I am a SAS programmer and am trying to help out a mate doing a project for work. He has tested 7 different treatments (growth cultures) across 31 days, I have a value from each treatment for each of the 31 days. The days go from Day 0 to Day 31, and the nature of the testing is that the values at day one are 0 and increase at day 31 to +1000.

I have tried fitting distributions to the data but none are statistcally fitting (Minitab p values all <0.05). So we can't assume normality and use a simple ANOVA with Tukey's Studentized Range (HSD) Test.

I am going to test these using non-parametric testing, using the Wilcoxon rank test on the differences between each treatment, so using day as variable to pair the data, use the differences and then test for a difference in median. The outcome of these tests is that all treatment medians are significantly different but also most of the distributions are significantly different using Kolmogorov-Smirnov Two-Sample Test (Asymptotic) testing.

Does this mean that we can only use the significant values for median differences when the distributions are equal or does it impact the analysis at all?

Can anyone suggest any other testing methods I could use here?


1 Answer 1


First, ANOVA does not require normally distributed variables, it assumes normally distributed residuals from the model. (Technically, normally distributed error, but that is measured by the residuals).

Second, with multiple time points, you ought not do simple ANOVA anyway: You will probably want some form of mixed model. These are pretty complex, statistically. They are one way of accounting for the fact that your data are not independent. Since you mention that you use SAS, the PROCs to look into are MIXED and possibly GLIMMIX.


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