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) 2021 APA, all rights reserved)

中文翻译：

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基于回归的测试和问卷标准化的样本量计算和优化设计。

为了防止心理评估中的错误，测试规范的精确性很重要。这可以通过绘制大量规范样本并使用基于回归的规范来实现。基于该归一化方法，提出了一个样本量规划程序，以对 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，并利用这些公式得到了常模样本的最优设计，即最优预测分布，从而最大限度地提高了估计精度。这是在具有定量和分类预测变量的五个回归模型下完成的，不同之处在于它们是否允许相互作用和非线性。在回归模型不确定的情况下，给出了有效的稳健设计。此外，提供公式来计算规范样本量，以便可以使用预先指定的功效和精度评估个人相对于派生规范的位置。（PsycInfo 数据库记录 (c) 2021 APA，保留所有权利）