Question

In my work I often have to make different treatment comparisons using Anova and Tukey tests to determine which of multiple treatments in one factor experiments are statistically distinct from one another.

The code I have attached yields two separate figures: one with treatment distribution of values (example graph1) and another with the Tukey test results showing which pair of treatments are significantly different from one another (example graph2).

What I have done in the past is to look at the Tukey results and manually edit the first graph with letters indicating groups of statistically equivalent groups (example graph3). I have been looking at different r libraries for ways to automatically produce something similar to graph 3 that summarizes such groupings but have not yet found a way. Does anyone have any suggestions?

PS- I am sorry if the graph routine below is a little cumbersome, but it is essentially a fragment of a much more comprehensive set of functions that I have developed to test data distribution, conditionally apply relevant tests and produce output tables and figures.

The code I have written to make the first two graphs is below. t?usp=sharing

Group=c("G1","G1","G1","G1","G2","G2","G2","G2","G3","G3","G3","G3")
Vals=c(runif(4),runif(4)+0.5,runif(4)+0.1)
data=data.frame(Group)
data=cbind(data, Vals)  
anova_results=aov(Vals~Group,data=data)
anova_results2=anova(anova_results)[1, ]
anova_significance=anova_results2[1,"Pr(>F)"]
significant=anova_significance[1]<=0.05
if (significant==1) {
  Tukey_results=TukeyHSD(anova_results,"Group")
  Tukey_results=Tukey_results$Group
}  
plot(data$Group, data$Vals) 
if (significant==1) {
  plot(TukeyHSD(anova_results,"Group"), las=1)   
}

Answer 1

Roman Lustrik’s suggestions on the comments above were spot on. I ended up finding two alternative ways to do it based on two related libraries. After running the code posted in the question, to create the grouped treatment plots run:

#simple looking solution
library(multcomp)
tuk <- glht(anova_results, linfct = mcp(Group = "Tukey"))
summary(tuk)          # standard display
tuk.cld <- cld(tuk)   # letter-based display
opar <- par(mai=c(1,1,1.5,1))
plot(tuk.cld)
par(opar)

#more fancy looking solution using the multcompView library with a lot of ways to 
#alter the plot appearance as necessary
library(multcompView)
multcompBoxplot(Vals~Group,data=data)

# Now, the solution below is my favorite solution as the text direction of the groups 
#work very well if you have many treatments that you are comparing
opar <- par()  
par(oma = c(6, 0, 0, 0)) #extra space for extra large treatment names
xzx <-multcompBoxplot(Vals~Group,data=data,sortFn=median,  decreasing=FALSE,    
                      horizontal=FALSE,
                      plotList=list(
                        boxplot=list(fig=c(0,  1,  0,  1),  las=3,
                                     cex.axis=1.5),                      
                        multcompLetters=list(
                          fig=c(0.87,  0.97,  0.115,  0.923), #0.1108, 0.9432 Top of     
#page 18 manual for very convoluted explanation (c(y bottom, y top,x L, x R))
                          type='Letters') ) )
par(opar)