I have a dataset that has four treatment groups (AX, AY, BX, BY). I am trying to determine if there is a significant difference in a response variable (Length) between any of these four treatment groups. I am also considering a random variable called Experiment. All this information is in the R object d below:
set.seed(1) d = data.frame(Length = c(rnorm(9,0), rnorm(9,-0.5)), Drug = c(rep("A",9), rep("B",9)), Location = rep(c(rep("X",3), rep("Y",3)),3), Treatment = paste0(c(rep("A",9), rep("B",9)), rep(c(rep("X",3), rep("Y",3)),3)), Experiment = sample(c(1,2), 18, replace = TRUE)) # Linear mixed effect model lmeOut = lme(Length ~ Treatment, data=d, random = ~1|Experiment) # General linear hypothesis and multiple comparison summary(glht(lmeOut, linfct=mcp(Treatment="Tukey")), test = adjusted("BH"))
I am unsure how to describe my code above. There is a linear mixed effect model (lme), general linear hypothesis and multiple comparison (glht), and both Tukey and Benjamini-Hochburg used (BH).
Would it be fair for me to say:
"A linear mixed effect model was used with the Experiment treated as a random variable. A pairwise combination was performed using a general linear model with Benjamini-Hochburg correction".
I am planning to have letters over a bar chart for groups AX, AY, BX, BY. As can be seen by running my code above, none of the six pairwise combinations reach significance (adjusted p-value < 0.05). So, I would just have letter "a" over each bar. Should I call this Tukey HSD letters? If not, what should I call these letters?
Very confused about the wording here and any advice would be much appreciated.