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A cautionary note on the finite sample behavior of maximal reliability
Miguel I Aguirre-Urreta1, Mikko Rönkkö2, Cameron N McIntosh3
1Jerry S. Rawls College of Business Administration, Texas Tech University.
Psychological Methods
|August 24, 2018
Summary
Maximal reliability (Hancock's H) shows bias in small samples. Composite reliability is a more stable alternative for smaller datasets in psychological research.
Area of Science:
- Psychological measurement
- Psychometrics
- Reliability analysis
Background:
- Coefficient alpha is being replaced by model-based reliability coefficients in psychological research.
- Composite reliability and maximal reliability are leading alternatives, assuming unidimensionality and independent errors.
- Maximal reliability (Hancock's H) is gaining attention for its ability to weight indicators differently.
Purpose of the Study:
- To examine the finite-sample behavior of maximal reliability statistics.
- To investigate bias in sample-based maximal reliability estimators.
- To compare the bias of maximal reliability with composite reliability in small samples.
Main Methods:
- Derivation of maximal reliability weights using population quantities.
- Examination of the finite-sample behavior of these weights.
- Simulation or analysis comparing bias in small-sample scenarios.
Main Results:
- Sample maximal reliability is positively biased compared to population maximal reliability.
- Composites using sample-derived maximal reliability weights have lower true reliability than population values.
- These biases are more pronounced in small samples (n < 100).
Conclusions:
- Maximal reliability statistics exhibit significant bias in small samples.
- Composite reliability estimators show substantially less bias in small samples.
- Composite reliability is recommended over maximal reliability for small-sample psychological research.
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