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Inference for Disattenuated Correlations.

Jonas Moss1

  • 1Department of Data Science and Analytics, BI Norwegian Business School, Oslo, Norway.

Applied Psychological Measurement
|April 2, 2026
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Summary
This summary is machine-generated.

This study introduces a new statistical method to improve inference on Spearman correlations when only summary data is available. The enhanced method accounts for reliability estimate uncertainty, offering more accurate results than the standard Hunter-Schmidt interval.

Keywords:
confidence intervalsdisattenuated correlationmeasurement error

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Area of Science:

  • Psychometrics
  • Statistical Inference
  • Correlation Analysis

Background:

  • The Hunter-Schmidt interval is standard for Spearman's disattenuated correlation inference using summary statistics.
  • It assumes reliability estimates are known constants, ignoring their sampling variability.
  • This can lead to inaccurate inferences in meta-analyses.

Purpose of the Study:

  • To develop a novel statistical method for inference on Spearman's disattenuated correlation.
  • To account for the sampling variability of reliability estimates.
  • To provide a more accurate confidence interval when only summary statistics are available.

Main Methods:

  • Derived a delta method variance to incorporate uncertainty of all estimates.
  • Utilized summary statistics commonly available in published studies.
  • Assumed bivariate normality of scores and coefficient alpha from a normal parallel model.

Main Results:

  • The new delta method variance provides an asymptotically valid confidence interval.
  • Simulations show the corrected interval achieves coverage near nominal levels.
  • The Hunter-Schmidt interval significantly undercovers when reliability is imprecisely estimated.

Conclusions:

  • The proposed delta method variance offers a superior alternative to the Hunter-Schmidt interval for Spearman correlation inference.
  • This method enhances the accuracy of meta-analytic findings by accounting for reliability uncertainty.
  • Researchers can use this approach with readily available summary statistics for more robust conclusions.