Optimal sample sizes for Welch’s test under various allocation and cost considerations

2016

PLoS ONE

Self Cite

Equivalent testing has been strongly recommended for demonstrating the comparability of treatment effects in a wide variety of research fields including medical studies. Although the essential properties of the favorable two one-sided tests of equivalence have been addressed in the literature, the associated power and sample size calculations were illustrated mainly for selecting the most appropriate approximate method. Moreover, conventional power analysis does not consider the allocation restrictions and cost issues of different sample size choices. To extend the practical usefulness of the two one-sided tests procedure, this article describes exact approaches to sample size determinations under various allocation and cost considerations. Because the presented features are not generally available in common software packages, both R and SAS computer codes are presented to implement the suggested power and sample size computations for planning equivalence studies. The exact power function of the TOST procedure is employed to compute optimal sample sizes under four design schemes allowing for different allocation and cost concerns. The proposed power and sample size methodology should be useful for medical sciences to plan equivalence studies.

Section: Introductionmentioning

confidence: 99%

Exact Power and Sample Size Calculations for the Two One-Sided Tests of Equivalence

2016

PLoS ONE

Self Cite

“…In the next two sections, we will synthesize the ideas of Jan and Shieh (2011) and Kupper and Hafner (1989) to develop exact procedures of precise interval estimation with four different design and budget settings under the expected width and tolerance probability considerations, respectively. All calculations are performed using programs written with SAS/IML (SAS Institute, 2008a), and they are available in the supplementary files.…”

Section: Precise Interval Estimationmentioning

confidence: 99%

“…However, researchers have explored design strategies that take into account the impact of different constraints of the sample scheme and project funding while maintaining adequate power (Allison, Allison, Faith, Paultre, & Pi-Sunyer, 1997, and references therein). Jan and Shieh (2011) considered the problem of determining optimal sample sizes to meet a designated power for Welch's test under various allocation and cost considerations that call for independent random samples from two normal populations with possibly unequal variances. The same principles would apply for a study seeking a precise estimate of the mean difference between two treatments.…”

Section: Introductionmentioning

confidence: 99%

Optimal sample sizes for precise interval estimation of Welch’s procedure under various allocation and cost considerations

Jan²

2011

Behav Res

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Welch's (Biometrika 29: 350-362, 1938) procedure has emerged as a robust alternative to the Student's t test for comparing the means of two normal populations with unknown and possibly unequal variances. To facilitate the advocated statistical practice of confidence intervals and further improve the potential applicability of Welch's procedure, in the present article, we consider exact approaches to optimize sample size determinations for precise interval estimation of the difference between two means under various allocation and cost considerations. The desired precision of a confidence interval is assessed with respect to the control of expected half-width, and to the assurance probability of interval half-width within a designated value. Furthermore, the design schemes in terms of participant allocation and cost constraints include (a) giving the ratio of group sizes, (b) specifying one sample size, (c) attaining maximum precision performance for a fixed cost, and (d) meeting a specified precision level for the least cost. The proposed methods provide useful alternatives to the conventional sample size procedures. Also, the developed programs expand the degree of generality for the existing statistical software packages and can be accessed at brm.psychonomic-journals.org/ content/ supplemental.

“…The exact distribution of Welch's test statistic V is comparatively complicated and may be expressed in different forms (see Wang, 1971;Lee and Gurland, 1975;Nel, van der Merwe, & Moser 1990 for technical derivation and related details). In order to facilitate the implementation of sample size procedures, we consider the following alternative expression of V described in Jan and Shieh (2011) for its ease of numerical computation:…”

Section: Sample Size Calculationsmentioning

confidence: 99%

Confidence intervals and sample size calculations for the standardized mean difference effect size between two normal populations under heteroscedasticity

2013

Behav Res

The use of effect sizes and associated confidence intervals in all empirical research has been strongly emphasized by journal publication guidelines. To help advance theory and practice in the social sciences, this article describes an improved procedure for constructing confidence intervals of the standardized mean difference effect size between two independent normal populations with unknown and possibly unequal variances. The presented approach has advantages over the existing formula in both theoretical justification and computational simplicity. In addition, simulation results show that the suggested one-and two-sided confidence intervals are more accurate in achieving the nominal coverage probability. The proposed estimation method provides a feasible alternative to the most commonly used measure of Cohen's d and the corresponding interval procedure when the assumption of homogeneous variances is not tenable. To further improve the potential applicability of the suggested methodology, the sample size procedures for precise interval estimation of the standardized mean difference are also delineated. The desired precision of a confidence interval is assessed with respect to the control of expected width and to the assurance probability of interval width within a designated value. Supplementary computer programs are developed to aid in the usefulness and implementation of the introduced techniques. Kirk (1996), Kline (2004), Olejnik and Algina (2000), Richardson (1996), Rosenthal, Rosnow, and Rubin (2000), Rosenthal (2003), andVacha-Haase andThompson (2004). It has steadily become a general consensus in the methodological literature of behavior, education, management, and related disciplines that effect sizes accompanied by their corresponding confidence intervals are perhaps the best approach for conveying quantitative information in applied research.According to the general review of Ferguson (2009), effect sizes can be categorized into four general classes: (1) group difference, (2) strength of association, (3) corrected estimates, and (4) risk estimates. The group difference indices estimate the magnitude of difference between two or more groups, and Cohen's d (Cohen, 1969) is the most commonly used measure across virtually all disciplines of the social sciences. Specifically, Cohen's d is an estimate of the standardized mean difference that reflects the difference between two sample means divided by their pooled sample standard deviation under homoscedasticity. For the purpose of measuring the size of effect between two treatment groups with unequal variances, Cohen's d is no longer a proper estimator, because its standardizer, the Electronic supplementary material The online version of this article