data one_way_repeat;
do subject = 1 to 10;
do timepoint = 1 to 4;
response = round(rand('Uniform',10,50));
output;
end;
end;
run;
proc print;
run;Friedman Chi-Square test using SAS
Introduction
The Friedman test is a non-parametric statistical test developed by Milton Friedman similar to the parametric repeated measures ANOVA. It is used to detect differences in groups across multiple blocks. The procedure involves ranking each row (or block) together, then considering the values of ranks by columns. Applicable to complete block designs, it is thus a special case of the Durbin test.
The Friedman test is used for one-way repeated measures analysis of variance by ranks. In its use of ranks it is similar to the Kruskal–Wallis one-way analysis of variance by ranks.
SAS version
SAS 9.4
Data used
Simulated dataset of 10 subjects(blocks) with continuous endpoints are generated for single-drug repeated measurements to check whether any significance exists between the responses(y) at different time points(4 time points simulated)(groups). The p-value will indicate whether differences in response for different time points are significant.
Data source
Overview
The FREQ procedure computes CMH statistic, Friedman’s test is identical to the ANOVA (row means scores) CMH statistic when the analysis uses rank scores (SCORES=RANK). The TABLES statement creates a three-way table i.e., timepoint and response stratified by subject. The output produces following statistics along with its degrees of freedom and p-value(Prob):
Nonzero Correlation
Row Mean Scores Differ
The row corresponding to ‘Row Mean Scores Differ’ gives the required statistic and p-value for Friedman’s test.
Handling missing Values
When the data contains missing response, the procedure discards the corresponding row and calculates the required statistic with a message about number of missing responses below the test statisitc output.
Example Code for Friedman Chi-square test
proc freq data=one_way_repeat;
tables subject*timepoint*response /
cmh2 scores=rank noprint;
run;Results
The FREQ Procedure
Summary Statistics for timepoint by response
Controlling for subject
Cochran-Mantel-Haenszel Statistics (Based on Rank Scores)
Statistic Alternative Hypothesis DF Value Prob
---------------------------------------------------------------
1 Nonzero Correlation 1 0.0276 0.8682
2 Row Mean Scores Differ 3 3.6429 0.3027
Total Sample Size = 40