The impact of faking on Cronbach's alpha for dichotomous and ordered rating scores

In many psychological inventories (i.e., personnel selection surveys and diagnostic tests) the collected samples often include fraudulent records. This confronts the researcher with the crucial problem of biases yielded by the usage of standard statistical models. In this paper we applied a recent probabilistic perturbation procedure, called sample generation by replacement (SGR)-(Lombardi and Pastore, Multivar. Behav. Res 47: 519-546, 2012), to study the sensitivity of Cronbach's alpha index to fake perturbations in dichotomous and ordered data, respectively. We used SGR to perform two distinct SGR simulation studies involving two sample size conditions, three item set sizes, and twenty levels of faking perturbations. Moreover, in the second SGR simulation study we also evaluated an additional factor, type of faking model, to study sample reliability under different modulations of graded faking (uniform faking, average faking, slight faking, and extreme faking). To simulate these more complex faking models we proposed a novel extension of the SGR perturbation procedure based on a discrete version of the generalized beta density distribution. We also applied the new procedure to real behavioral data on emotional instability.