Diminishing returns as a function of the association between within-individual average performance and variance

Area of Science:

• Psychology
• Statistics
• Cognitive Science

Background:

• The worst performance rule (WPR) effect is known to arise from statistical dependencies in data.
• Spearman's law of diminishing returns (SLODR) describes a phenomenon in psychometrics, but its underlying causes require further investigation.

Purpose of the Study:

• To investigate whether statistical dependencies in data can also explain Spearman's law of diminishing returns (SLODR).
• To examine the proposed criteria for SLODR in light of potential statistical artifacts.

Main Methods:

• Utilized four diverse, publicly available datasets.
• Analyzed the relationship between within-individual average performance and variance in test scores.
• Evaluated two proposed SLODR criteria: skewness of latent ability and its correlation with within-individual residual variance.

Main Results:

• Both SLODR criteria were significantly affected by the correlation between within-individual performance and score variance.
• The influence of this correlation on the two criteria operated in opposing directions.
• This suggests that achieving unambiguous support for SLODR may be challenging due to these statistical effects.

Conclusions:

• Statistical dependencies, specifically the correlation between within-individual performance and score variance, can impact measures related to SLODR.
• Findings indicate that research attributing results solely to cognitive functioning may overlook simpler statistical explanations.
• Future research should carefully consider and control for these statistical dependencies to avoid misinterpretations in psychometric and cognitive research.