Shadish William R, Hedges Larry V, Pustejovsky James E
School of Social Sciences, Humanities and Arts, University of California, Merced, USA.
Institute for Policy Research, Northwestern University, USA.
J Sch Psychol. 2014 Apr;52(2):123-47. doi: 10.1016/j.jsp.2013.11.005. Epub 2013 Dec 27.
This article presents a d-statistic for single-case designs that is in the same metric as the d-statistic used in between-subjects designs such as randomized experiments and offers some reasons why such a statistic would be useful in SCD research. The d has a formal statistical development, is accompanied by appropriate power analyses, and can be estimated using user-friendly SPSS macros. We discuss both advantages and disadvantages of d compared to other approaches such as previous d-statistics, overlap statistics, and multilevel modeling. It requires at least three cases for computation and assumes normally distributed outcomes and stationarity, assumptions that are discussed in some detail. We also show how to test these assumptions. The core of the article then demonstrates in depth how to compute d for one study, including estimation of the autocorrelation and the ratio of between case variance to total variance (between case plus within case variance), how to compute power using a macro, and how to use the d to conduct a meta-analysis of studies using single-case designs in the free program R, including syntax in an appendix. This syntax includes how to read data, compute fixed and random effect average effect sizes, prepare a forest plot and a cumulative meta-analysis, estimate various influence statistics to identify studies contributing to heterogeneity and effect size, and do various kinds of publication bias analyses. This d may prove useful for both the analysis and meta-analysis of data from SCDs.
本文提出了一种用于单病例设计的d统计量，其度量与随机实验等被试间设计中使用的d统计量相同，并给出了为何这样一个统计量在单病例设计研究中有用的一些原因。d统计量有正式的统计推导，配有适当的功效分析，并且可以使用用户友好的SPSS宏进行估计。我们讨论了d统计量与其他方法（如先前的d统计量、重叠统计量和多水平建模）相比的优缺点。它至少需要三个病例进行计算，并假设结果呈正态分布且具有平稳性，文中对这些假设进行了详细讨论。我们还展示了如何检验这些假设。文章核心部分深入演示了如何为一项研究计算d统计量，包括自相关的估计以及病例间方差与总方差（病例间方差加病例内方差）的比率，如何使用宏计算功效，以及如何在免费软件R中使用d统计量对单病例设计的研究进行元分析，附录中包含了相关语法。该语法包括如何读取数据、计算固定效应和随机效应平均效应量、绘制森林图和累积元分析、估计各种影响统计量以识别导致异质性和效应量的研究，以及进行各种类型的发表偏倚分析。这种d统计量可能对单病例设计数据的分析和元分析都有用。
