Asymptotic T to Z and F to Z Statistic Transformations

FMRIB Technical Report TR00MJ1

Mark Jenkinson and Mark Woolrich

Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB),
Department of Clinical Neurology, University of Oxford, John Radcliffe Hospital,
Headley Way, Headington, Oxford, UK

Abstract:

This report describes a mathematical approximation to convert from T to Z and F to Z statistic values. The approximation is asymptotic as it is becomes more accurate for higher values of T, F and Z. Since these values correspond to low values of probability, p, the actual transformation uses log(p) as the intermediary, and so can be calculated with normal C/C++ float variables, without having problems with underflow.