Laczo Roxanne M, Sackett Paul R, Bobko Philip, Cortina José M
Department of Psychology, University of Minnesota, Minneapolis, MN 55455-0344, USA.
J Appl Psychol. 2005 Jul;90(4):758-64. doi: 10.1037/0021-9010.90.4.758.
The authors discuss potential confusion in conducting primary studies and meta-analyses on the basis of differences between groups. First, the authors show that a formula for the sampling error of the standardized mean difference (d) that is based on equal group sample sizes can produce substantially biased results if applied with markedly unequal group sizes. Second, the authors show that the same concerns are present when primary analyses or meta-analyses are conducted with point-biserial correlations, as the point-biserial correlation (r) is a transformation of d. Third, the authors examine the practice of correcting a point-biserial r for unequal sample sizes and note that such correction would also increase the sampling error of the corrected r. Correcting rs for unequal sample sizes, but using the standard formula for sampling error in uncorrected r, can result in bias. The authors offer a set of recommendations for conducting meta-analyses of group differences.
作者讨论了基于组间差异进行原始研究和荟萃分析时可能出现的混淆。首先，作者表明，基于相等组样本量的标准化均数差（d）的抽样误差公式，如果应用于明显不相等的组样本量，可能会产生严重有偏差的结果。其次，作者表明，当使用点二列相关进行原始分析或荟萃分析时，同样存在这些问题，因为点二列相关（r）是d的一种变换。第三，作者研究了针对不相等样本量校正点二列r的做法，并指出这种校正也会增加校正后r的抽样误差。对不相等样本量的r进行校正，但在未校正的r中使用抽样误差的标准公式，可能会导致偏差。作者为进行组间差异的荟萃分析提供了一系列建议。
