Beyond Simple Averaging: Combining Scores, Reliabilities, and Validities of Multiple Intelligence Tests

Area of Science:

• Psychometrics
• Psychological assessment
• Statistical modeling

Background:

• Applied diagnostics often use arithmetic averaging to combine intelligence test scores.
• This method is statistically imprecise, failing to account for test correlations and variance reduction.
• Such imprecision can cause significant misjudgments in high-stakes assessments.

Purpose of the Study:

• To investigate the prevalence of simple averaging in combining intelligence scores.
• To propose a statistically valid method for combining multiple intelligence test scores.
• To provide tools for practical adoption of the proposed method.

Main Methods:

• Survey of 75 psychologically educated individuals on score combination practices.
• Monte Carlo simulations to validate a new score combination method across various test characteristics.
• Development of an open-source R package and Shiny web application.

Main Results:

• 77.33% of surveyed individuals used simple averaging, ignoring statistical considerations.
• Monte Carlo simulations demonstrated virtually perfect accuracy (r = 1.00) for the proposed method.
• The method's accuracy was robust across different numbers of tests, score distributions, and intercorrelations.

Conclusions:

• Simple arithmetic averaging of intelligence test scores is a common but flawed practice.
• A statistically valid method for combining scores was developed and validated.
• Accessible tools (R package, Shiny app) are provided to support the adoption of this improved method in applied diagnostics.