I am running lsmeans to determine the means and standard error for each group within a 4x3 experiment, consisting of three subject types and four treatments. When I run the following it does display the means and error, however the SE for each subject type is exactly the same.

> myModel <- lme(y ~ Treatment * SubjectType * Year, random=list(SubjectNum=~1, Location=~1), control=ctrl, method="REML", data = dframe1, na.action="na.exclude")

> lsmeans(myModel, pairwise~SubjectType, adjust="tukey")

NOTE: Results may be misleading due to involvement in interactions
 SubjectType    lsmean           SE  df lower.CL upper.CL
 Type1          5.601792 0.06719405 168 5.469139 5.734446
 Type2          5.164734 0.06719405 168 5.032080 4.297387
 Type3          4.791922 0.06719405 168 4.659269 4.924576

Results are averaged over the levels of: Treatment, Year 
Confidence level used: 0.95 

 contrast             estimate          SE  df t.ratio p.value
 Type1 - Type2        0.5370586 0.09502674 168   4.599  <.0001
 Type1 - Type3        0.9098701 0.09502674 168   8.523  <.0001
 Type2 - Type3        0.4728115 0.09502674 168   3.923  0.0004

Results are averaged over the levels of: Inoculant, Year 
P value adjustment: tukey method for comparing a family of 3 estimates 

Does anyone have an explanation? The same thing happens when I run it by treatment - each treatment has the same SE.

  • $\begingroup$ Why do you think the standard errors should be different? $\endgroup$
    – Dason
    Commented Jul 25, 2017 at 18:06
  • 3
    $\begingroup$ It's important to remember that least squares means summarize a model, not the data. Since your model assumes homogeneous error structures, and since the design is evidently balanced, the standard errors are all the same. $\endgroup$
    – Russ Lenth
    Commented Jul 26, 2017 at 12:30

1 Answer 1


It makes perfect sense if your data are balanced, i.e., you have the same number of observations in each Treatment * SubjectType * Year combination. (That's how ANOVA was done in the 1940s, and balance like that was the reason ANOVA was feasible in 1940s ☺ ).


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