What question did this study set out to answer?

This research aims to improve inference techniques for disattenuated correlations using available summary statistics.

April 1, 2026Applied Psychological Measurement0 citationsOpen Access

Inference for Disattenuated Correlations

Key Points

This research aims to improve inference techniques for disattenuated correlations using available summary statistics.
Developed a delta method variance to address reliability estimate variability.
Assumed bivariate normality of scores and coefficient alpha.
Simulated corrected intervals to compare coverage against the Hunter–Schmidt method.
The new delta method variance achieves near-nominal coverage.
Hunter–Schmidt intervals often undercovered, particularly with imprecise reliability estimates.

Abstract

When only summary statistics from published studies are available, the Hunter–Schmidt interval is the standard tool for inference on Spearman’s disattenuated correlation, but it treats reliability estimates as known constants and ignores their sampling variability. We derive a simple delta method variance that accounts for the uncertainty of all estimates while requiring nothing beyond the summaries already at hand. Under bivariate normality of scores and coefficient alpha from a normal parallel model, the corrected interval is asymptotically valid. In simulations it achieves coverage near nominal, while Hunter–Schmidt can undercover substantially when reliability is imprecisely estimated.

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