Validity and reliability are important psychometric properties for specialists who try to understand human behavior with measurement tools. There are many factors that affect psychometric properties, and one of them is aberrant response behavior. Person-fit statistics are one way to detect aberrant individuals. The general purpose of the study was to specify the effects of possible aberrant individuals on fit indices in the Confirmatory Factor Analysis and their effects on estimated parameters by using the Mokken Homogeneity Model and the Graded Response Model. Satisfaction with Life Scale (SWLS) and the Positive and Negative Affect Scale (PANAS) were used in accordance with the purpose of this research. Flagged individuals were determined according to parametric and non-parametric person-fit statistics for both SWLS and PANAS. These individuals were removed from the data sets, and the trimmed data sets were created. Trimmed and untrimmed data sets were compared. It is seen that individuals who were flagged as aberrant generally affected the statistical results. Especially from the data sets trimmed by the parametric person-fit statistic more discriminative items were obtained. According to the research results, searching for aberrant responses can be suggested in scale development and scale adaptation studies.