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Friedman Test

The Friedman Test is a non-parametric test that examines the differences in the different treatments over many trials. Much like the parametric ANOVA test, repeated measures are considered in the test statistic where each row is first ranked, then the values of each rank are considered by column. Part of the reason for doing this test is actually in verifying if the data can be used for this test. The following assumptions must be met:

1. One group must be measured on at least three different trials

2. The group being measured is a random sample

3. The dependent variable must be measured at the interval level (for example, a point scale)

4. The group sample does not need to be normally distributed

For example, say a researcher wanted to see if different types of music have an affect on a student’s grade. The dependent variable would be the grades at school, while the independent variable is the type of music. If all the assumptions are met, like in the above example, then the creation of the table and the ranking can proceed. The test statistic is as follows:


Q = SS_t/SS_e



SS_t = n∑(r_j-r)^2

SS_e = (1/n(k-1))∑n∑k(r_ij-r)^2



r_j = 1/n∑r_ij

= 1/nk∑n∑k(r_ij)


After deriving the value of Q, one can look at distribution tables for the Q-statistic to obtain the p-value. If the p-value is smaller than 0.05, then the difference between the different test treatments is significant. However, if the p-value is higher than 0.05 then the difference between test treatments is not significant. Thus, understanding the Friedman Test is crucial for examining different treatments which are not applicable for study using the ANOVA Test.




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