In this paper, we study the effect of the elimination of items from a scale so that only those items that correlate highly are chosen. Using a simulation, we estimate the impact on Cronbach's alpha as a function of the total number of items in a scale, the number of items chosen, the true correlation among the items, and the sample size. The results suggest that a substantial effect can exist. Not surprisingly, the effect is larger when sample sizes are smaller, when a smaller fraction of the original items is retained, and when there is greater variation in the true item-total correlations of the measures.
Kopalle, Praveen, and Donald Lehmann. "Alpha Inflation? The Impact of Eliminating Scale Items on Cronbach's Alpha." Organizational Behavior and Human Decision Processes 70, no. 3 (June 1997): 189-97.
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