Hi there,
I'm analysing my mycorrhizal root colonisation from a multi-factorial split plot designed field trial with fixed and random factors by ANOVA (nlme-package) and post-hoc by TUKEY HSD (multcomp-package) in R. I would like to report means +/- SE and Tukey letters, but I've noticed that I get quite different results (especially in Tukey tests) if I transform by arcsine ( Excel= ARCSINE(SQRT(%-root colonisation/100)), or not. Some papers state that they transformed their colonisation data, but I know that arcsine-transformation has been critised many times in the past. So, what's your opinion on that, transform or not transform?
I will not transform my data. Rather, I will run the logistic regression analysis.
I wouldn't think you should apply the arcsine transformation without a reason. That is, the idea of that transformation is to normalize the data and improve the homoscedasticity. So I'd say the first step is to run the model without the transformation, and examine the residuals (qq-plot or histogram of residuals, and residuals vs. predicted values. Also, plot (my.nlme.model) will give you one of these plots). If you don't have a problem with these residuals, then you may not have a reason to apply a transformation.
I would say the arcsine transformation is a little antiquated. Ideally you would use an appropriate generalized linear model. In the case of proportions, it might be a beta regression (assuming no values are exactly 0 or 1). The problem here might be finding a function for beta regression that handles mixed models. It looks like the glmmTMB package should be able to do this, and that you can use emmeans for post-hoc tests.
As a final note, in multcomp, "tukey" doesn't necessarily mean that it's doing anything related to Tukey HSD tests. "tukey" there really just means "compare all pairs of treatments".
Thank you! That was my issue, I thought arcsine needs to be applied for the sake of proportional adjustment. But since my data is nicely normal distributed without it, I might just skip it.
And thanks for the hint regarding multcomp and the emmeans function! I just encountered some issues with my code here, so will have a look into that as an alternative.
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA