# Statistical analysis of data heteroscedasticity and non-normal residuals

I am dealing with a data set that contains a continuous positive response variable (weight of a beetle that feeds on plants) and two treatments (categorical variables with each 2 levels). It's a controlled experiment where two beetles are feeding per plant. Plants were subject to different treatments (15-18 plants per treatment). I looked at the residuals of a linear model (Weight~Treatment A X Treatment B).Inspection of residuals shows me, however, that I probably cannot assume normality and that the variance is not homogenous. The experiment has been replicated with similar results. I did several different transformations including boxcox but it did not improve. While I know several ways to deal with heteroscedasticity when residuals are normally distributed, I don't know how to deal with data that violates both assumptions. Any advice would be greatly appreciated. I also attached a residual plots of untransformed data to give you an idea how it looks like.

• I'd probably try to use another conditional distribution, such as a Gamma distribution (a Gamma-GLM) instead of the normal distribution. Jun 22 '20 at 8:15
• Many thanks! I tried a Gamma GLM as well, but this is also not dealing with the heteroscedasticity, which is the more severe problem. I am not a statistics expert but I thought that people must come fairly regular across data like this in life sciences and that there is a way to deal with that. Jun 23 '20 at 7:06
• Because the two beetles are feeding on the same plant, you might consider using a summarizing parameter of weight per plant like "mean of beetle weight" or "sum of beetle weight" per plant instead of the 2 weights like they were independent. Jun 23 '20 at 7:22
• The problem with using the two weights instead of one summarizing parameter is that if the two weights are correlated in one way or another (which that obviously are because it is the same plant thus is it is "bad nutrients" the two insects will grow less together and are thus not independent from each other) then any test you will perform, any model you will fit, will be breaking the rule of independence of residuals. You will then risk of wrongly reject null hypothesis more often than what you think (#pseudoreplication) Jun 23 '20 at 7:30
• Taking into consideration the fact of non independence of the residuals might also improve, as a side effect, your problems of normality and variance of your residuals. Jun 23 '20 at 7:45