# Standard error all the same in lsmeans on a mixed model [duplicate]

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")

NOTE: Results may be misleading due to involvement in interactions
$lsmeans SubjectType lsmean SE df lower.CL upper.CL Type1 5.601792 0.06719405 168 5.469139 5.734446 Type2 5.164734 0.06719405 168 5.032080 4.297387 Type3 4.791922 0.06719405 168 4.659269 4.924576 Results are averaged over the levels of: Treatment, Year Confidence level used: 0.95$contrasts
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.

## marked as duplicate by gung♦ r StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jul 25 '17 at 19:22

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 ☺ ).