Statistics for everyone: ch.4 Wilcoxon rank sum test

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ch.4 Wilcoxon rank sum test

If there is data that does not satisfy normality, be careful with using parametric tests like t-tes. Wilcoxon test, a nonparametric test, is an alternative to the t-test.

The variable selection is the same as before.

The ‘Wilcoxon rank sum test’ does not reject the null hypothesis. In other words, it cannot be said that the two groups are different.

Parametric tests

Nonparametric tests

Student t-test

t-test

Two sample t-test

Independent t-test

Independent sample t-test

Mann–Whitney U test

Wilcoxon rank sum test

Mann–Whitney–Wilcoxon test

Wilcoxon–Mann–Whitney test

It is very common to call the same thing by a different name, such as calling ‘USA’ or ‘America’. The 5 tests on the left in the table above are all the same, and the 4 tests on the right are the same. These tests are used in a wide variety of ways, sometimes written differently, which confuses beginners. I don’t know why so many statistical books don’t tell you this point.

Parametric tests	Nonparametric tests
Usually for normal distribution	called distribution-free test

A parameter test assumes a specific distribution, usually a normal distribution, so it is performed when the distribution has a parameter, such as a mean or standard deviation. If the distribution go thorugh a normality test, it is common to perform a parametric test, and when it is not, a nonparametric test.

The plot showing the results of the Wilcoxon rank sum test is almost identical to the plot used in the t-test, but this is recommended only when it is a normal distribution.

These two plots can hide the sample size, so I would recommend using them only if the sample size is large enough.

If you have a small number of samples, this might be better.

So far, the common point is that both statistical tests and plots handle the same variables. In other words, they have in common that they only treat the situations that ‘result variables in both groups are continuous variables’.

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