Asymptotically Distribution Free (Adf) Interval Estimation of Coefficient Alpha
Posted: 20 Sep 2007
Date Written: May 12, 2006
Abstract
Asymptotic distribution free (ADF) interval estimators for coefficient alpha were introduced in the context of an application by Yuan, Guarnaccia, and Hayslip (2003). Here, simulation studies were performed to investigate the behavior of ADF vs. normal theory (NT) interval estimators of coefficient alpha for tests composed of ordered categorical items under varied conditions of sample size, item skewness and kurtosis, number of items, and average inter-item correlation. NT intervals were found to be inaccurate when item skewness > 1 or kurtosis > 4. But for sample sizes over 100 observations, ADF intervals provide an accurate perspective of the population coefficient alpha of the test regardless of item skewness and kurtosis. A formula for computing ADF confidence intervals for coefficient alpha for tests of any size is provided, along with its implementation as a SAS macro.
Keywords: coefficient omega, reliability, Likert-type Ãtems.
JEL Classification: C00
Suggested Citation: Suggested Citation