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Psychological tests traditionally rely on single-measurement occasions to measure constructs like self-esteem and depression. Recent advances emphasize the benefits of multiple-data-point (MDP) measurement, which captures variability across different times or situations to provide a better understanding of psychological constructs. Despite these advancements, the validity of MDP measurements hinges on the assumption of measurement invariance. Measurement noninvariance can lead to inaccurate assessments and unfair classifications, such as incorrect military selections or biased academic admissions. This study investigates how measurement noninvariance affects the correlation between sample estimates and true latent constructs, as well as the accuracy of classifications based on these metrics. By addressing these gaps, this research aims to improve the reliability and fairness of psychological assessments in practical settings.