A Stein-Type Two-Sample Procedure for Comparing Normal Means

摘要

In this article, we propose a Stein-type two-sample procedure for comparing the means of k(>1) experimental normal populations among themselves and with the reference to the mean of a controlled normal population, when the variances of all (k+1) populations are unequal and unknown. Our selection formulation follows closely to that by Bechoffer and Turnbull (1978), who considered the comparison of k normal means with a specific nonrandom standard value, when the variances are either known or unknown and equal. Instead of comparing the k experimental populations to a nonrandom standard value, our comparison is made with reference to a random controlled normal population. Moreover, we broaden their assumption of equal unknown variances to unequal unknown variances. The proposed procedure satisfies two probability requirements: (1) the probability of selecting the control is at least prespecified P-0(*) when the largest experimental mean is significantly smaller than the mean of the control and (2) the probability of selecting the largest experimental mean is at least prespecified P-1(*) when the largest experimental mean is significantly largest than the second largest experimental mean and the mean of the control.