Robust Coefficients Alpha and Omega and Confidence Intervals With Outlying Observations and Missing Data: Methods and...

Area of Science:

• Psychometrics
• Statistical modeling
• Social sciences research

Background:

• Cronbach's alpha is a standard reliability measure in social, behavioral, and education sciences.
• Traditional alpha and McDonald's omega estimation methods assume complete, normally distributed data.
• Non-tau-equivalent items necessitate alternatives like McDonald's omega.

Purpose of the Study:

• To develop robust procedures for estimating Cronbach's alpha and McDonald's omega.
• To address limitations of traditional methods concerning outlying observations and missing values.
• To provide accurate standard errors and confidence intervals for reliability estimates.

Main Methods:

• Development of robust estimation procedures for alpha and omega.
• Investigation of the influence of outliers and missing data via simulation studies.
• Creation of an R package (coefficientalpha) for practical application.

Main Results:

• Robust methods yield improved estimates for alpha and omega compared to conventional techniques.
• Enhanced coverage rates for confidence intervals using the robust approach.
• Demonstrated effectiveness of the coefficientalpha R package for reliable estimation.

Conclusions:

• Robust estimation procedures offer superior accuracy for reliability coefficients in the presence of data imperfections.
• The developed R package facilitates the application of these improved methods in research.
• This work enhances the reliability of psychological and educational measurements.