Table 4.

Expected mean squares for the conventional test-by-reader-by-case factorial ANOVA model (7).

Mean square	Expected mean square
MS (T)	$\frac{rc}{(t-1)}{\sum }_{i=1}^t{\tau }_i^2+c{\sigma }_{TR}^2+r{\sigma }_{TC}^2+{\sigma }^2$
MS (R)	$tc{\sigma }_R^2+c{\sigma }_{TR}^2+t{\sigma }_{RC}^2+{\sigma }^2$
MS (C)	$tr{\sigma }_C^2+r{\sigma }_{TC}^2+t{\sigma }_{RC}^2+{\sigma }^2$
MS (T * R)	$c{\sigma }_{TR}^2+{\sigma }^2$
MS (T * C)	$r{\sigma }_{TC}^2+{\sigma }^2$
MS (R * C)	$t{\sigma }_{RC}^2+{\sigma }^2$
MS (T * R * C)	${\sigma }^2\equiv {\sigma }_{TRC}^2+{\sigma }_{\epsilon }^2$