摘要
目的探究非平衡设计下在单因素方差分析和Kruskal-Wallis H检验中各组样本量与检验效能的关系。方法通过SAS程序估计出两种方法在给定参数下所需的样本量,利用蒙特卡罗模拟,分别研究总样本量固定及不固定时,组间样本量比值对检验效能的影响。结果单因素方差分析中,总样本量固定时,增加均方误较大组的样本量可使检验效能提高,组间样本量差异过大会导致检验效能降低;总样本量不固定时,所增加样本量组的均方误越大,其检验效能增幅越高。Kruskal-Wallis H检验中,总样本量固定时,即便在组间样本量差异较大情况下,增加均方误较大组的样本量仍可提高检验效能;总样本量不固定时,结果与单因素方差分析类似,且其增幅与总样本量固定时增加均方误较大组的样本量近似。结论检验效能与组间样本量比值的关系受均方误的影响,增加均方误较大组的样本量能够提高检验效能;对于Kruskal-Wallis H检验,相较于增加总样本量,通过仅增加均方误较大组的样本量亦能获得较高检验效能,且更具有成本优势。
Objective To explore the relationship between sample size in the groups and statistical power of ANOVA and Kruskal-Wallis H test with an imbalanced design.Methods The sample sizes of the two tests were estimated by SAS program with given parameter settings,and Monte Carlo simulation was used to examine the changes in power when the total sample size varied or remained fixed.Results In ANOVA,when the total sample size was fixed,increasing the sample size in the group with a larger mean square error improved the statistical power,but an excessively large difference in the sample sizes between groups led to reduced power.When the total sample size was not fixed,a larger mean square error in the group with increased sample size was associated with a greater increase of the statistical power.In Kruskal-wallis H test,when the total sample size was fixed,increasing the sample size in groups with large mean square errors increased the statistical power irrespective of the sample size difference between the groups;when total sample size was not fixed,a larger mean square error in the group with increased sample size resulted in an increased statistical power,and the increment was similar to that for a fixed total sample size.Conclusion The relationship between statistical power and sample size in groups is affected by the mean square error,and increasing the sample size in a group with a large mean square error increases the statistical power.In Kruskal-Wallis H test,increasing the sample size in a group with a large mean square error is more cost-effective than increasing the total sample size to improve the statistical power.
作者
梁绮红
余晓琳
安胜利
LIANG Qihong;YU Xiaolin;AN Shengli(Department of Biostatistics,School of Public Health,Southern Medical University,Guangzhou 510515,China)
出处
《南方医科大学学报》
CAS
CSCD
北大核心
2020年第5期713-717,共5页
Journal of Southern Medical University
基金
国家自然科学基金(71673126)
南方医科大学大学生创新创业训练计划项目(201912121272)。
