Constructing a group distribution from individual distributions

Area of Science:

• Cognitive Psychology
• Mathematical Psychology
• Psychometrics

Background:

• Group distributions are syntheses of individual data distributions.
• Adequate group distribution methods must preserve existing characteristics and avoid introducing new ones.
• Quantile averaging is a common but inadequate method for response time distributions.

Purpose of the Study:

• To evaluate the adequacy of quantile averaging for response time distributions.
• To propose and validate a generalized, adequate method for constructing group distributions.
• To demonstrate the applicability of the proposed method across different experimental tasks and participant data.

Main Methods:

• Analysis of empirical response times using quantile-quantile plots.
• Generalization of quantile averaging using nonlinear data transformation.
• Application of a log transform to response times after removing the base response time (or using geometric mean of quantiles).
• Proposal and evaluation of four estimates for base response times.

Main Results:

• Quantile averaging was shown to be inadequate for response time distributions.
• The proposed log transform method effectively constructs appropriate group distributions.
• The method demonstrated suitability for aggregating data across participants and training sessions.

Conclusions:

• The generalized quantile averaging method, using a log transform, is an adequate approach for creating group distributions.
• This validated method can be applied to aggregate response time data in various experimental contexts.
• The findings offer a robust technique for synthesizing individual response time data into meaningful group-level representations.