# Friedman Test, Kendall’s W, Cochran’s Q: Significance Tests for More Than Two Dependent Samples

There are three significance tests for cases involving more than two dependent samples.  These are the Friedman Test, the Kendall’s W test, and the Cochran’s Q test.

The Friedman test is the significance test for more than two dependent samples and is also known as the Friedman two-way analysis of variance; it is used to test the null hypothesis.  In other words, it is used to test that there is no significant difference between the size of ‘k’ dependent samples and the population from which these have been drawn.  In SPSS, the Friedman test is done by selecting “Nonparametric Tests” from the analyze menu and then selecting “K Related Samples.”  After this, select “Test Variables,” and then under the option test type, select “Friedman.”  The Friedman test statistic is distributed approximately as chi-square, with (k – 1) degrees of freedom. The Friedman test statistic for more than two dependent samples is given by the formula:

Chi-squareFriedman = (* – 3n(k + 1))

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Kendall’s W Test is referred to the normalization of the Friedman statistic. Kendall’s W is used to assess the trend of agreement among the respondents.  In SPSS, Kendall’s W Test is done by selecting “Nonparametric Tests” from the analyze menu, and then by clicking on “K Related Samples.”  After this, select “Test Variables,” and then under the option test type, select “Kendall’s W.” Kendall’s W ranges from 0 to 1.  The value ‘1’ refers to the complete agreement among/between the raters, and value ‘0’ refers to the complete.

The Cochran’s Q test is used to test whether or not the part of a given variable is the same across the multiple dependent samples.  In SPSS, the Cochran’s Q test is done by selecting “Nonparametric Tests” from the analyze menu, and then selecting “K Related Samples.”  After this, select “Test Variables,” and then under test type, select “Cochran’s Q.”  Cochran’s Q is a chi square statistic which is an extension of McNemar test.

Assumptions:

Random sampling is assumed in all significance tests for more than two dependent samples.

The three tests are non-parametric; they do not assume normal distribution.

The three tests in the significance tests for more than two dependent samples permit multiple dependent samples.