The sensitivity of three methods to nonnormality and unequal variances in interval estimation of effect sizes
The sensitivity of three methods to nonnormality and unequal variances in interval estimation of effect sizes
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DOI：
10.3758/s13428-014-0461-3
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发表时间：
2015-03-01
影响因子：
5.4
通讯作者：
Peng, Chao-Ying Joanne
中科院分区：
文献类型：
--
作者：
Chen, Li-Ting;Peng, Chao-Ying Joanne
效应量（ES）的置信区间（CI）估计提供了一系列由数据支持的可能的群体ES。在这篇文章中，我们研究了非中心t方法，Bonett的方法，和偏差校正和加速（BCa）自助法构建CI时，标准化的线性对比的均值被定义为一个ES。非中心t方法假设正态性和等方差，Bonett方法仅假设正态性，BCa自助法不做任何假设。我们模拟了三组和四组来自不同人群（一个正常和五个非正常）的数据，不同的方差比（1，2.25，4，8），人口ES（0，0.2，0.5，0.8）和样本量模式（一个相等，两个不等）。结果表明，在ES = 0和方差相等的联合条件下，非中心法的效果最好。在以下情况下，非中心方法的性能与其他两种方法相当：（1）样本量相等，每组权重不等，最后一组从尖峰分布中采样，或（2）当所有组均从正态人群中采样时，或仅最后一组从非正态分布中采样时，所有组的样本量相等，权重相等。在其余的条件下，Bonett的和BCa的自助方法比非中心的方法进行得更好。当每组样本量为30或更多时，BCa自助法是首选方法。这项研究的结果有影响的同时比较的手段和排名的手段之间和受试者内的设计。
Confidence interval (CI) estimation for an effect size (ES) provides a range of possible population ESs supported by data. In this article, we investigated the noncentral t method, Bonett's method, and the bias-corrected and accelerated (BCa) bootstrap method for constructing CIs when a standardized linear contrast of means is defined as an ES. The noncentral t method assumes normality and equal variances, Bonett's method assumes only normality, and the BCa bootstrap method makes no assumptions. We simulated data for three and four groups from a variety of populations (one normal and five nonnormals) with varied variance ratios (1, 2.25, 4, 8), population ESs (0, 0.2, 0.5, 0.8), and sample size patterns (one equal and two unequal). Results showed that the noncentral method performed the best among the three methods under the joint condition of ES = 0 and equal variances. Performance of the noncentral method was comparable to that of the other two methods under (1) equal sample size, unequal weight for each group, and the last group sampled from a leptokurtic distribution, or (2) equal sample size and equal weight for all groups, when all are sampled from a normal population, or only the last group sampled from a nonnormal distribution. In the remaining conditions, Bonett's and the BCa bootstrap methods performed better than the noncentral method. The BCa bootstrap method is the method of choice when the sample size per group is 30 or more. Findings from this study have implications for simultaneous comparisons of means and of ranked means in between- and within-subjects designs.