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An info‐gap approach to power and sample size calculations
Author(s) -
Fox David R.,
BenHaim Yakov,
Hayes Keith R.,
McCarthy Michael A.,
Wintle Brendan,
Dunstan Piers
Publication year - 2007
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.811
Subject(s) - sample size determination , context (archaeology) , parametric statistics , variance (accounting) , sample (material) , range (aeronautics) , statistics , econometrics , central limit theorem , power (physics) , statistical power , mathematics , limit (mathematics) , inference , computer science , economics , chemistry , materials science , accounting , physics , chromatography , quantum mechanics , artificial intelligence , composite material , biology , paleontology , mathematical analysis
Power and sample size calculations are an important but underutilised component of many ecological investigations. A key problem with these calculations is the need to estimate or guess the effect size and error variance (the design parameters) prior to the actual data collection. Furthermore, calculations associated with statistical power and sample size are invariably predicated on normal distribution theory. While the central limit theorem ensures the applicability of normal‐based inference for reasonably large sample sizes, the impact of violations of this assumed distributional form in the context of power and sample size determinations is rarely considered. This paper uses information‐gap theory to provide sample size guidelines that are robust to uncertainties associated with both the design parameters and distributional form. A simple information‐gap approach is developed for one‐ and two‐sided hypothesis tests. The model results quantify the extent to which minimum power demands can be protected from uncertainty by taking additional samples, and demonstrate the importance of the combined effects of standard deviation/effect size ratio and assumed distribution in these considerations. Info‐gap theory does not eliminate the need for an initial estimate or best guess of the design parameters or the specification of a parametric distribution from which to compute power. It does, however, measure the degree of insurance provided by additional samples in the face of uncertainties in each of these. Copyright © 2006 John Wiley & Sons, Ltd.