If a factorial experiment is run only for a single replicate then it
is not possible to test hypotheses about the main effects and interactions
as the error sum of squares cannot be obtained. [Note]
This is because the number of observations in a single replicate equals
the number of terms in the ANOVA model. Hence the model fits the data
perfectly and no degrees of freedom are available to obtain the error
sum of squares. For example, if the two factor experiment to study the
effect of speed and fuel additive type on mileage was run only as a single
replicate there would be only six response values. The model of Eqn.
(25) has six terms and therefore will fit the
six response values perfectly. The error sum of squares, 
, for this case will be equal to zero.
In some single replicate factorial experiments it is possible to assume
that the interaction effects are negligible. In this case, the interaction
mean square can be used as error mean square, 
, to test hypotheses about the main
effects. However, such assumptions are not applicable in all cases and
should be used carefully.
See Also:
