  In this note we introduce a generalized formula for Cohen's $d$ under the
presence of additional independent variables, providing a measure for the size
of a possible effect concerning the location difference of a variable in two
groups. This is done by employing the so-called Frisch-Waugh-Lovell theorem in
a partitioned linear regression model. The generalization is motivated by
demonstrating the relationship to appropriate $t$ and $F$ statistics. Our
discussion is further illustrated by inference from a publicly available data
set.
