What are the three cases when you should use nonparametric a

What are the three cases when you should use non-parametric analysis in place of parametric?

Solution

Nonparametric tests are like a parallel universe to parametric tests. The table shows related pairs of hypothesis tests that Minitab statistical software offers.

Parametric tests (means)

Nonparametric tests (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 one factor and one blocking variable

Friedman test

Reasons to Use Nonparametric Tests

Reason 1: Your area of study is better represented by the median

This is my favorite reason to use a nonparametric test and the one that isn’t mentioned often enough! The fact that you can perform a parametric test with nonnormal data doesn’t imply that the mean is the best measure of the central tendency for your data.

For example, the center of a skewed distribution, like income, can be better measured by the median where 50% are above the median and 50% are below. If you add a few billionaires to a sample, the mathematical mean increases greatly even though the income for the typical person doesn’t change.

When your distribution is skewed enough, the mean is strongly affected by changes far out in the distribution’s tail whereas the median continues to more closely reflect the center of the distribution. For these two distributions, a random sample of 100 from each distribution produces means that are significantly different, but medians that are not significantly different.

Two of my colleagues have written excellent blog posts that illustrate this point:

Reason 2: You have a very small sample size

If you don’t meet the sample size guidelines for the parametric tests and you are not confident that you have normally distributed data, you should use a nonparametric test. When you have a really small sample, you might not even be able to ascertain the distribution of your data because the distribution tests will lack sufficient power to provide meaningful results.

In this scenario, you’re in a tough spot with no valid alternative. Nonparametric tests have less power to begin with and it’s a double whammy when you add a small sample size on top of that!

Reason 3: You have ordinal data, ranked data, or outliers that you can’t remove

Typical parametric tests can only assess continuous data and the results can be significantly affected by outliers. Conversely, some nonparametric tests can handle ordinal data, ranked data, and not be seriously affected by outliers. Be sure to check the assumptions for the nonparametric test because each one has its own data requirements.