Estimates of subgroup differences are routinely used as part of a comprehensive validation system, and these estimates serve a critical role, including evaluating adverse impact. Unfortunately, under direct range restriction, a selected mean ( ) is a biased estimator of the population mean as well as the selected true score mean . This is due partly to measurement bias. This bias, as we show, is a factor of the selection ratio, the reliability of the measure, and the variance of the distribution. This measurement bias renders a subgroup comparison questionable when the subgroups have different selection ratios. The selected subgroup comparison is further complicated by the fact that the subgroup variances will be unequal in most situations where the selection ratios are not equal. We address these problems and present a corrected estimate of the mean difference, as well as an estimate of Cohen’s d* that estimates the true score difference between two selected populations, . In addition, we show that the measurement bias is not present under indirect range restriction. Thus, the observed selected mean is an unbiased estimator of selected true score mean . However, it is not an unbiased estimator of the population mean . These results have important implications for selection research, particularly when validating instruments.

中文翻译：

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比较选定亚组时的测量偏差问题

亚组差异的估计通常用作综合验证系统的一部分，这些估计起着关键作用，包括评估不利影响。不幸的是，在直接范围限制下，所选均值 ( ) 是总体均值和所选真实得分均值的有偏估计量. 这部分是由于测量偏差。正如我们所展示的，这种偏差是选择率、度量的可靠性和分布方差的一个因素。当子组具有不同的选择比率时，这种测量偏差会使子组比较变得有问题。由于在选择比率不相等的大多数情况下，子组方差将不相等，因此所选子组比较更加复杂。我们解决了这些问题，并提出了平均差异的修正估计值，以及 Cohen d* 的估计值，该值估计了两个选定群体之间的真实分数差异。此外，我们表明在间接范围限制下不存在测量偏差。因此，观察到的选定平均值是所选真实得分均值的无偏估计量。但是，它不是总体均值的无偏估计量。这些结果对选择研究具有重要意义，尤其是在验证仪器时。