kruskalwallis can take up to three input arguments:

• x contains the data and it can either be a vector or matrix. If x is a matrix, then each column is treated as a separate group. If x is a vector, it is a single group whichever way it lies, unless group is given; with one group there is nothing to compare, so p is NaN.
• group contains the names for each group. If x is a matrix, then group can either be a cell array of strings of a character array, with one row per column of x. If you want to omit this argument, enter an empty array ([]). If x is a vector, then group must be a vector of the same length, or a string array or cell array of strings with one row for each element of x. x values corresponding to the same value of group are placed in the same group.
• displayopt is an optional parameter for displaying the groups contained in the data in a boxplot. If omitted, it is ’on’ by default. If group names are defined in group, these are used to identify the groups in the boxplot. Use ’off’ to omit displaying this figure.

kruskalwallis can return 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 in a standard ANOVA table.
• stats is a structure containing statistics useful for performing a multiple comparison of means with the MULTCOMPARE function.

stats also holds the effect size of the test, an Octave extension: EtaSquared, the rank eta squared max (0, (H - k + 1) / (n - k)) for the statistic H over k groups and n observations, which is the share of the variance of the ranks the groups account for, corrected for bias, and EtaSquaredCI, its two-sided confidence interval at the level 100 (1 - alpha) percent. By default the interval inverts the noncentral chi-square distribution of H on k - 1 degrees of freedom, taken as H’s distribution under the alternative, which it is for large samples. Three options after displayopt, also an Octave extension, set it:

If kruskalwallis is called without any output arguments, then it prints the results in a one-way ANOVA table to the standard output. It is also printed when displayopt is ’on’.

Examples:

 x = meshgrid (1:6);
 x = x + normrnd (0, 1, 6, 6);
 [p, atab] = kruskalwallis(x);

 x = ones (50, 4) .* [-2, 0, 1, 5];
 x = x + normrnd (0, 2, 50, 4);
 group = {"A", "B", "C", "D"};
 kruskalwallis (x, group);

See also: anova1, friedman, ranksum, multcompare

Source Code: kruskalwallis