Guo Jiin-Huarng, Luh Wei-Ming
Department of Applied Mathematics, National Pingtung University of Education, Pingtung, Taiwan.
Br J Math Stat Psychol. 2009 May;62(Pt 2):283-98. doi: 10.1348/000711007X267289. Epub 2007 Dec 21.
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.
在规划一项研究时，确定样本量是研究人员面临的最重要任务之一。样本量将取决于研究目的、成本限制以及数据的性质。通过指定标准差比率和/或样本量比率，本研究考虑了Yuen两组检验中异方差和非正态性的问题，并开发了样本量公式，以最小化总成本或最大化检验效能。对于给定的效能，可以操纵样本量分配比率，以便所提出的公式能够最小化总成本、总样本量或总样本量与总成本之和。另一方面，对于给定的总成本，最优样本量分配比率可以最大化检验的统计效能。在确定样本量之后，本模拟将Yuen检验应用于生成的样本，然后根据I型错误和效能对该过程进行验证。模拟结果表明，所提出的公式可以在指定的各种条件下控制I型错误并实现所需的效能。最后，讨论了在实验研究中确定样本量的意义以及未来的研究方向。
