Statistics: friedman

### Function Reference: `friedman`

statistics: p = friedman (x)
statistics: p = friedman (x, reps)
statistics: p = friedman (x, reps, displayopt)
statistics: [p, atab] = friedman (…)
statistics: [p, atab, stats] = friedman (…)

Performs the nonparametric Friedman’s test to compare column effects in a two-way layout. `friedman` tests the null hypothesis that the column effects are all the same against the alternative that they are not all the same.

`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’.

`friedman` returns up to three output arguments:

- p is the p-value of the null hypothesis that all group means are equal.
- atab is a cell array containing the results in a Friedman’s ANOVA table.
- stats is a structure containing statistics useful for performing a multiple comparison of medians with the MULTCOMPARE function.

If friedman is called without any output arguments, then it prints the results in a one-way ANOVA table to the standard output as if displayopt is ’on’.

Examples:

     load popcorn;
     friedman (popcorn, 3);

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

See also: anova2, kruskalwallis, multcompare

Source Code: friedman

### Example: 1

     load popcorn;
     friedman (popcorn, 3);

                  Friedman's ANOVA Table
    Source            SS      df        MS    Chi-sq    Prob>Chi-sq
    ---------------------------------------------------------------
    Columns         99.7500     2    49.8750    13.76    0.0010
    Interaction      0.0833     2     0.0417
    Error           16.1667    12     1.3472
    Total          116.0000    17

### Example: 2

     load popcorn;
     [p, atab] = friedman (popcorn, 3, "off");
     disp (p);

    1.0289e-03