Innocenti Francesco, Tan Frans E S, Candel Math J J M, van Breukelen Gerard J P
Department of Methodology and Statistics.
Psychol Methods. 2023 Feb;28(1):89-106. doi: 10.1037/met0000394. Epub 2021 Aug 12.
To prevent mistakes in psychological assessment, the precision of test norms is important. This can be achieved by drawing a large normative sample and using regression-based norming. Based on that norming method, a procedure for sample size planning to make inference on Z-scores and percentile rank scores is proposed. Sampling variance formulas for these norm statistics are derived and used to obtain the optimal design, that is, the optimal predictor distribution, for the normative sample, thereby maximizing precision of estimation. This is done under five regression models with a quantitative and a categorical predictor, differing in whether they allow for interaction and nonlinearity. Efficient robust designs are given in case of uncertainty about the regression model. Furthermore, formulas are provided to compute the normative sample size such that individuals' positions relative to the derived norms can be assessed with prespecified power and precision. (PsycInfo Database Record (c) 2023 APA, all rights reserved).
为防止心理评估中出现错误，测试常模的精确性很重要。这可以通过抽取大量的常模样本并使用基于回归的常模制定方法来实现。基于该常模制定方法，提出了一种样本量规划程序，用于对Z分数和百分等级分数进行推断。推导了这些常模统计量的抽样方差公式，并用于获得规范样本的最优设计，即最优预测变量分布，从而最大化估计精度。这是在五个具有定量和分类预测变量的回归模型下完成的，这些模型在是否允许交互作用和非线性方面有所不同。在回归模型存在不确定性的情况下，给出了有效的稳健设计。此外，还提供了计算公式来计算常模样本量，以便能够以预先设定的功效和精度评估个体相对于推导常模的位置。（PsycInfo数据库记录（c）2023美国心理学会，保留所有权利）
