The Effects of an Arcsin Square Root Transform on a Binomial Distributed Quantity.

Imaging Science and Biomedical Engineering Division; Medical School, University of Manchester, M13 9PT, Manchester; Imaging Science and Biomedical Engineering Division Medical School, University of Manchester Manchester, M13 9PT, UK

ABSTRACT This document provides proofs of the following: • The binomial distribution can be approximated with a Gaussian distribution at large values of N . • The arcsin square-root transform is the variance stabilising transform for the binomial distribution. • The Gaussian approximation for the binomial distribution is more accurate at smaller values of N after the variance stabilising transform has been applied. The conclusion contains some comments concerning the relationship between the variance stabilising transform and the improved accuracy of the Gaussian approximation, which holds for both the binomial and Poisson distributions.

  • Source
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper identifies the important role that covariance estimation has to play in the construction of analysis systems. The problem of co-registration for inter-modality clinical volumes is often solved by maximising the so-called mutual information measure. This paper extends the existing theory in this area and suggests a viable way of constructing co- variances for mutual information approaches by treating this algorithm as a bootstrapped likelihood based approach. We provide both theoretical and practical tests of the validity of this method. In doing so we identify important subtleties in the current use of these measures for coregistration. These issues suggest potential improvements in the way that such measures might be constructed and used.
  • [Show abstract] [Hide abstract]
    ABSTRACT: Sheep less than 1 year of age consistently yield approximately 20% less methane than older adult sheep. This has implications for New Zealand's National Inventory of Greenhouse Gas Emissions. The aim of this study was to determine if emissions from young farmed deer also increase with age. Methane emissions of 20 red deer stags grazing permanent perennial ryegrass‐based pasture were measured four times post‐weaning, at 4.5, 6.5, 9 and 11.5 months of age, using the sulphur hexafluoride technique. Methane production and methane yield increased with age (P < 0.05) and appeared lower (26%) than previous measurements from adult deer on similar pasture. The results from this study imply that total methane emissions from young deer recorded in the New Zealand greenhouse gas inventory are likely to be overestimated if values used for the inventory are based on adult methane emissions.
    New Zealand Journal of Agricultural Research 09/2007; 50(3):407-416. · 0.84 Impact Factor


Available from