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The Impact of Outliers on Cronbach’s Coefficient Alpha Estimate of Reliability: Ordinal/Rating Scale Item Responses
Yan Liu,
Amery D. Wu,
and
Bruno D. Zumbo*
University of British Columbia, Canada
* To whom correspondence should be addressed. E-mail: bruno.zumbo{at}ubc.ca.
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Abstract |
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In a recent Monte Carlo simulation study, Liu and Zumbo showed that outliers can severely inflate the estimates of Cronbach’s coefficient alpha for continuous item response data—visual analogue response format. Little, however, is known about the effect of outliers for ordinal item response data—also commonly referred to as Likert, Likert-type, ordered categorical, or ordinal/rating scale item responses. Building on the work of Liu and Zumbo, the authors investigated the effects of outlier contamination for binary and ordinal response scales. Their results showed that coefficient alpha estimates were severely inflated with the presence of outliers, and like the earlier findings, the effects of outliers were reduced with increasing theoretical reliability. The efficiency of coefficient alpha estimates (i. e. , sample-to-sample variation) was inflated as well and affected by the number of scale points. It is worth noting that when there were no outliers, the alpha estimates were downward biased because of the ordinal scaling. However, the alpha estimates were, in general, inflated in the presence of outliers leading to positive bias.
First published on September 2, 2009
Educational and Psychological Measurement 2009, doi:10.1177/0013164409344548
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