Let’s say you want to report mean differences among groups (after ANOVA and post-hoc multiple comparison test such as Tukey), and assume that you want to inform the reader about the ‘spread’ of the data points around the mean of each group.
My understanding is that in such case, you are supposed to present standard deviation with the mean, and NOT standard error (because standard error indicates the ‘precision’ of the estimated mean relative to a true population mean).
My question is when you use lsmeans statement with proc glm or mixed to run ANOVA, what information do you present with lsmeans (= estimated mean values) to indicate the ‘spread’ of the data points? Or do you not present the ‘spread’ with the estimated mean values?
If you personally use standard error with the means, what is the rational? Especially, when standard errors are identical across different groups (which happens sometimes), is it meaningful to present, for example, means X, Y, and Z all having identical standard error values?