🤖 AI Summary
Current psychometric practice relies on separate descriptive statistics (mean and standard deviation) to assess item quality, lacking a standardized diagnostic tool that integrates both to quantify raw deviation from scale midpoints and its uncertainty—especially problematic in small-sample settings.
Method: We propose a Standardized Projected Deviation Index (SPDI), derived from Cohen’s *d*, which unifies the magnitude and variability of an item’s raw deviation from the scale midpoint into a single, bounded, scale-invariant, and bias-controlled quality metric.
Results: Through theoretical derivation and small-sample simulation studies, we demonstrate that SPDI is interpretable, invariant across items, and robust under limited data. It provides empirically grounded, actionable thresholds for identifying formative indicator redundancy and evaluating reflective indicator consistency—thereby enabling objective, quantitative item-level diagnostics in both exploratory and confirmatory measurement contexts.
📝 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.