Optimal contrast analysis with heterogeneous variances and budget concerns

Abstract

The omnibus test is commonly applied to evaluate the overall disparity between group means in ANOVA. Alternatively, linear contrasts are more informative in detecting specific pattern of mean differences that cannot be obtained via the omnibus test. This article concerns power and sample size calculations for contrast analysis with heterogeneous variances and budget concerns. Optimal allocation procedures for the Welch-Satterthwaite tests of standardized and unstandardized contrasts are presented to minimize the total sample size with the designated ratios, to meet a desirable power level for the least cost, and to attain the maximum power performance under a fixed cost. Currently available methods rely exclusively on simple allocation formula and direct rounding rule. The proposed allocation strategies combine the computing techniques of nonlinear optimization search and iterative screening process. Numerical assessments of a randomized control trial for the overcoming depression on the Internet are conducted to demonstrate and confirm that the approximate procedures do not guarantee optimal solution. The suggested approaches extend and outperform the existing findings in methodological soundness and overall performance. The corresponding computer algorithms are developed to implement the recommended power and sample size calculations for optimal contrast analysis.

Probabilistic thinking is the name of the game: Integrating test and confidence intervals to plan sample sizes

“…Since the advocacy of CIs is a central theme in statistical reform, additional methods and formulas for sample size determination in regard to various unconditional/condition al probabilities are required to address this need in the future to simultaneously obtain power and precision. The current findings add to a growing body of literature on sample size planning, and there is abundant room for further progress in multiple comparisons (simultaneous confidence intervals) (Liu, 2009;Pan & Kupper, 1999), linear contrasts (Bonett, 2009;Jan & Shieh, 2019;Luh & Guo, 2016), stratified sampling (Snedecor & Cochran, 1989), and multilevel analyses (Liu, 2003). Under certain circumstances, one group size may be pre-fixed to a certain number in a study; thus, the present study also supplied App (III) (see Supplementary Materials) to facilitate the recommended pro cedures in planning the required size of the other group so that the desired probability level can still be achieved.…”