Department of Psychology, Universidad de Oviedo, Oviedo, Spain.
Department of Psychology, Universidad de Murcia, Murcia, Spain.
Behav Res Methods. 2019 Jun;51(3):1216-1243. doi: 10.3758/s13428-018-1059-y.
In this study, two approaches were employed to calculate how large the sample size needs to be in order to achieve a desired statistical power to detect a significant group-by-time interaction in longitudinal intervention studies-a power analysis method, based on derived formulas using ordinary least squares estimates, and an empirical method, based on restricted maximum likelihood estimates. The performance of both procedures was examined under four different scenarios: (a) complete data with homogeneous variances, (b) incomplete data with homogeneous variances, (c) complete data with heterogeneous variances, and (d) incomplete data with heterogeneous variances. Several interesting findings emerged from this research. First, in the presence of heterogeneity, larger sample sizes are required in order to attain a desired nominal power. The second interesting finding is that, when there is attrition, the sample size requirements can be quite large. However, when attrition is anticipated, derived formulas enable the power to be calculated on the basis of the final number of subjects that are expected to complete the study. The third major finding is that the direct mathematical formulas allow the user to rigorously determine the sample size required to achieve a specified power level. Therefore, when data can be assumed to be missing at random, the solution presented can be adopted, given that Monte Carlo studies have indicated that it is very satisfactory. We illustrate the proposed method using real data from two previously published datasets.
在这项研究中，采用了两种方法来计算为了在纵向干预研究中达到检测显著的组-时间交互作用所需的样本量——一种是基于普通最小二乘法估计的推导公式的功效分析方法，另一种是基于限制最大似然估计的经验方法。这两种方法在四种不同情况下的性能进行了检验：（a）具有同方差的完整数据，（b）具有同方差的不完整数据，（c）具有异方差的完整数据，以及（d）具有异方差的不完整数据。这项研究有几个有趣的发现。首先，在存在异质性的情况下，为了达到所需的名义功效，需要更大的样本量。第二个有趣的发现是，当存在流失时，样本量的要求可能相当大。然而，当预期会出现流失时，推导公式可以根据预计完成研究的最终受试者数量来计算功效。第三个主要发现是，直接的数学公式允许用户严格确定达到特定功效水平所需的样本量。因此，当可以假设数据是随机缺失时，可以采用所提出的方法，因为蒙特卡罗研究表明，它非常令人满意。我们使用两个先前发表的数据集中的真实数据来说明所提出的方法。
