Standardized Descriptive Index for Measuring Deviation and Uncertainty in Psychometric Indicators

TL;DR

This paper introduces a standardized deviation index based on Cohen's d for psychometric item analysis, providing a unified measure of deviation and uncertainty suitable for small samples.

Contribution

It repurposes Cohen's d as a diagnostic tool for psychometric items, integrating mean and standard deviation into a single, objective index.

Findings

The index is bounded, scale-invariant, and unbiased.

Analytical properties facilitate threshold setting for item quality.

Supports small sample psychometric testing.

Abstract

The use of descriptive statistics in pilot testing procedures requires objective, standard diagnostic tools that are feasible for small sample sizes. While current psychometric practices report item-level statistics, they often report these raw descriptives separately rather than consolidating both mean and standard deviation into a single diagnostic tool to directly measure item quality. By leveraging the analytical properties of Cohen's d, this article repurposes its use in scale development as a standardized item deviation index. This measures the extent of an item's raw deviation relative to its scale midpoint while accounting for its own uncertainty. Analytical properties such as boundedness, scale invariance, and bias are explored to further understand how the index values behave, which will aid future efforts to establish empirical thresholds that characterize redundancy among formative indicators and consistency among reflective indicators.