Question

What are the differences between inpedenpedent samples t-test, paired sample t-test, Wilcoxon rank-sum test, and the Wilcoxon signed ranks test? Thank you!

Answer 1

Independent Samples t Test. The Independent Samples t Test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different. The Independent Samples t Test is a parametric test.

Paired Sample T-Test. The paired sample t-test, sometimes called the dependent sample t-test, is a statistical procedure used to determine whether the mean difference between two sets of observations is zero. In a paired sample t-test, each subject or entity is measured twice, resulting in pairs of observations.The same set of observations are observed again after some period of time.

The Mann Whitney U test, sometimes called the Mann Whitney Wilcoxon Test or the Wilcoxon Rank Sum Test, is used to test whether two samples are likely to derive from the same population (i.e., that the two populations have the same shape). Some investigators interpret this test as comparing the medians between the two populations. Recall that the parametric test compares the means (H₀: μ₁=μ₂) between independent groups.

In contrast, the null and two-sided research hypotheses for the nonparametric test are stated as follows:

H₀: The two populations are equal versus

H₁: The two populations are not equal.

The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test).

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