Non-parametric statistics are used in some types of research because they do not require the data to be normally distributed. This is often the case with observational data, which is data that is collected without manipulating the variables.

Normal distribution is a bell-shaped curve that is symmetrical and has a single peak. It is the most common distribution of data in statistics, and many parametric tests assume that the data is normally distributed. However, if the data is not normally distributed, the results of parametric tests can be unreliable.

Non-parametric tests do not make any assumptions about the distribution of the data. This makes them a more robust option for analyzing observational data and data that is not normally distributed.

Two examples of where non-parametric statistics would be used:

1. Comparing two groups of participants on a categorical variable. For example, you might want to compare the gender distribution of two groups of students. One way to do this would be to use a non-parametric test called the chi-squared test.
2. Determining whether there is a relationship between two ordinal variables. For example, you might want to determine whether there is a relationship between the level of education and the level of income. One way to do this would be to use a non-parametric test called the Spearman’s rank correlation coefficient.

Here are some additional examples of where non-parametric statistics might be used:

• Comparing the median values of two groups.
• Determining whether the distribution of a variable is different in two groups.
• Identifying outliers in a dataset.
• Testing for the presence of a trend in a dataset.

Benefits of using non-parametric statistics:

• Non-parametric statistics are more robust to violations of assumptions, such as normality.
• Non-parametric statistics are easier to understand and interpret than some parametric tests.
• Non-parametric statistics can be used to analyze a wider variety of data types, such as categorical and ordinal data.

Limitations of using non-parametric statistics:

• Non-parametric tests are often less powerful than parametric tests, meaning that they are less likely to detect a statistically significant difference between groups when there is one.
• Non-parametric tests can be more difficult to find for certain types of hypotheses.

Overall, non-parametric statistics are a valuable tool for researchers who are analyzing observational data and data that is not normally distributed. By using non-parametric tests, researchers can be more confident that their results are reliable and accurate.

Here is an example of how non-parametric statistics might be used in a research study:

A researcher wants to compare the effectiveness of two different teaching methods on student achievement. The researcher randomly assigns students to one of the two teaching methods and then measures their achievement at the end of the course.

The researcher uses a non-parametric test called the Mann-Whitney U test to compare the median achievement scores of the two groups. The Mann-Whitney U test is a non-parametric test that can be used to compare two groups on a continuous variable when the data is not normally distributed.

The results of the Mann-Whitney U test show that there is a statistically significant difference in the median achievement scores of the two groups. The students who received the first teaching method had a higher median achievement score than the students who received the second teaching method.

This example shows how non-parametric statistics can be used to analyze data from a research study and draw conclusions about the effects of different variables.