The PairedtTest Under Artificial Pairing

Suppose that in the situation of a paired t test natural pairing, such as the use of twins, is not possible. Reduction in variability is then often achieved artificially, for example by pairing animals of similar birth weight. This article points out that, unless such pairing is ineffective, the usual assumptions underlying the paired t test are violated. Nevertheless, simulation indicates that, with randomization in the allocation of treatments, the standard procedure gives good results. Our bivariate normal model provides the factor by which the length of the confidence interval for the mean treatment difference is reduced as a result of the pairing. Another form of pairing sometimes used is shown to be incorrect. Nonparametric analogs are also briefly considered.