Browsing by Author "Jan, Show-Li"

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A systematic approach to designing statistically powerful heteroscedastic 2 x 2 factorial studies while minimizing financial costs
(2016-08-31)
Jan, Show-Li
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Shieh, Gwowen
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管理科學系
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Department of Management Science
Background: The 2 x 2 factorial design is widely used for assessing the existence of interaction and the extent of generalizability of two factors where each factor had only two levels. Accordingly, research problems associated with the main effects and interaction effects can be analyzed with the selected linear contrasts. Methods: To correct for the potential heterogeneity of variance structure, the Welch-Satterthwaite test is commonly used as an alternative to the t test for detecting the substantive significance of a linear combination of mean effects. This study concerns the optimal allocation of group sizes for the Welch-Satterthwaite test in order to minimize the total cost while maintaining adequate power. The existing method suggests that the optimal ratio of sample sizes is proportional to the ratio of the population standard deviations divided by the square root of the ratio of the unit sampling costs. Instead, a systematic approach using optimization technique and screening search is presented to find the optimal solution. Results: Numerical assessments revealed that the current allocation scheme generally does not give the optimal solution. Alternatively, the suggested approaches to power and sample size calculations give accurate and superior results under various treatment and cost configurations. Conclusions: The proposed approach improves upon the current method in both its methodological soundness and overall performance. Supplementary algorithms are also developed to aid the usefulness and implementation of the recommended technique in planning 2 x 2 factorial designs.
Determining Sample Size With a Given Range of Mean Effects in One-Way Heteroscedastic Analysis of Variance
(2013-07-03)
Shieh, Gwowen
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Jan, Show-Li
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交大名義發表
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管理科學系
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National Chiao Tung University
The authors examined 2 approaches for determining the required sample size of Welch's test for detecting equality of means when the greatest difference between any 2 group means is given. It is shown that the actual power obtained with the sample size of the suggested approach is consistently at least as great as the nominal power. However, the sample size given by the method of Guo and Luh (2008) does not always guarantee the minimum power performance. Furthermore, the computed sample size and associated power of their formula tend to be larger than those provided with the proposed procedure. A supplementary computer program is provided to aid the implementation of the proposed technique in planning analysis of variance designs.
Determining Sample Sizes for Precise Contrast Analysis With Heterogeneous Variances
(2014-04-01)
Jan, Show-Li
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Shieh, Gwowen
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交大名義發表
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National Chiao Tung University
The analysis of variance (ANOVA) is one of the most frequently used statistical analyses in practical applications. Accordingly, the single and multiple comparison procedures are frequently applied to assess the differences among mean effects. However, the underlying assumption of homogeneous variances may not always be tenable. This study examines the sample size procedures for precise interval estimation of linear contrasts within the context of one-way heteroscedastic ANOVA models. The desired precision of both individual and simultaneous confidence intervals is evaluated with respect to the control of expected half width and to the tolerance probability of interval half width within a designated value. Supplementary computer programs are developed to aid the usefulness and implementation of the proposed techniques. The suggested sample size procedures improve upon the existing approaches and extend the methodology development in the statistical literature.
On the Extended Welch Test for Assessing Equivalence of Standardized Means
(1970-01-01)
Jan, Show-Li
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Shieh, Gwowen
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管理科學系
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Department of Management Science
This article proposes a useful extension of the ANOVA F-test for examining mean differences for evaluating the comparability of standardized mean effects. The equivalence procedure presumably suffers from the same disadvantage as the traditional ANOVA F-statistic regarding the violations of homogeneous variance assumption. In view of the absence of vital clarification for theory development and supportive technique, this article provides a critical exposition of the extended Welch test for the equivalence of standardized means. To enhance the usefulness of equivalence testing, the theoretical properties and practical implications of the Welch-type procedure are demonstrated. Moreover, the corresponding power and sample size algorithms are described for advance planning of equivalence studies. Despite the approximate nature, the accuracy of Type I error rate, statistical power, and sample size calculations of the suggested equivalence test is justified under a wide range of model configurations. The proposed procedures are demonstrated with the data of a clinical trial regarding the comparative study of four antihypertensive treatments. A complete set of computer codes is presented to calculate the corresponding critical values, p-values, power levels, and sample sizes for data analysis and design planning of equivalence studies.
Optimal contrast analysis with heterogeneous variances and budget concerns
(2019-03-26)
Jan, Show-Li
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Shieh, Gwowen
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管理科學系
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Department of Management Science
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.
