Can a linear model (LM) sample calculation be used for Linear mixed model (lmm) I need to calculate the sample size for a study. In the studiy, we will let participants answer ranking questions about 16 pictures of 4 persons in 4 postures. Because we want to control for the postures and persons, we will use lmm for the procedure.
For the sample size calculation I didn't find any easy to use application (I know there's longpower, I don't understand hardly any parameter). I tend to use a sample size calculation for linear model. Would this be appropriate?
Thank you any idea.
 A: No, you can't usually just use the sample size that you calculated for a linear model for a mixed effects model, because the "effective" sample size is reduced as a consequence of the non-independence of observations within each group, subject, item, or whatever it is that we specify random intercepts for in order to handle this non-independence (often just called "clusters". Consider the following two extreme scenarios:

*

*The observations are actually independent, even though there is clustering. In this case the effective sample size is the overall sample size and you can use the sample size from the linear model


*The observations in each cluster are all identitical, apart from some overall residual variance. In this case the effective sample size is simply the number of clusters.
In the typical situation where there is imperfect correlation within clusters (known as intra-class correlation, ICC), the effective sample size will be between the overall sample size and the number of clusters. This loss of effectiveness is known as the design effect :
$$ DE = 1 +(m-1)\rho$$
where $m$ is the average cluster size and $\rho$ is the ICC. So the sample size obtained through a calculation that ignores clustering is inflated by $DE$ to obtain a sample size that allows for clustering.
