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Sample size planning with the cost constraint for testing superiority and equivalence of two independent groups

Authors

  • Jiin-Huarng Guo,

    1. Department of Applied Mathematics, National Pingtung University of Education, Pingtung City, Taiwan
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  • Hubert J. Chen,

    1. Department of Accountancy, National Cheng Kung University, Tainan City, Taiwan
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  • Wei-Ming Luh

    Corresponding author
    1. Institute of Education, National Cheng Kung University, Tainan City, Taiwan
      Dr Wei-Ming Luh, Institute of Education, National Cheng Kung University, 1 University Road, Tainan City 701, Taiwan (e-mail: luhwei@mail.ncku.edu.tw).
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  • Note: Corrections have been added to this version of the article on 27 May 2011 after first publication online on 10 August 2010.

Dr Wei-Ming Luh, Institute of Education, National Cheng Kung University, 1 University Road, Tainan City 701, Taiwan (e-mail: luhwei@mail.ncku.edu.tw).

Abstract

The allocation of sufficient participants into different experimental groups for various research purposes under given constraints is an important practical problem faced by researchers. We address the problem of sample size determination between two independent groups for unequal and/or unknown variances when both the power and the differential cost are taken into consideration. We apply the well-known Welch approximate test to derive various sample size allocation ratios by minimizing the total cost or, equivalently, maximizing the statistical power. Two types of hypotheses including superiority/non-inferiority and equivalence of two means are each considered in the process of sample size planning. A simulation study is carried out and the proposed method is validated in terms of Type I error rate and statistical power. As a result, the simulation study reveals that the proposed sample size formulas are very satisfactory under various variances and sample size allocation ratios. Finally, a flowchart, tables, and figures of several sample size allocations are presented for practical reference.

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