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Detecting social desirability (SD) bias in self-reported educational or psychological assessments is essential to measure true values of what researchers aim to study. To accurately estimate the main factor, it is necessary to identify a person who responded in a socially desirable way different from his or her own condition, or an item that is greatly affected by SD. This study helps researchers to utilize factor mixture model (FMM) practically by the purposes of the researchers (discrimination of people with high SD or items affected by SD) through the investigation of adequate sample size according to the number of items of the main factor under various conditions when using FMM to detect SD bias by Monte Carlo simulation study.