title: The Prep statistic as a measure of confidence in model fitting.
abstract: In traditional statistical methodology (e.g., the ANOVA), confidence in the observed results is often assessed by computing thep value or the power of the test. In most cases, adding more participants to a study will improve these measures more than will increasing the amount of data collected from each participant. Thus, traditional statistical methods are biased in favor of experiments with large numbers of participants. This article proposes a method for computing confidence in the results of experiments in which data are collected from a few participants over many trials. In such experiments, it is common to fit a series of mathematical models to the resulting data and to conclude that the best-fitting model is superior. The probability of replicating this result (i.e., Prep) is derived for any two nested models. Simulations and empirical applications of this new statistic confirm its utility in studies in which data are collected from a few participants over many trials.
authors.affiliation: Department of Psychology, University of California, Santa Barbara, California 93106, USA. ashby@psych.ucsb.edu
authors.forename: F Gregory
authors.initials: FG
authors.lastname: Ashby
authors.forename: Jeffrey B
authors.initials: JB
authors.lastname: O'Brien
mesh_terms: D000704:Analysis of Variance; D001499:Bayes Theorem; D016001:Confidence Intervals; D003625:Data Collection / Q000706:statistics & numerical data*; D003661:Decision Support Techniques; D004193:Discrimination Learning; D006801:Humans; D016014:Linear Models; D008432:Mathematical Computing; D015233:Models, Statistical; D008962:Models, Theoretical; D010364:Pattern Recognition, Visual; D011597:Psychomotor Performance; D015203:Reproducibility of Results