Optimal sample size allocation for Welch's test in one-way heteroscedastic ANOVA
(2015-06-01)
Shieh, Gwowen
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Jan, Show-Li
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管理科學系
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Department of Management Science
The determination of an adequate sample size is a vital aspect in the planning stage of research studies. A prudent strategy should incorporate all of the critical factors and cost considerations into sample size calculations. This study concerns the allocation schemes of group sizes for Welch\'s test in a one-way heteroscedastic ANOVA. Optimal allocation approaches are presented for minimizing the total cost while maintaining adequate power and for maximizing power performance for a fixed cost. The commonly recommended ratio of sample sizes is proportional to the ratio of the population standard deviations or the ratio of the population standard deviations divided by the square root of the ratio of the unit sampling costs. Detailed numerical investigations have shown that these usual allocation methods generally do not give the optimal solution. The suggested procedures are illustrated using an example of the cost-efficiency evaluation in multi-disciplinary pain centers.
Optimal Sample Size Determinations for the Heteroscedastic Two One-Sided Tests of Mean Equivalence: Design Schemes and Software Implementations
(2017-04-01)
Jan, Show-Li
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Shieh, Gwowen
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管理科學系
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Department of Management Science
Equivalence assessment is becoming an increasingly important topic in many application areas including behavioral and social sciences research. Although there exist more powerful tests, the two one-sided tests (TOST) procedure is a technically transparent and widely accepted method for establishing statistical equivalence. Alternatively, a direct extension of Welch's solution for the Behrens-Fisher problem is preferred in equivalence testing of means when the homogeneity of variance assumption is violated. For advance planning of equivalence studies, this article describes both exact and nearly exact power functions of the heteroscedastic TOST procedure and develops useful approaches to optimal sample size determinations under various allocation and cost considerations. Detailed numerical illustrations and simulation studies are presented to demonstrate the distinct features of the suggested techniques and the potential deficiency of existing method. Moreover, computer programs are provided to facilitate the implementation of the described sample size procedures. The proposed formulas and algorithms are recommended over the current results for their technical transparency, overall performance, and diverse utility.
Optimal sample sizes for precise interval estimation of Welch's procedure under various allocation and cost considerations
(2012-03-01)
Shieh, Gwowen
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Jan, Show-Li
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管理科學系
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Department of Management Science
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.
Optimal sample sizes for Welch's test under various allocation and cost considerations
(2011-12-01)
Jan, Show-Li
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Shieh, Gwowen
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管理科學系
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Department of Management Science
The issue of the sample size necessary to ensure adequate statistical power has been the focus of considerableattention in scientific research. Conventional presentations of sample size determination do not consider budgetary and participant allocation scheme constraints, although there is some discussion in the literature. The introduction of additional allocation and cost concerns complicates study design, although the resulting procedure permits a practical treatment of sample size planning. This article presents exact techniques for optimizing sample size determinations in the context of Welch (Biometrika, 29, 350-362, 1938) test of the difference between two means under various design and cost considerations. The allocation schemes include cases in which (1) the ratio of group sizes is given and (2) one sample size is specified. The cost implications suggest optimally assigning subjects (1) to attain maximum power performance for a fixed cost and (2) to meet adesignated power level for the least cost. The proposed methods provide useful alternatives to the conventional procedures and can be readily implemented with the developed R and SAS programs that are available as supplemental materials from brm.psychonomic-journals.org/content/supplemental.
Power and sample size calculations for testing linear combinations of group means under variance heterogeneity with applications to meta and moderation analyses
(2015-01-01)
Shieh, Gwowen
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Jan, Show-Li
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交大名義發表
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管理科學系
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National Chiao Tung University
The general formulation of a linear combination of population means permits a wide range of research questions to be tested within the context of ANOVA. However, it has been stressed in many research areas that the homogeneous variances assumption is frequently violated. To accommodate the heterogeneity of variance structure, the Welch-Satterthwaite procedure is commonly used as an alternative to the t test for detecting the substantive significance of a linear combination of mean effects. This article presents two approaches to power and sample size calculations for the Welch-Satterthwaite test. The usefulness and diversity of the suggested techniques are illustrated with two of the potential applications in meta and moderation analyses. The numerical assessments showed that the proposed approaches outperform the existing methods on the accuracy of power calculations and sample size determinations for meta and moderation studies. Computer algorithms are also developed to implement the recommended procedures in actual research designs.
Power and sample size determinations for theWilcoxon signed-rank test
(2007)
Shieh, Gwowen
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Jan, Show-Li
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Randles, Ronald H.
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管理科學系
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Department of Management Science
The problem of calculating power and sample size for the Wilcoxon signed-rank test is discussed. The exact variance large-sample method is examined and explicit formulas are derived for observations from uniform, normal and Laplace distributions. Numerical results are presented to evaluate the exact variance procedure and compare its performance with two simplified approximations that have been suggested in the statistical literature. From the simulation results, it is evident that the exact variance approach is more accurate than the two approximate methods. To facilitate practical use, tabulated values of the estimated sample sizes are provided.
