Distributions' shape - comparison - more than 2 groups

[Silvia Cannas]

Hi all,

I am using Stata 18 to analyze data from a survey experiment.

Given that my main dependent variable is distributed in a way that does not allow the use of ANOVA, I am trying to understand if the Kruskal-Wallis equality-of-populations rank test is applicable in my case. For this purpose, I would need to test if distributions of the dependent variable in each group of the independent variable have the same shape. Unfortunately, the Kolmogorov-Smirnov equality-of-distributions test is not applicable in my case. As far as I understood, it can only be used when the grouping variable takes two values, whereas mine takes five.

What tests could I use in this case?

Thanks in advance for your time and help!
Silvia

[Nick Cox]

Helpful advice is difficult here as there is no precise information on your data here beyond your suspicion that the data are unsuitable for ANOVA. Precisely why do you say that?

Kruskal-Wallis is 1950s statistics and its use is both limited and pessimistic.

Generalized linear models are 1970s statistics and allow modelling and testing with many shapes of distributions. That could be much better for most purposes.