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Asymptotically distribution-free (ADF) interval estimation of coefficient alpha.
Alberto Maydeu-Olivares1, Donna L Coffman, Wolfgang M Hartmann
1Department of Psychology, University of Barcelona, Barcelona, Spain. amaydeu@ub.edu
Psychological Methods
|June 15, 2007
Summary
Sample coefficient alpha estimates can mislead reliability assessments due to downward bias. Using interval estimators, particularly asymptotically distribution-free (ADF) ones for larger samples, provides a more accurate reliability measure for test scores.
Area of Science:
- Psychometrics
- Statistical Reliability
- Educational Measurement
Background:
- Coefficient alpha is a widely used reliability estimate.
- Point estimates of coefficient alpha are consistently biased downward, potentially misrepresenting test score reliability.
- This bias is most pronounced with small sample sizes and low population reliability.
Purpose of the Study:
- To investigate the accuracy of asymptotically distribution-free (ADF) and normal-theory interval estimators for coefficient alpha.
- To compare the performance of these estimators under varying conditions of item skewness and kurtosis.
- To provide a method for computing ADF confidence intervals for coefficient alpha.
Main Methods:
- Simulation studies were conducted to evaluate interval estimator behavior.
- Conditions included varied item skewness, excess kurtosis, and sample sizes.
- Asymptotically distribution-free (ADF) and normal-theory interval estimators were compared.
Main Results:
- Normal-theory intervals showed reduced accuracy when item skewness or excess kurtosis exceeded 1.
- ADF intervals were found to be more accurate and preferable for sample sizes over 100 observations.
- The accuracy of ADF intervals was consistent across different levels of item skewness and kurtosis.
Conclusions:
- Interval estimation for coefficient alpha is crucial for accurate reliability assessment.
- ADF confidence intervals offer a more robust and accurate estimation of reliability, especially in non-normal data and larger samples.
- A formula and SAS macro for computing ADF confidence intervals are provided for practical application.
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