data means versus fitted means

Data means are the average of the raw data.

Fitted means are the means for each factor level or combination of factor levels that you would expect to get if your design were balanced.

To calculate the fitted means:

1    Find the fitted value for every possible combination of factor levels (or cell) when all covariates are set at their overall mean.

2    Using only one fitted value per cell, find the average of the fitted values from step 1 for each factor level or combination of factor levels. These averages are the least squares means.

For a balanced design with no covariates, the fitted mean for each factor level or combination of factor levels is the same as the average of the response values for that level or combination.