Sample size calculations for model validation in linear regression analysis
(2019-03-12)
Jan, Show-Li
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Shieh, Gwowen
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管理科學系
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Department of Management Science
BackgroundLinear regression analysis is a widely used statistical technique in practical applications. For planning and appraising validation studies of simple linear regression, an approximate sample size formula has been proposed for the joint test of intercept and slope coefficients.MethodsThe purpose of this article is to reveal the potential drawback of the existing approximation and to provide an alternative and exact solution of power and sample size calculations for model validation in linear regression analysis.ResultsA fetal weight example is included to illustrate the underlying discrepancy between the exact and approximate methods. Moreover, extensive numerical assessments were conducted to examine the relative performance of the two distinct procedures.ConclusionsThe results show that the exact approach has a distinct advantage over the current method with greater accuracy and high robustness.
Sample size determinations for Welch's test in one-way heteroscedastic ANOVA
(2014-02-01)
Jan, Show-Li
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Shieh, Gwowen
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交大名義發表
;
管理科學系
;
National Chiao Tung University
For one-way fixed effects ANOVA, it is well known that the conventional F test of the equality of means is not robust to unequal variances, and numerous methods have been proposed for dealing with heteroscedasticity. On the basis of extensive empirical evidence of Type I error control and power performance, Welch's procedure is frequently recommended as the major alternative to the ANOVA F test under variance heterogeneity. To enhance its practical usefulness, this paper considers an important aspect of Welch's method in determining the sample size necessary to achieve a given power. Simulation studies are conducted to compare two approximate power functions of Welch's test for their accuracy in sample size calculations over a wide variety of model configurations with heteroscedastic structures. The numerical investigations show that Levy's (1978a) approach is clearly more accurate than the formula of Luh and Guo (2011) for the range of model specifications considered here. Accordingly, computer programs are provided to implement the technique recommended by Levy for power calculation and sample size determination within the context of the one-way heteroscedastic ANOVA model.
Simultaneous identifications of the minimum effective dose in each of several groups
(2007-02-01)
Jan, Show-Li
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Chen, Yuh-Ing
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Shieh, Gwowen
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交大名義發表
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National Chiao Tung University
One primary goal in dose-response studies for drug development is to identify the minimum effective dose (MED) which is the lowest dose level with an effect that exceeds that of the zero dose control. In this paper, we consider step-down closed testing procedures on the basis of pairwise and Helmert contrasts suggested by Tamhane et al. [ Tamhane, A. C., Hochberg, Y., and Dunnett, C. W., 1996, Multiple test procedures for dose finding. Biometrics, 52, 21 - 37.] for the situation where one wishes to make all such MED identifications simultaneously in each of several groups. An example is given to illustrate the proposed tests. The Monte Carlo studies are further implemented to compare the relative error rate and power performances of the proposed tests.
The Bland-Altman range of agreement: Exact interval procedure and sample size determination
(2018-09-01)
Jan, Show-Li
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Shieh, Gwowen
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管理科學系
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Department of Management Science
The Bland-Altman analysis has been widely used to assess the agreement between two quantitative methods of measurement. The range of agreement is thus represented by the designated central proportion of the distribution of the paired differences. This article aims to provide concrete guidance on the use of accurate confidence intervals of the range of agreement. Theoretical examination and numerical comparison are conducted to support the exact approach and to demonstrate the disadvantages of the currently suggested methods for confidence interval estimation of the range of agreement. For the purpose of design planning, the associated sample size calculations for precise interval estimation of the range of agreement are delineated under the expected width and assurance probability considerations. To enhance the utility of the recommended confidence interval and sample size procedures in practical applications, both SAS and R computer algorithms are also developed.
The power of approximate degrees of freedom tests in heteroscedastic factorial designs
(2015-09-01)
Jan, Show-Li
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Shieh, Gwowen
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管理科學系
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Department of Management Science
Several viable approaches have been proposed for conducting factorial analysis when the homogeneous variances assumption is violated. Although robust type I error control and excellent power performance are desirable properties of a test procedure for making statistical inferences, the corresponding power calculations must also be considered to extend its applicability in planning research studies. This article presents the power functions of two approximate degrees of freedom tests within the context of two-way factorial designs. Both theoretical examination and empirical investigation are performed to demonstrate the underlying features of the two approaches. Simulation results showed that the suggested procedures provide remarkably good approximations over a wide range of model configurations. In view of the overall accuracy, the power functions are recommended for enhancing the usefulness of the associated test procedures. To facilitate the adoption of the suggested methodology in factorial research designs, computer code is presented for implementing the described power calculations.