friedman requires one up to three input arguments:

• x contains the data and it must be a matrix of at least two columns and two rows.
• reps is the number of replicates for each combination of factor groups. If not provided, no replicates are assumed.
• displayopt is an optional parameter for displaying the Friedman’s ANOVA table, when it is ’on’ (default) and suppressing the display when it is ’off’. MATLAB renders the table in a figure window; this package prints it to the standard output, as anova2 does.

friedman returns up to three output arguments:

• p is the p-value of the null hypothesis that all group means are equal.
• tbl is a cell array containing the results of the Friedman’s test in ANOVA table format. Its first row holds the column labels Source, SS, df, MS, Chi-sq and Prob>Chi-sq, followed by a row per source: Columns, [Interaction], Error and Total. An entry that does not apply to a row, such as the chi-square statistic of the Error row, is empty.
• stats is a structure containing statistics useful for performing a multiple comparison of medians with the MULTCOMPARE function.

stats also holds the effect size of the test, an Octave extension: KendallsW, Kendall’s coefficient of concordance, and KendallsWCI, its two-sided confidence interval at the level 100 (1 - alpha) percent. With b blocks of r replicates over c columns, W = Q / Q_max, where Q is the test statistic, corrected for ties, and Q_max = b r^2 (c^2 - 1) / (r c + 1) the value it takes when every block ranks the columns in the same order; without replicates this is the usual W = Q / (b (c - 1)). By default the interval inverts the noncentral chi-square distribution of Q on c - 1 degrees of freedom, taken as Q’s distribution under the alternative, which it is for many blocks, and bounds the expected value of W, (c - 1 + lambda) / Q_max for the noncentrality lambda; the lower bound is therefore above zero, W itself averaging 1/b where the columns do not differ. Three options after displayopt, also an Octave extension, set it:

If friedman is called without any output arguments, then it prints the results in a Friedman’s ANOVA table to the standard output.

Examples:

 load popcorn;
 friedman (popcorn, 3);

 [p, anovatab, stats] = friedman (popcorn, 3);
 disp (p);

See also: anova2, kruskalwallis, multcompare

Source Code: friedman