Regression toward the mean in a two-stage selection program. II. Correlated within-subject observations

Area of Science:

• Statistics
• Biostatistics
• Psychometrics

Background:

• Two-stage selection programs are common in various scientific fields.
• Understanding within-subject variation is crucial for accurate selection.
• Regression toward the mean can impact selection outcomes.

Purpose of the Study:

• To develop a statistical model for two-stage selection programs.
• To analyze the impact of within-subject variation on selection accuracy.
• To provide guidance on optimizing observation timing in selection processes.

Main Methods:

• A mathematical model was developed for normally distributed variables.
• Within-subject variation was modeled using a stationary first-order autoregressive process.
• Expected regression toward the mean, mean, and variance of retained subjects were analyzed.

Main Results:

• Selection outcomes are functions of classification points, number of observations, autocorrelation, and time intervals.
• The time interval between observations significantly affects within-subject correlation.
• Increased time intervals decrease correlation, especially with high autocorrelation.

Conclusions:

• The time interval between observations is a critical factor in designing effective selection programs.
• Wider spacing of observations is advised to mitigate high autocorrelation.
• Optimizing observation intervals enhances the information gained from a given number of observations.