Premium
Equivalence of the statistics for replicability and area under the ROC curve
Author(s) -
Irwin R. John
Publication year - 2009
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711008x334760
Subject(s) - statistics , equivalence (formal languages) , statistic , mathematics , receiver operating characteristic , sign (mathematics) , statistical power , mathematical analysis , discrete mathematics
Two statistics, one recent and one well known, are shown to be equivalent. The recent statistic, p rep , gives the probability that the sign of an experimental effect is replicable by an experiment of equal power. That statistic is equivalent to the well‐known measure for the area under a receiver operating characteristic (ROC) curve for statistical power against significance level. Both statistics can be seen as exemplifying the area theorem of psychophysics.