Range statistics and the exact modeling of discrete non-gaussian distributions on learnability data

Abstract

A measure called i-bar is presented, which is the inverse of the mid-range derived from data on trials-to-criterion in tasks that require practice. This measure is interpreted as a conjoint measurement scale, permitting: (a) evaluation of sensitivity of the principal performance measure (which is used to set the metric for trials to criterion); (b) evaluation of the learnability of the work method (i.e. the goodness of the software tool); (c) evaluation of the resilience of the work method. It is possible to mathematically model such order statistics using negative binomial and logistic growth equations, and derive methods for generating prediction intervals. This approach involves novel ways of thinking about statistical analysis for "practical significance." The is applicable to the study of the effects of any training or intervention, including software interventions designed to improve legacy work methods and interventions that involve creating entirely new cognitive work systems. © 2011 Springer-Verlag.