Root Mean Square Error as a Robust Index of Gradient Speech Perception

This study introduces the root mean square error (RMSE) as a new metric for quantifying gradient speech perception in visual analog scale (VAS) tasks. By measuring the deviation of individual responses from an ideal linear mapping between stimulus and percept, RMSE offers a theoretically transparent alternative to traditional metrics like slope, response consistency, and the quadratic coefficient. To validate these metrics, we first used simulated data representing five distinct perceptual response profiles: ideal gradient, categorical, random, midpoint-biased, and conservative. The results revealed that only RMSE correctly tracked the degree of true gradiency, increasing monotonically from the ideal gradient profile (RMSE = 5.48) to random responding (RMSE = 42.16). In contrast, traditional metrics failed critically; for example, slope misclassified non-gradient, midpoint-biased responding as highly gradient (slope = 0.24). When applied to published empirical VAS data, RMSE demonstrated strong convergent validity, correlating robustly with response consistency (r ranging from -0.44 to -0.89) while avoiding the ambiguities of other measures. Crucially, RMSE exhibited moderate-to-high cross-continuum stability (mean r = 0.51), indicating it captures a stable, trait-like perceptual style. By providing a more robust and interpretable measure, RMSE offers a clearer lens for investigating the continuous nature of phonetic categorization and individual differences in speech perception.