Abstract
Gini’s (1912) coefficient of concentration is recommended as the basis for a significance test to compare the dispersions of two negative binomial populations. The data are assumed to be quadrat counts, and the jackknife technique is used to estimate standard error. Simulation studies indicate that as few as 20 quadrats may be adequate for some negative binomial populations. Application is made to the comparison of dispersions of the adult southern green stinkbug (Nezara Viridula) on three row crops.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barnett, F. C., K. Mullen, & J. G. Saw. 1967. Linear estimates of a population scale parameter. Biometnka54: 551 – 4.
David, H. A. 1968. Gini’s mean difference rediscovered. Biometnka55: 573 – 5.
Downton, F. 1966. Linear estimates with polynomial coefficients. Biometnka53: 129 – 41.
Fager, E. W. 1972. Diversity: a sampling study. Amer. Natural106: 293 – 310.
Gini, C. 1912. Variabilitae Mutabilità. Studi Economico—Giuridici della R. Universita de Caglri, Anno 3, Part 2, pp. 80.
Hoeffding, W. 1948. A class of statistics with asymptotically normal distribution. Ann. Math Statist19: 293 – 325.
Lloyd, M. 1967. Mean crowding. J. Anim. Ecol. 36: 1 – 30.
Lomnicki, Z. A. 1952. The standard error of Gini’s mean difference. Ann. Math. Statist.23: 635 – 7.
Lorenz, M. O. 1905. Methods of measuring concentration of wealth. J. Amer. Statist Assoc9: 209 – 19.
Lyons, N. I. & K. Hutcheson. 1988. Distributional properties of the number of moves index of diversity. Biometrics (to appear).
Marshall, A. W., & I. Olkin. 1979. Inequalities: The Theory of Majorization. Academic Press, New York.
Morisita, M. 1962. index, a measure of dispersion of individuals. Res. Pop. Ecol. 4:1–7.
Nair, U. S. 1936. The standard error of Gini’s mean difference. Biometrika28: 428 – 36.
Paloheimo, J. E., & A. M. Vukov. 1976. On measures of aggregation and indices of contagion. Math. Biosci.30: 69 – 97.
Patii, G. P., & C. Taillie. 1982. Diversity as a concept and its measurement. J. Amer. Statist Assoc.77: 548 – 67.
Ramasubban, T. A. 1958. The mean difference and the mean deviation of some discontinuous distributions. Biometrika45: 549 – 56.
Ramasubban, T. A. 1959. The generalized mean differences of the binomial and Poisson distributions. Biometrika46: 223 – 9.
Reed, W. J. 1983. Confidence estimation of ecological aggregation indices based on counts — a robust procedure. Biometrika39: 987 – 98.
Simpson, E.H. 1949. Measurement of diversity. Nature163: 688.
Solomon, D. L. 1979. A comparative approach to species diversity in Ecological Diversity. In Theory and Practice [eds.] Grassle, J. F., et al. International Cooperative Publishing House. Fairland, Maryland.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lyons, N.I., Hutcheson, K. (1989). Measures of the Dispersion of a Population Based on Ranks. In: McDonald, L.L., Manly, B.F.J., Lockwood, J.A., Logan, J.A. (eds) Estimation and Analysis of Insect Populations. Lecture Notes in Statistics, vol 55. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3664-1_26
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3664-1_26
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96998-5
Online ISBN: 978-1-4612-3664-1
eBook Packages: Springer Book Archive