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I'm doing an experiment with 7 groups (batches) of 12 measurements of a certain chemical, where one group (b0) is considered the baseline case. The research question is to find out which groups have significantly deviating measurements of the chemical, in comparison with the base case.

From my understanding, I can use pair-wise ANOVA testing with the base case, using bonferroni adjustment for this experiment.

However, the data and the residuals are not normally distributed and neither are the residual variances equal between the groups. I tried several Box-Cox transformations but these did not provide evidence not to reject heteroskedasticity (p=0.0128).

Can anyone explain whether using ANOVA would still be a valid test method, even when assumptions are not met, or should I consider non-parametric tests like Kruskall-Wallis?

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