My experiment looks at the effect of 6 different treatments on various (usually 18) physical and chemical properties of the test material (silage), at several different time points. I do my statistical analysis using R. I had been using ANOVA (aov()) (with Tukey's test (HSD.test()) for post hoc analysis), but was often finding that my data was not normally distributed (using shapiro.test()) and/or had unequal variance (leveneTest() – car package). I therefore started testing all my data, regardless of normality, using Kruskal-Wallis test (kruskal() – from the agricolae package, which also gives a post hoc analysis…).
I usually present my data as mean values, with the standard deviation in parenthesis. I also include the result of the post hoc test as a letter to indicate statistically significant differences within a column.
Other researchers, such as Arriola et al 2011, present and analyse their data differently. They talk about using GLM in SAS (not R) as follows:
“The data were analyzed as a completely randomized design using the GLM procedure of SAS (v. 9.2 SAS Institute Inc., Cary, NC). The general model was Yij = μ + Ti + eij, where Yij = response variable, μ = overall mean, T = effect of treatment i, and eij = error term. The F-protected least significant difference test was used to compare least squares means and significance was declared at P < 0.05.”
I am unclear if the 'GLM' analysis they describe is a General Linear Model or a Generalized Linear Model (and also do not understand what the difference is). I also note that this description does not mention testing for normality of the data or homogeneity of variance. Is it the case that GLM, unlike ANOVA/Kruskal- Wallis, does not rely on assumptions regarding the normality and variance of the data? Also, they don’t present standard deviations, only reporting the mean (with letters to indicate significant differences between means), but give SEM (standard error of the mean?), and sometimes also P value.
So, my questions are as follows:
- Assuming I wish to replicate the analysis of Arriola et al above, ideally using R, which analysis (General Linear Model or Generalized Linear Model) should I be trying to do here?
- Does this GLM require normal data and homogeneity of variance? (I often find that my data are not normally distributed and can not easily be transformed to normality).
- Can I look for interactions (e.g. treatment vs time) using GLM, similar to that done using ANOVA?
- Does a GLM provide a post hoc type analysis to demonstrate which means are significantly different; something like the Tukey's HSD used with ANOVA? If not, can a post hoc analysis be applied to the result of the GLM?
- Can I do all of the above in R, allowing me to report mean values, along with SEM and a P value, as shown by Arriola et al?