Dear Dr. Camacho,

both are post-hoc statistical tests. They are applied only once you have analysed the effect of an independent variable (e.g. days following the start of holiday in a sample of n persons, with levels such as Day 1, Day 2, Day 3, etc.) on a dependent variable (e.g. mood rating). Only if there is a significant overall main effect between the different levels of the independent variable (i.e. in this case between the different days), you are allowed to perform a post-hoc test to see which days differ significantly from each other in terms of mood-rating. The post-hoc test you would then perform is either a Tukey, a Nemenyi or another post-hoc test (there are other tests such as Scheffé, Bonferroni, etc.).

The Tukey test is typically applied following an analysis of variance, which requires your data to be normally distributed and the level has to be at least on interval scale. If your data do not fulfil these requirements, you cannot perform an analysis of variance. As a result, you would not perform a Tukey test either.

The Nemenyi test is a post-hoc test following a significant result in a Friedman test. A Friedman test neither requires your data to be on interval scale nor does it require them to be normally distributed. A Friedman test is the equivalance of a repeated measurements analysis of variance without the need to have normally distributed data and without the need to have the values on interval scale level. If you decide in favour of a Friedman test because your data do not fulfil the requirements of an analysis of variance, and you gain a significant effect, you would then perform the Nemenyi test to see which levels of a variable differ significantly from each other. In our example, mood might not differ between Day 1 and Day 2 of the holidays, but between the first and the last day of the holidays.

I hope this helps a bit.

Yours sincerely,

Rainer

How to report results for Nemenyi test post-hoc if difference between groups A nd D is significant?