I have 11 groups, each consist of about 200 observations, and each observation has 2 variables (which are actually the first two PLS components if it makes any difference). Each group is a substance with increasing amounts of contaminant. The first group has 0% contamination, the second group has 1% contamination.... the 11th group consists of 10% contamination. When I plot all the groups, base on the two variables I get the following:
My data is organized in
pandas dataframe and looks like this:
score1 score2 H01 -0.153515 0.013216 H01 -0.149235 0.007089 H01 -0.152169 0.006924 H01 -0.160296 0.008324 H01 -0.158890 0.017218 H01 -0.160165 0.011170
I would like to know which group is significantly different from which group and which one is not. I know that if you have only one variable, you can use Tukey’s test and then, each group will get a label, where similar groups will get similar labels. However, this does not apply to multi-variant cases, such as in my case where I have 2 variables. I tried MANOVA but it only tells me if there is at least one group which is different but does not tell me which one is different from which. Is there a statistical test I can apply that take into consideration both variables simultaneously in order to look for significant differences between groups? I prefer the solution to be in python libraries if possible, but any direction for a solution would be appreciated.
I run MANOVA using python-
statsmodels.multivariate.manova as suggested, for H12 and H14 and I got weird-look results:
Value Num DF Den DF F Value Pr > F Wilks' lambda 0.0321726 2 354 5324.57 6.6844e-265 Pillai's trace 0.967827 2 354 5324.57 6.6844e-265 Hotelling-Lawley trace 30.0823 2 354 5324.57 6.6844e-265 Roy's greatest root 30.0823 2 354 5324.57 6.6844e-265
If I understand correctly, all methods have the same extremely low P value (6.6844e-265), which mean that the groups are significantly different, but as can be seen in the plot, H12 and H14 are practically on top of each other. Am I interpreting the MANOVA table correctly?