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Social desirability bias (SDB) introduces measurement error in educational assessment and threatens the validity of results. Generally, SDB questionnaires have been administered accompanied by the main test to identify SDB responding. The goal of this paper is to use the parametric and nonparametric person-fit indices in an effort to detect SDB responding as well as to compare the strength of machine learning classifiers of logistic regression and random forest according to receiver operating curve (ROC) analysis and the percentage of area under the curve (AUC). It is expected that random forest enhances the classification and improves SDB detection.