# Hypothesis Testing – Null Hypothesis and Statistical Tests

## What is a hypothesis test needed for?

A hypothesis test is needed to determine whether there is a significant relationship between two or more variables. To do this, a hypothesis is first made stating that there is such a relationship. Then, data is collected and a statistical test is performed to check the validity of the hypothesis.

If the result of the test shows that the hypothesis is likely to be true, it is considered confirmed. However, if the result shows that the hypothesis is unlikely, it is considered rejected. Hypothesis testing is often used in science and business to make decisions based on data and facts.

There is always some uncertainty about whether the hypothesis is actually true, even if the result of the test suggests it is. It is possible that the observations that were made occurred purely by chance and that there is no actual relationship between the variables that were studied. Therefore, one can never be 100% certain that a hypothesis is true.

To gain knowledge about a larger population, a representative sample is often used instead of testing the entire population. By selecting a sample that is representative of the population in terms of important characteristics, conclusions can be drawn about what the results would be for the entire population. The results obtained based on the analysis of the sample can then be used to make decisions about the population.

## What is a null hypothesis?

Hypothesis tests help to make informed decisions based on facts and evidence and help to assess the quality of research. They make it possible to identify patterns and trends in large amounts of data and to assess whether there are significant differences between different groups.

To formulate a null hypothesis, you should first identify the variables you want to study. Then you formulate the hypothesis in a sentence that states that there is no relationship between these variables. It is important that the null hypothesis is clear, concise, and unambiguously describes the variables being studied.

### Examples of the null hypothesis

• There is no difference in the average life expectancy of people in urban and rural populations.
• There is no difference in the average number of high school diplomas between males and females.
• There is no relationship between fast food consumption and body mass index (BMI).

### Alternative hypothesis explained

The alternative hypothesis is the opposite of the null hypothesis. It states that there is a difference or relationship between the variables under study.

For example, the alternative hypothesis might be:

1. People in urban populations have a higher average life expectancy than people in rural populations.
2. On average, women have more school-leaving qualifications than men.
3. There is a correlation between fast food consumption and body mass index (BMI).

### Hypothesis test in comparison

Null hypothesis:μ = μ0. States that no relationship exists.
Alternative hypothesis:μ ≠ μ0. States that a relationship exists and is not based on chance alone.

μ stands for the average value in the population. μ0 is therefore the average value under the null hypothesis.

## Testing hypotheses step by step

Hypothesis testing is an important analytical tool used to determine whether a significant relationship exists between two or more variables. The process begins with the formulation of a hypothesis stating that such a relationship exists. Data are then collected and a statistical test is performed to determine the validity of the hypothesis. It is important that the test is performed correctly and that the result is interpreted carefully so that false conclusions are not drawn.

Formulate and test hypotheses

1. ### Formulate hypotheses

To formulate a null hypothesis, you should first identify the variables you want to study. Then you formulate the hypothesis in a sentence that states that there is no relationship between these variables. It is important that the null hypothesis is clear, concise, and unambiguously describes the variables being studied.

2. ### Collection of data

There are several ways you can collect data to confirm a hypothesis. One way is to conduct an experiment in which you manipulate the variable you want to study and observe the effects on another variable. For example, if you want to study whether there is a relationship between smoking and lung function, you could ask a group of people to smoke for a certain period of time while a control group does not smoke cigarettes. Then you could measure the lung function of both groups and see if there is a difference.

Another option is to conduct a survey or observation where you use questions or observations to record the variables you want to study. For example, if you want to investigate whether there is a relationship between a person’s income and where they live, you could send out questionnaires to people in different neighborhoods and ask about income.

It is important that you use a large sample to ensure that your results are representative. It is also important that you include and control for all relevant variables to ensure that your results are truly attributable to the variable you are studying.

3. ### Statistical analyses

Statistical analyses are an important tool for using data to confirm or reject hypotheses. They make it possible to identify patterns and trends in large amounts of data and to assess whether there are significant differences between different groups.

There are many different types of statistical analyses that can be used, depending on the type of data and the type of questions being asked. Some examples of common statistical tests are the t-test, the ANOVA test, and the correlation coefficient.

