On some treatment analyses

Abstract

Fawzy et al. [1] and Jamigorn et al. [2] illustrate systemic incorrect statistical analysis, in their use of two-sample t tests, paired or independent. These tests compare normal population means assuming unknown equal variances. The central limit theorem fully justiWes normality for inferences on means, but unknown variances need not be equal. This makes two-sample t tests, together with analysis of variance, unsuitable for general mean inferences. Since Linnik [3] has shown that two-sample t-statistics for the diVerence of means based on their suYcient statistics do not exist when variances are unknown, this Behrens–Fisher problem is not avoided by uselessly [4] testing for the equality of variances. Nor is it bypassed with rank tests such as the Mann–Whitney test. Being a comparison of distributions, these rank tests say nothing about means if signiWcant, and are biased [5] to one side in a two-sided test. Tsakok [6] has solved the Behrens–Fisher problem of comparing the means of normal distributions with unknown variances at exact signiWcant levels and shown that the Tsakok solution is more eVective in detecting signiWcant mean diVerences even with unknown equal variances. There is an indication [7] that the Tsakok solution applies to dependent samples. Its exposition [8] is available. The software GSP implements the Tsakok technique, and is used to compare means at 0.02 signiWcance level (one signiWcant Wgure) per pair. For Table 2 [1], there are signiWcant mean diVerences between the enoxaparin group and placebo in their estimated gestational age (EGA) at birth, EGA at spontaneous vaginal delivery (SVD) and EGA at caesarean section. For Table 4 [1], there is signiWcant mean diVerence between placebo and the enoxaparin group in their EGA at loss. For Table 2 [2], there is signiWcant mean diVerence between the acupressure group and the vitamin B6 group in their weight at the end of the trial. After the attention given to the data, they deserve correct analysis. The Tsakok technique is extended to the non-parametric two-sample problem with the article by Tsakok [9] on constructing exact uniformly most powerful unbiased tests, superseding above rank tests. The Tsakok articles are reprinted [10] with further results.