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Function Reference: friedman

statistics: p = friedman (x)
statistics: p = friedman (x, reps)
statistics: p = friedman (x, reps, displayopt)
statistics: [p, tbl] = friedman (…)
statistics: [p, tbl, 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’. 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.

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

 load popcorn;
 friedman (popcorn, 3);
Source                 SS     df         MS     Chi-sq  Prob>Chi-sq
Columns           99.7500      2    49.8750    13.7586       0.0010
Interaction        0.0833      2     0.0417                      
Error             16.1667     12     1.3472                      
Total            116.0000     17
 load popcorn;
 [p, atab] = friedman (popcorn, 3, 'off');
 disp (p);
1.0289e-03