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Studies in the variability of pock counts

Published online by Cambridge University Press:  15 May 2009

P. Armitage
P. Armitage
Affiliation:
Statistical Research Unit of the Medical Research Council, London School of Hygiene and Tropical Medicine
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1. The relationship has been examined between the variance and the mean of pock counts made by a number of different workers.

2. In all cases the variance was considerably greater than that expected if the distributions were of the Poisson form. Recent work of Westwood et al. (1957) suggests that variation approaching the Poisson expectation can be achieved by appropriate technical measures.

3. With one exception, there appeared to be a linear relationship between the logarithm of the variance and the logarithm of the mean. The slope of this line varied from one laboratory to another, but not, apparently, from one occasion to another in any one laboratory.

4. The hypothesis that for any set of egg membranes the expectations of the pock counts bear constant ratios to each other, irrespective of the virus density, was untenable: the observed variances increase less rapidly with high counts than would have been expected on this theory.

5. Statistical methods are proposed for comparing and combining sets of counts at different dilutions. If Poisson variability were achieved, simpler methods would be available.

I am much indebted to Dr L. Collier, Prof. A. W. Downie, Dr C. Kaplan and Dr F. O. McCallum for permission to use their unpublished data; to Dr J. C. N. Westwood for discussing with me his (then) unpublished work; to Miss Irene Allen for computing assistance; and to Mrs G. M. Young for the preparation of the diagrams.

Type
Research Article
Information
Journal of Hygiene , Volume 55 , Issue 4 , December 1957 , pp. 564 - 581
Copyright
Copyright © Cambridge University Press 1957

References

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