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# Statistical Tests

A statistical test enables the calculation of the significance level of a distribution or a comparison. Usually, the latter corresponds with the probability of an alpha-error (p-value)

The selection of the correct test requires knowlegde of the data's nature and the kind of question.

Parametric methods
Kind of study Test Conditions
Cross sectional study t-Test for unpaired samples s & n, nearly Gaussian distribution
ANOVA s & x*n
F-Test s & n
Longitudinal study t-Test for paired samples 2*s
Non-parametrical methods
Kind of study Test Conditions
Cross sectional study Kolmogoroff-Smirnoff-Test s & n (2 groups)
Kruskall-Wallis-Test s & n (3 levels)
U-Test (Mann-Whitney-Test) s & n (2 levels)
Wald-Wolfowitz-Test s & n (2 groups)
Fisher-Yates-Test x*x (frequencies, 2 groups, respectively)
Longitudinal study Wilcoxon-Test 2*s
Paired sign test 2*s
Friedman-Test x*s, x>=3

Legend: s: continuous data, n: nominal data, x: frequency.

Examples: s & n: Continuous data, nominal criterion; 2*s: Two groups with continuous data