You will likely never have to perform Dunn’s Test by hand since it can be performed using statistical software (like R, Python, Stata, SPSS, etc.) but the formula to calculate the z-test statistic for the difference between two groups is: If the p-value of the Kruskal-Wallis test is below a certain threshold, it can be said that the three drugs produce different effects.įollowing this, the researcher could then perform Dunn’s Test to determine which drugs produce statistically significant effects. The researcher can perform a Kruskal-Wallis test to determine if the median back pain is equal among the three drugs. He recruits 30 subjects for the study and randomly assigns them to use Drug A, Drug B, or Drug C for one month and then measures their back pain at the end of the month. If the results of a Kruskal-Wallis test are statistically significant, then it’s appropriate to conduct Dunn’s Test to determine exactly which groups are different.ĭunn’s Test performs pairwise comparisons between each independent group and tells you which groups are statistically significantly different at some level of α.įor example, suppose a researcher wants to know whether three different drugs have different effects on back pain. It is considered to be the non-parametric equivalent of the One-Way ANOVA. A Kruskal-Wallis test is used to determine whether or not there is a statistically significant difference between the medians of three or more independent groups.

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