ANOVA test, popular among various statistical tests, is used to determine if the experiment or the survey outcomes are significant. I.e. it lets you figure out if the null hypothesis needs to be rejected or accept the alternative hypothesis. It must be noted that ANOVA test is quite sturdy with respect to the breach of the assumptions, providing the k groups are of the same size. Although in the correlated-samples ANOVA this provision is completely satisfied, there are few correlated-samples situations where there is a violation of one or more assumptions. In such cases, an alternative test known as the Friedman’s test can be used.
The Friedman test is a non-parametric test employed to determine the differences between the groups when the dependent variable is at the minimum ordinal. However, this test has become the most preferred test over that of ANOVA, especially if the data is significantly different from that of the normally distributed.
As with any statistical test, one needs to consider few assumptions while performing Friedman’s test, of which include:
- There is a group of test subjects that are calculated on three or more different events
- The samples need not be distributed normally
- The group is a random sample of the population
- The dependent variable is ordinal or continuous (percentage, time, etc.)
- The variable pairs are independent
To effectively perform this test and obtain an accurate answer, one must set up the hypotheses. That is,
- The null hypothesis is that the median treatment impact of the population is the same. Simply said, the treatments have zero effect.
- The impact of alternative hypotheses is not the same. This indicates that there is a detectable variation in the treatment effect.
- The data that is dealt with reflects the situation where T treatments are compared with N subjects. However, the subjects are organised randomly to the different groups and the comparison is made within each group and not between the groups.
Once the test is conducted (maybe in R, SPSS, or any other statistical software), you will have to interpret the results and this is done via ‘P’ value.
The Friedman test ranks the values in each row from lower order to higher and then sums the ranks in each column. If the sums vary, then the P-value is small, else they are higher than the significance value.
- If the P value is smaller than/equal to the significance value, you need to reject the null hypothesis and assume that not all the group medians are identical. Also, determine if the differences are practically significant.
- If the P value is greater than the significance value, the difference between medians is not significant and you need not have sufficient evidence to reject the null hypothesis. Also ensure that your test has the potential to detect the differences that are practically significant.
Now that you know everything about this alternative test to ANOVA, use it in case of violation of assumptions in correlated-sample situations and perform the test accurately. To know the steps involved in conducting Friedman’s test in SPSS or R language, visit https://www.spss-tutorials.com/spss-friedman-test-simple-example/ & http://tutorial.math.trinity.edu/content/friedman-test-r.