Optimum sample size allocation to minimize cost or maximize power for the two‐sample trimmed mean test

Abstract

When planning a study, sample size determination is one of the most important tasks facing the researcher. The size will depend on the purpose of the study, the cost limitations, and the nature of the data. By specifying the standard deviation ratio and/or the sample size ratio, the present study considers the problem of heterogeneous variances and non-normality for Yuen's two-group test and develops sample size formulas to minimize the total cost or maximize the power of the test. For a given power, the sample size allocation ratio can be manipulated so that the proposed formulas can minimize the total cost, the total sample size, or the sum of total sample size and total cost. On the other hand, for a given total cost, the optimum sample size allocation ratio can maximize the statistical power of the test. After the sample size is determined, the present simulation applies Yuen's test to the sample generated, and then the procedure is validated in terms of Type I errors and power. Simulation results show that the proposed formulas can control Type I errors and achieve the desired power under the various conditions specified. Finally, the implications for determining sample sizes in experimental studies and future research are discussed.

Dimensional Deviation Estimation for Parts with Free-Form Surfaces

“…In theory, the more the samples, the more accurate the estimation of dimension deviation, meanwhile, the more the workload and cost [10].…”

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

“…Instead, an iterative search is required to resolve the issue for statistical reasoning and exactness. Nevertheless, Guo and Luh (2009) applied Eq. 9 with r S = θ to determine optimal sample sizes when target power is fixed and total cost needs to be minimized.…”

“…For the purpose of comparison, we performed an extensive numerical examination of sample size calculations for the model settings in Table 4 of Guo and Luh (2009). To our knowledge, no research to date has compared the performance of the available approximate procedures with the exact method.…”

“…Detailed analytical and empirical examinations are presented later to demonstrate the underlying drawbacks associated with the approximate procedures of Schouten and Singer. Moreover, Luh and Guo (2007), Luh (2009), andGuo (2010) extended the approximations of Schouten and Singer to the two-sample trimmed mean test with unequal variances under allocation and cost considerations. Basically, when the trimming proportion is 0, the procedures of Guo and Luhare applicable for the Behrens-Fisher problem.…”

Minimizing the Cost in Sample Size Computation

“…Allison et al [3] have discussed strategies in minimizing the financial cost while minimizing the cost, but their paper lacks depth in computing. Guo and Luh [4] have studied how to compute sample size with fixed cost for comparing two trimmed means. Luo, Wang and Meza [5] have proven the formulas of sample size with maximal precision for difference and ratio of two binary data and maximal power for detecting the difference of two proportions, two survival rates and two correlations under financial constraints.…”