A main effect is the effect of one factor in a factorial experiment after averaging over the levels of the other factors. For two factors
and 
with cell means 
, the main effect of changing 
from level 
to level 
can be expressed, under equal weighting, as
![1/bsum_(j=1)^b[mu_(i^'j)-mu_(ij)].](/images/equations/MainEffect/NumberedEquation1.svg) |
Different weighting conventions can be needed in unbalanced designs.
A main effect summarizes an average comparison and can conceal an interaction. If the effect of 
varies strongly with the level of 
, the factor-level comparisons and the interaction are generally
more informative than the main effect alone.
