Least Squares Mean

This is a mean estimated from a linear model. In contrast, a raw or arithmetic mean is a simple average of your values, using no model. Least squares means are adjusted for other terms in the model (like covariates), and are less sensitive to missing data. Theoretically, they are better estimates of the true population mean.

As a simple example, suppose you have a treatment applied to 3 trees (experimental unit), and 2 observations (samples) are collected on each. However, one observation is missing, giving values of (45, 36), (56, ), and (37, 41), where parentheses are around each tree. The raw average is simply (45+36+56+37+41)/5 = 43, and note the reduced influence of the second tree since it has fewer values. The least squares mean would be based on a model u + T + S(T), resulting in an average of the tree averages, as follows.

Least squares mean =[ (45+36)/2 + 56 + (37+41)/2 ] / 3 = 45.17 This more accurately reflects the average of the 3 trees, and is less affected by the missing value.