“How do you conduct research?” Well, there are many answers to it. You gather the required materials and information and then you conduct the research. But I get that you need materials or technologies to conduct the research, but what about information? If you are using the previous information, then should you call this “research” or just a normal search? Then how will you conduct research without even knowing a single piece of information? Please lend me your attention for the next few moments.
While conducting research, you have to make an assumption about the underlying data distribution, right? But what if I tell you you don’t have to assume anything? That’s where the nonparametric test comes into play. In this blog, we will discuss choosing the right nonparametric test for your Ph.D. results section which is the data analysis portion in a stepbystep manner. But first, let us understand what a nonparametric test is. So let’s get started.
Nonparametric tests are statistical tests that do not make any assumptions about the underlying distribution of the data. Unlike parametric tests, which assume that the data comes from a specific distribution (e.g., normal distribution), nonparametric tests do not have any assumptions about the underlying distribution of the data.
Nonparametric tests are often used when the data is not normally distributed or when the sample size is small, and there is not enough information to make assumptions about the distribution of the data. These tests are also used when the data is not continuous and is instead categorical or ordinal.
Examples of nonparametric tests include the Wilcoxon ranksum test, the KruskalWallis test, the MannWhitney U test, the chisquare test, and Fisher's exact test.
It is important to note that nonparametric tests generally have lower statistical power compared to parametric tests, meaning that they may have a higher probability of failing to detect a significant difference if one exists.
I hope you know about data analysis in Ph.D. research. If you don’t know or forgot about it, let’s summarise a little about what data analysis is.
Data analysis is an essential step in a Ph.D. research project. It involves the systematic examination and interpretation of the data collected for the study, with the goal of answering the research questions and testing the hypotheses. The specific methods and techniques used for data analysis will depend on the type of data being analyzed, the research questions, and the design of the study.
Now, another question just popped into my head while creating this blog. Why a nonparametric test? I mean apart from grabbing onto any type of assumption, can it help me in other ways or not? Then let’s know what are the ways in which nonparametric tests can help us in our research.
Nonparametric tests are statistical tests that don't assume a specific distribution of the data, unlike parametric tests which typically assume that the data follows a normal distribution. Nonparametric tests can be useful in research because they offer several advantages:

Distribution flexibility: Nonparametric tests don't require assumptions about the underlying distribution of the data, making them appropriate for use with data that is not normally distributed.

Robustness: Nonparametric tests are often more robust to violations of assumptions that are made in parametric tests.

Small sample size: Nonparametric tests are often appropriate for use with small sample sizes, where the assumptions of parametric tests might not be met.

Categorical data: Nonparametric tests are wellsuited for analyzing categorical data, where the data is divided into discrete categories rather than continuous ones.

Missing data: Nonparametric tests can often handle missing data better than parametric tests, which might lead to biased results if the missing data are not missing at random.
Some common examples of nonparametric tests include the Wilcoxon ranksum test, the KruskalWallis test, the MannWhitney test, and the chisquared test.
So, there are numerous benefits of using nonparametric tests but what about the drawbacks? As research cannot get successful if the researcher does not have total knowledge about it, hence you cannot fully utilize the nonparametric test if you don’t know about its problems. So, let’s dive deep into the problems of it.
While nonparametric tests offer several advantages, they also have some limitations and problems:

Power: Nonparametric tests often have lower statistical power compared to parametric tests, which means that they may have a lower ability to detect a difference or association in the data if it exists.

Complexity: Some nonparametric tests can be more complex to understand and interpret compared to parametric tests, especially for researchers who are less familiar with these methods.

Multiple comparisons: Nonparametric tests may not be as effective in controlling type I error rates when multiple comparisons are being made, as is often the case in multiple regression models or in experiments with multiple treatments or groups.

Assumptions: Although nonparametric tests don't make assumptions about the underlying distribution of the data, they do make other assumptions about the data that must be met for the tests to be valid.

Less efficient: Nonparametric tests are typically less efficient than parametric tests, meaning that they require larger sample sizes to detect a difference or association of a given size.

Interpretation: Interpreting the results of nonparametric tests can be more difficult compared to parametric tests, especially when the data is not well understood or when the relationships in the data are complex.
Now, we can choose the right nonparametric test for our Ph.D. research project that can help us to conduct groundbreaking research. It has helped me enormously and I hope that it will also help you in your research. So, here we go.
Choosing the right nonparametric test for your Ph.D. Results section (data analysis) requires careful consideration of the type of data you are working with, the research question you are trying to answer, and the assumptions of each test. You can adhere to the general rules listed below:

Determine the type of data you have: The first step in choosing a nonparametric test is to determine the type of data you are working with, such as continuous, ordinal, or nominal data.

Identify the research question: Determine what type of relationship you are trying to investigate, such as a difference in means or an association between two variables.

Consider the sample size: For small sample sizes (less than 30), nonparametric tests may be more appropriate than parametric tests.

Evaluate the assumptions of each test: It is important to consider the assumptions of each test and determine if they are appropriate for your data and research question.

Consider previous research: Look at the previous research in your field to see what tests have been used and what their results have been.

Seek advice from a statistical consultant: If you are unsure about which test to choose, consider seeking advice from a statistical consultant or a more experienced researcher in your field.
Based on these guidelines, here are some examples of nonparametric tests that you might consider for specific types of data and research questions:

For comparing two independent groups with continuous or ordinal data, you might consider the MannWhitney U test or the Wilcoxon ranksum test.

For comparing more than two independent groups with continuous or ordinal data, you might consider the KruskalWallis test.

For investigating the relationship between two ordinal or nominal variables, you might consider the chisquared test for independence.

For investigating the relationship between a continuous variable and an ordinal or nominal variable, you might consider the KruskalWallis test or the JonckheereTerpstra test.
Note that these are just examples and that the appropriate test will depend on the specific data and research question you have.
Give us your suggestions on the topics you need and kindly share if you think that we have helped you in any way.