Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-06-09T10:17:42.801Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 A. W. Downie, Dr C. Kaplan and Dr F. O. McCallum for permission to use their unpublished data; to Dr J. C. N. Westwood for discussing with me his (then) unpublished work; to Miss Irene Allen for computing assistance; and to Mrs G. M. Young for the preparation of the diagrams.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

REFERENCES

Beveridge, W. I. B. & Burnet, F. M. (1946). The cultivation of viruses and rickettsiae in the chick embryo. Spec. Rep. Ser. Med. Res. Coun. Lond. no. 256.Google Scholar
Burnet, F. M. & Faris, D. D. (1942). The technique of quantitative chorioallantoic virus titration. J. Bact. 44, 241–8.CrossRefGoogle ScholarPubMed
Burnet, F. M. & Lush, D. (1939). The inactivation of herpes virus by immune sera: experiments using the chorio-allantoic membrane technique. J. Path. Bact. 48, 275–86.CrossRefGoogle Scholar
Cochran, W. G. (1937). Problems arising in the analysis of a series of similar experiments. Suppl. J. R. statist. Soc. 4, 102–18.CrossRefGoogle Scholar
Cochran, W. G. & Carroll, S. P. (1953). A sampling investigation of the efficiency of weighting inversely as the estimated variance. Biometrics, 9, 447–459.CrossRefGoogle Scholar
Fenner, F., Marshall, I. D. & Woodroofe, G. M. (1953). Studies in the epidemiology of infectious myxomatosis of rabbits. I. Recovery of Australian wild rabbits (Oryctolagus cuniculus) from myxomatosis under field conditions. J. Hyg., Camb., 51, 225–44.CrossRefGoogle ScholarPubMed
Fenner, F. & McIntyre, G. A. (1956). Infectivity titrations of myxoma virus in the rabbit and the developing chick embryo. J. Hyg., Camb., 54, 246–57.CrossRefGoogle ScholarPubMed
Fisher, R. A. & Healy, M. J. R. (1956). New tables of Behrens' test of significance. J. B. statist. Soc., B, 18, 212–16.Google Scholar
Fisher, R. A. & Yates, F. (1953). Statistical Tables for Biological, Agricultural and Medical Research, 4th ed. London: Oliver and Boyd.Google Scholar
French, E. L. & Reeves, W. C. (1954). A group of viruses isolated from naturally infected mosquitoes collected in the Murray Valley area of Victoria and New South Wales. J. Hyg., Camb., 52, 551–62.Google ScholarPubMed
James, G. S. (1951). The comparison of several groups of observations when the ratios of the population variances are unknown. Biometrika, 38, 324–9.CrossRefGoogle Scholar
James, G. S. (1956). On the accuracy of weighted means and ratios. Biometrika, 43, 304–21.CrossRefGoogle Scholar
Kleczkowski, A. (1949). The transformation of local lesion counts for statistical analysis. Ann. appl. Biol. 36, 139–52.CrossRefGoogle ScholarPubMed
McCarthy, K., Downie, A. W. & Armitage, P. (1958). The antibody response in man following infection with viruses of the Pox group. I. An evaluation of the Pock counting method for measuring neutralizing antibody. J. Hyg., Camb. (In the press).CrossRefGoogle Scholar
Meier, P. (1953). Variance of a weighted mean. Biometrics, 9, 59–73.CrossRefGoogle Scholar
Newbold, E. M. (1927). Practical applications of the statistics of repeated events, particularly to industrial accidents. J. R. statist. Soc. 90, 487–535.CrossRefGoogle Scholar
Pearson, E. S. & Hartley, H. O. (1954). Biometrika Tables for Statisticians, vol. 1. Cambridge University Press.Google Scholar
Polissar, M. T. & Shimkin, M. B. (1954). A quantitative interpretation of the distribution of induced pulmonary tumours in mice. J. nat. Cancer. Inst. 15, 377–403.Google ScholarPubMed
Reid, D. B. W., Crawley, J. F. & Rhodes, A. J. (1949). A study of fowl pox virus titration on the chorio-allantois by the pock counting technique. J. Immunol. 63, 165–71.CrossRefGoogle Scholar
Trickett, W. H., Welch, B. L. & James, G. S. (1956). Further critical values for the two-means problem. Biometrika, 43, 203–5.CrossRefGoogle Scholar
Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38, 330–36.CrossRefGoogle Scholar
Westwood, J. C. N., Phipps, P. H. & Boulter, E. A. (1957). The titration of vaccinia virus on the chorio-allantoic membrane of the developing chick-embryo. J. Hyg., Camb., 55, 123–39.CrossRefGoogle Scholar