basically used significance level which is 0.05.
• Collection of facts: It is a stage where you will require gathering information about pipes and their diameters.
• Comparison between P values: After completion of the hypothesis test you will obtain P-value. Suppose here the P-value which results in 0.04 which is less than the significance level that is 0.05. on the basis of comparison between P values, you need to make a decision whether to reject the null hypothesis or not.

Read Also: Thematic Analysis for Research

Stuck During Your Dissertation

Our top dissertation writing experts are waiting 24/7 to assist you with your university project,from critical literature reviews to a complete PhD dissertation.

Other Related Guides

• Research Project Questions
• Types of Validity in Research – Explained With Examples
• Schizophrenia Sample Research Paper
• Quantitative Research Methods – Definitive Guide
• Research Paper On Homelessness For College Students
• How to Study for Biology Final Examination
• Textual Analysis in Research / Methods of Analyzing Text

A Guide to Start Research Process – Introduction, Procedure and Tips

Research findings – objectives , importance and techniques.

• Topic Sentences in Research Paper – Meaning, Parts, Importance, Procedure and Techniques

Recent Research Guides for 2023

Get 15% off your first order with My Research Topics

Connect with a professional writer within minutes by placing your first order. No matter the subject, difficulty, academic level or document type, our writers have the skills to complete it.

My Research Topics is provides assistance since 2004 to Research Students Globally. We help PhD, Psyd, MD, Mphil, Undergrad, High school, College, Masters students to compete their research paper & Dissertations. Our Step by step mentorship helps students to understand the research paper making process.

Research Topics & Ideas

• Sociological Research Paper Topics & Ideas For Students 2023
• Nurses Research Paper Topics & Ideas 2023
• Nursing Capstone Project Research Topics & Ideas 2023
• Unique Research Paper Topics & Ideas For Students 2023
• Teaching Research Paper Topics & Ideas 2023
• Literary Research Paper Topics & Ideas 2023
• Nursing Ethics Research Topics & Ideas 2023

Research Guide

Disclaimer: The Reference papers provided by the Myresearchtopics.com serve as model and sample papers for students and are not to be submitted as it is. These papers are intended to be used for reference and research purposes only.