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Non-Parametric Tests

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Ansari-Bradley Test

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Apply this test to assess whether two independent samples have the same variance.

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Shapiro-Wilk Test

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Use this test to determine whether a sample comes from a normally distributed population.

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McNemar's Test

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Apply this test to paired nominal data to determine whether the row and column marginal frequencies are equal (test for symmetry of the variables).

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Mood's Median Test

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Use to test the equality of medians from two or more populations and can be a non-parametric alternative to the one-way ANOVA for medians.

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Durbin-Watson Test

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Apply this test to detect the presence of autocorrelation at lag 1 in the residuals from a regression analysis.

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Lilliefors Test

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Use this adaptation of the Kolmogorov-Smirnov Test to test if data come from a normally distributed population when the parameters (mean and variance) of the normal distribution are not known.

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Friedman Test

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Use to test for differences between groups when the dependent variable is ordinal and the groups are related; can be considered a non-parametric alternative to repeated measures ANOVA.

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Van der Waerden Test

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Apply this test, which uses normal scores (z-scores) of ranks, to test for differences in means between two or more groups for ordinal or continuous data that are not normally distributed.

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Median Test

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A simple non-parametric test for finding whether two or more independent samples come from populations with the same median.

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Rank Sum Test

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A general term that can refer to any non-parametric test that compares the central tendency of two independent samples using the ranks of their data.

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Cochran's Q Test

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This test is used to determine if there are differences in proportions across three or more matched or related samples.

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Wilcoxon Signed-Rank Test

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Apply this test for comparing two related samples to find differences between them when the data are continuous but not normally distributed.

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Run Test

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Use this test to examine the randomness of a sequence of data points, often used to test the randomness of residuals in a regression model.

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Kendall's Tau

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Use this non-parametric measure of correlation to assess the strength and direction of the relationship between two variables measured on at least an ordinal scale.

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Mann-Whitney U Test

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Use this test to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed.

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Kruskal-Wallis H Test

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Use this test to compare more than two independent groups to determine if there are statistically significant differences between them with an ordinal or continuous dependent variable that is not normally distributed.

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Goodman-Kruskal Gamma

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Use this measure of association for ordinal data to determine whether there is a monotonic relationship between two variables.

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Siegel-Tukey Test

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Use this test to compare the variability or spreads of two groups that are independent.

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Spearman's Rank Correlation Coefficient

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Use this to measure the strength and direction of association between two ranked variables.

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Page's Trend Test

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Utilize this test for ordered alternatives, i.e., when testing for a trend across several independent samples.

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