**Figure 2:** Diagram illustrating how estimation of the variance can a_ect
the interpretation of the mean di_erence, under di_erent scenarios. (a)
Conventional situation, where each condition (M, N) has the same small
variance, mean di_erence is viewed as signi_cant, because it is big relative
to the small variance. (b) One condition (N) has higher variance than the
other, ignoring the di_erence, and pooling the variances would increase the
length of the ruler upon which the di_erence is gauged, to the extent that
the di_erence is not considered to be signi_cant. (c) Addition of an extra
treatment level (B), that has larger variance, but this has no e_ect because
each level of the treatments (A, B) is handled as separate samples { di_
erence is still seen as signi_cant. (d) Variances across treatments (A, B) are
pooled, which increases the length of the ruler upon which the di_erence is
measured, resulting in no signi_cant di_erence. |