If Nonparametric Test Can You Continue With the 6 Steps of Hypothesis Testing

Nonparametric tests don't require that your data follow the normal distribution. They're also known as distribution-free tests and can provide benefits in certain situations. Typically, people who perform statistical hypothesis tests are more comfortable with parametric tests than nonparametric tests.

You've probably heard it's best to use nonparametric tests if your data are not normally distributed—or something along these lines. That seems like an easy way to choose, but there's more to the decision than that.

In this post, I'll compare the advantages and disadvantages to help you decide between using the following types of statistical hypothesis tests:

• Parametric analyses to assess group means
• Nonparametric analyses to assess group medians

In particular, I'd like you to focus on one key reason to perform a nonparametric test that doesn't get the attention it deserves! If you need a primer on the basics, read my hypothesis testing overview.

Related Pairs of Parametric and Nonparametric Tests

Nonparametric tests are a shadow world of parametric tests. In the table below, I show linked pairs of statistical hypothesis tests.

Parametric tests of means	Nonparametric tests of medians
1-sample t-test	1-sample Sign, 1-sample Wilcoxon
2-sample t-test	Mann-Whitney test
One-Way ANOVA	Kruskal-Wallis, Mood's median test
Factorial DOE with a factor and a blocking variable	Friedman test

Additionally, Spearman's correlation is a nonparametric alternative to Pearson's correlation. Use Spearman's correlation for nonlinear, monotonic relationships and for ordinal data. For more information, read my post Spearman's Correlation Explained!

For this topic, it's crucial you understand the concept of robust statistical analyses. Learn more in my post, What are Robust Statistics?

Advantages of Parametric Tests

Advantage 1: Parametric tests can provide trustworthy results with distributions that are skewed and nonnormal

Many people aren't aware of this fact, but parametric analyses can produce reliable results even when your continuous data are nonnormally distributed. You just have to be sure that your sample size meets the requirements for each analysis in the table below. Simulation studies have identified these requirements. Read here for more information about these studies.

Parametric analyses	Sample size requirements for nonnormal data
1-sample t-test	Greater than 20
2-sample t-test	Each group should have more than 15 observations
One-Way ANOVA	For 2-9 groups, each group should have more than 15 observations For 10-12 groups, each group should have more than 20 observations

You can use these parametric tests with nonnormally distributed data thanks to the central limit theorem. For more information about it, read my post: Central Limit Theorem Explained.

Related posts: The Normal Distribution and How to Identify the Distribution of Your Data.

Advantage 2: Parametric tests can provide trustworthy results when the groups have different amounts of variability

It's true that nonparametric tests don't require data that are normally distributed. However, nonparametric tests have the disadvantage of an additional requirement that can be very hard to satisfy. The groups in a nonparametric analysis typically must all have the same variability (dispersion). Nonparametric analyses might not provide accurate results when variability differs between groups.

Conversely, parametric analyses, like the 2-sample t-test or one-way ANOVA, allow you to analyze groups with unequal variances. In most statistical software, it's as easy as checking the correct box! You don't have to worry about groups having different amounts of variability when you use a parametric analysis.

Related post: Measures of Variability

Advantage 3: Parametric tests have greater statistical power

In most cases, parametric tests have more power. If an effect actually exists, a parametric analysis is more likely to detect it.

Related post: Statistical Power and Sample Size

Advantages of Nonparametric Tests

Advantage 1: Nonparametric tests assess the median which can be better for some study areas

Now we're coming to my preferred reason for when to use a nonparametric test. The one that practitioners don't discuss frequently enough!

For some datasets, nonparametric analyses provide an advantage because they assess the median rather than the mean. The mean is not always the better measure of central tendency for a sample. Even though you can perform a valid parametric analysis on skewed data, that doesn't necessarily equate to being the better method. Let me explain using the distribution of salaries.

Salaries tend to be a right-skewed distribution. The majority of wages cluster around the median, which is the point where half are above and half are below. However, there is a long tail that stretches into the higher salary ranges. This long tail pulls the mean far away from the central median value. The two distributions are typical for salary distributions.

These two distributions have roughly equal medians but different means.

In these distributions, if several very high-income individuals join the sample, the mean increases by a significant amount despite the fact that incomes for most people don't change. They still cluster around the median.

In this situation, parametric and nonparametric test results can give you different results, and they both can be correct! For the two distributions, if you draw a large random sample from each population, the difference between the means is statistically significant. Despite this, the difference between the medians is not statistically significant. Here's how this works.

For skewed distributions, changes in the tail affect the mean substantially. Parametric tests can detect this mean change. Conversely, the median is relatively unaffected, and a nonparametric analysis can legitimately indicate that the median has not changed significantly.

You need to decide whether the mean or median is best for your study and which type of difference is more important to detect.

Related posts: Determining which Measure of Central Tendency is Best for Your Data and Median: Definition and Uses

Advantage 2: Nonparametric tests are valid when our sample size is small and your data are potentially nonnormal

Use a nonparametric test when your sample size isn't large enough to satisfy the requirements in the table above and you're not sure that your data follow the normal distribution. With small sample sizes, be aware that normality tests can have insufficient power to produce useful results.

This situation is difficult. Nonparametric analyses tend to have lower power at the outset, and a small sample size only exacerbates that problem.

Advantage 3: Nonparametric tests can analyze ordinal data, ranked data, and outliers

Parametric tests can analyze only continuous data and the findings can be overly affected by outliers. Conversely, nonparametric tests can also analyze ordinal and ranked data, and not be tripped up by outliers. Learn more about Ordinal Data: Definition, Examples & Analysis.

Sometimes you can legitimately remove outliers from your dataset if they represent unusual conditions. However, sometimes outliers are a genuine part of the distribution for a study area, and you should not remove them.

You should verify the assumptions for nonparametric analyses because the various tests can analyze different types of data and have differing abilities to handle outliers.

If your data use the ordinal Likert scale and you want to compare two groups, read my post about which analysis you should use to analyze Likert data.

Related posts: Data Types and How to Use Them and 5 Ways to Find Outliers in Your Data

Advantages and Disadvantages of Parametric and Nonparametric Tests

Many people believe that choosing between parametric and nonparametric tests depends on whether your data follow the normal distribution. If you have a small dataset, the distribution can be a deciding factor. However, in many cases, this issue is not critical because of the following:

• Parametric analyses can analyze nonnormal distributions for many datasets.
• Nonparametric analyses have other firm assumptions that can be harder to meet.

The answer is often contingent upon whether the mean or median is a better measure of central tendency for the distribution of your data.

• If the mean is a better measure and you have a sufficiently large sample size, a parametric test usually is the better, more powerful choice.
• If the median is a better measure, consider a nonparametric test regardless of your sample size.

Lastly, if your sample size is tiny, you might be forced to use a nonparametric test. It would make me ecstatic if you collect a larger sample for your next study! As the table shows, the sample size requirements aren't too large. If you have a small sample and need to use a less powerful nonparametric analysis, it doubly lowers the chance of detecting an effect.

If you're learning about hypothesis testing and like the approach I use in my blog, check out my Hypothesis Testing book! You can find it at Amazon and other retailers.

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Source: https://statisticsbyjim.com/hypothesis-testing/nonparametric-parametric-tests/

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