On the distribution of the unpaired t-statistic with paired data.
I derive the exact distribution of the unpaired t-statistic computed when the data actually come from a paired design. I use this to prove a result Diehr et al. obtained by simulation, namely that the type I error rate of this procedure is no greater than alpha regardless of the sample size. I provide a formula to use in computation of power and type I error rate.
Proschan
M A
MA
National Heart, Lung, and Blood Institute, II Rockledge Center, Bethesda, MD 20892, USA.
D000704:Analysis of Variance; D015982:Bias; D016009:Chi-Square Distribution; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D018401:Sample Size