Transformations for within-subject designs: a Monte Carlo investigation

Area of Science:

• Psychology
• Statistics
• Experimental Design

Background:

• Within-subject designs often collect multiple measures per participant per condition.
• Averaging these measures is common but may not optimize statistical power.
• Alternative data transformations exist but their impact on error rates is less understood.

Purpose of the Study:

• To evaluate the effectiveness of various data transformations in enhancing statistical power for within-subject designs.
• To compare the influence of transformations on Type I and Type II error probabilities.
• To identify optimal transformations for different data distributions, including skewed data.

Main Methods:

• Utilized Monte Carlo simulations to rigorously assess transformation effects.
• Compared simple averaging against Z-score and range correction transformations.
• Investigated performance under both normal and highly skewed data distributions.

Main Results:

• Z-score and range correction transformations substantially increased power with normally distributed data compared to averaging.
• These transformations also performed well across various conditions with highly skewed data.
• Outlier correction, particularly trimming, proved beneficial for increasing power.

Conclusions:

• Data transformations, specifically Z-scores and range correction, offer significant advantages for improving statistical power in within-subject designs.
• These methods are robust across different data distributions, including skewed data common in psychological research.
• Employing appropriate transformations and outlier handling (trimming) is recommended for more sensitive and reliable experimental findings.