# Nonparametric Statistics Notes - Friedman ANOVA and Kendall Concordance

These two tests are somewhat different in nature, however, they require similar user input. Friedman ANOVA is a nonparametric alternative to one-way repeated measures analysis of variance. The Kendall concordance statistic is similar to Spearman R (nonparametric correlation between two variables) except that it expresses the relationship between multiple cases. For Friedman ANOVA, the procedure expects the data to be arranged in the same way as you would arrange a data file for a within-subjects (repeated measures) analysis of variance with ANOVA/MANOVA. Specifically, the values for each level of the repeated measures factor should be contained in a different variable. Select Comparing multiple dep. samples (variables) from the Nonparametric Statistics Startup Panel - Quick tab to display the Friedman ANOVA by Ranks dialog box, in which you select a list of variables.

Assumptions and interpretation: Friedman ANOVA. The Friedman ANOVA by ranks test assumes that the variables (levels) under consideration were measured on at least an ordinal (rank order) scale. The null hypothesis for the procedure is that the different columns of data (i.e., STATISTICA variables) contain samples drawn from the same population, or specifically, populations with identical medians. Thus, the interpretation of results from this procedure is similar to that of a repeated measures ANOVA.

Assumptions and interpretation: Kendall concordance. The Kendall concordance coefficient expresses the simultaneous association (relatedness) between k sets of rankings (i.e., cases; correlated samples). For example, this statistic is commonly used to assess inter-judge reliability. Basically, the concordance coefficient is the average of all Spearman Rs between cases; specifically:

average Spearman R = (k * concordance -1) / (k-1)

Thus the general assumptions of this test are identical to that of the Spearman rank order correlation.

The range of Kendall concordance is from 0 to +1. Values close to zero represent lack of agreement in the rankings of the variables (e.g., objects) among cases (e.g., judges), while values close to 1 represent perfect agreement in the rankings of the variables (objects) among cases (judges).

See Friedman ANOVA by Ranks - Quick tab for further details.