12  Marginal Means & Contrasts

library(nlme); library(emmeans); library(performance)
library(lme4)

12.1 Estimated Marginal Means

Compact letter display

#library(multcomp); library(multcompView)

#cld(m1, Letters= letters)

The letters indicating significant differences can be generated using cld() function from the ‘multcomp’ package”. In the output below, groups sharing a letter in the .group are not statistically different from each other.

Cautionary Note about CLD

It’s important to note that we cannot conclude that treatment levels with the same letter are the same. We can only conclude that they are not different.

There is a separate branch of statistics, “equivalence testing” that is for ascertaining if things are sufficiently similar to conclude they are equivalent.

See Section 2.0.4 for additional warnings about problems with using compact letter display.