Overall, statistical analyses are an important tool for using data to confirm or reject hypotheses and to make informed decisions based on facts and evidence.

4. ### Interpretation of the results

The result of a statistical analysis is given in the form of a P-value, which indicates how likely it is that the observed result occurred by chance. If the P-value is small, it means that the observed result is unlikely and that there is a significant relationship between the variables under study. However, if the P-value is large, it means that the observed result is likely to be due to chance and that there is no significant relationship between the variables. The smaller the P value, the less likely it is that the observed result occurred by chance and the more likely it is that there is a significant relationship between the variables.
The significance level, also referred to as the alpha value, is the threshold used to determine whether or not the P value is significant. There is no set alpha value that is used for all tests; it is set by the researchers. Typically, an alpha value of 0.05 or 0.01 is used. If the P-value is less than the fixed alpha level, the hypothesis is considered significant and is considered confirmed. However, if the P-value is greater than the alpha level, the hypothesis is considered not significant and is considered rejected.

Effect size describes the magnitude of the effect that exists between the variables under study. It can be calculated using various measures such as the correlation coefficient or Cohen’s d. The effect size indicates how strong the relationship between the variables is and can be used to assess the practical significance of the result. For example, a small effect might have little practical significance, while a large effect might have greater practical significance.

## Possible mistakes in the mortgage tests

In hypothesis testing, there are two types of errors that can occur: the 1st type error and the 2nd type error. (Type I error and the Type II error).

• A Type I error, also called a false positive, occurs when the hypothesis is considered significant when in fact it is not. That is, the hypothesis is assumed to be true when in fact it is false. Type I error is determined by the alpha level used to determine whether or not the P value is significant. If the alpha level is chosen too low, there is a greater chance of a Type I error because the hypothesis is considered significant even though it is not in fact significant.
• A Type II error, also referred to as a false negative, occurs when the hypothesis is considered not significant even though it is in fact significant. That is, the hypothesis is assumed to be false when it is actually true. The Type II error is in some ways the opposite of the Type I error and occurs when the hypothesis is considered not significant when in fact it is significant.

It is important to consider both Type I error and Type II error when performing hypothesis testing

## Frequently Asked Questions: Hypothesis Testing

### Why are hypothesis tests needed?

Hypothesis tests are needed to determine whether there is a significant relationship between two or more variables. They are often used in research to test hypotheses about the relationship between different variables and to interpret the results of studies.

Hypothesis tests are important because they allow informed decisions to be made based on facts and evidence. They help test the validity of theories and assumptions and assess whether they are applicable to real-world relationships.

Hypothesis tests are also important because they help improve the accuracy of results and predictions. They allow us to identify patterns and trends in large amounts of data and can help develop better models and theories.

Overall, hypothesis testing is an important tool for understanding the relationships between different variables and for making informed decisions based on facts and evidence.

### What are the types of hypothesis tests?

There are many different types of hypothesis tests that can be used depending on what type of data is available and what type of questions are asked. Some examples of common hypothesis tests are:

T-test: The t-test is used to determine if there is a difference between two groups. There are different types of t-tests, such as the simple t-test, the paired t-test, and the multiple t-test.

ANOVA test: The Analysis of Variance (ANOVA) test is used to determine if there is a difference between three or more groups.

Correlation Coefficient: The correlation coefficient is used to determine if there is a linear relationship between two variables.

Chi-square test: The chi-square test is used to determine if there is a significant difference between different categories.

There are many other types of hypothesis tests, depending on what type of data is available and what type of questions are asked.

### External resources for hypothesis testing

Der Wikipedia Artikel: hier
Universität Ruhr Bochum: hier

### What kind of errors can occur during hypothesis testing?

A Type I error, also known as a false positive, occurs when the hypothesis is considered significant when in fact it is not. That is, the hypothesis is assumed to be true when in fact it is false.

A Type II error, also referred to as a false negative result, occurs when the hypothesis is considered not significant when in fact it is significant. That is, the hypothesis is assumed to be false when it is actually true. The Type II error is in some ways the opposite of the Type I error and occurs when the hypothesis is considered not significant when in fact it is significant.