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**::::here 'signed' means 'take into account signs of differences of paired data'
→Comparing Means
::where <math>\bar{d}</math> is the mean of differences of paired observations
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*'''Wilcoxon rank sum test'''**AKA <br>='''Mann-Whitney test'''::<math>H_0</math> is distribution of outcomes in both two population'''s''' are the same:#To rank whole combined observations of two groups:#To separate back the ranks into two groups:#To look up ''critical range'' relevant to '''sum of ranks''' in '''the group of smaller number of observation'''
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*'''Wilcoxon signed rank test'''
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|''Small sample size <30 in a group''
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*'''Kruskall-Wallis test'''
::<math>H_0</math> is distribution of outcomes in all population'''s''' are the same
:#To rank whole combined observations of all groups
:#To separate back the ranks into original groups
:#To make sum of ranks in each group
::<math>H = \frac{n-1}{n} \sum_{i=1}^k \frac{n_i(\bar{R}-E_R)}{s^2}</math>
::<math>H</math> is Kruskal-Wallis statistics
::<math>n_i</math> is number of observations in group <math>i</math>
::<math>\bar{R}</math> is the mean of rank sum in group <math>i</math>
::<math>E_R</math> is expected value of the rankings
::<math>s^2</math> is the variance of rank
::To look up ''critical values'' relevant to '''sum of ranks''' in '''the group of smaller number of observation'''
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<nowiki>*</nowiki>needs try to transform data into parametric (e.g., logarithmic), or other considerations
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