One-sided and two-sided nonparametric tests for heterogeneity comparisons
DOI:
https://doi.org/10.6092/issn.1973-2201/3521Abstract
This work consists of an inferential procedure that allows for a solution to the problem of hypothesis testing, in which the objective is that of comparing the heterogeneity of two populations on the basis of sampling data, i.e. to test the hypothesis that the heterogeneity of one population is greater or not equal than that of another. The simulation study ighlights the good behaviour of the tests, i.e. the proposed tests are well approximated and powerful.References
A. AGRESTI, B. KLINGENBERG (2005), Multivariate tests comparing binomial probabilities, with application to safety studies for drugs, “Applied Statistics”.
E. BRUNNER, U. MUNZEL (2000), The nonparametric Behrens-Fisher problem: asymptotic theory and small-sample approximation, “Biometrical Journal”, 42, pp. 17-25.
A. COHEN, J.H.B. KEMPERMAN, D. MADIGAN, H.B. SAKROWITZ (2000), Effective directed tests for models with ordered categorical data. “Australian and New Zealand Journal of Statistics”, 45, pp. 285-300.
C. CORRAIN, F. MEZZAVILLA, F. PESARIN, U. SCARDELLATO (1977), Il valore discriminativo di alcuni fattori Gm, tra le poplazioni pastorali del Kenya, in “Atti e Memorie dell’Accademia Patavina di Scienze, Lettere ed Arti”, LXXXIX, Parte II: Classe di Scienze Matematiche e Naturali, pp. 55-63.
B.V. FROSINI (1981), Heterogeneity indeces and distances between distributions, “Metron”, XXXIX, pp. 3-4.
C. GINI (1912), Variabilità e mutabilità, in “Studi economico-giuridici della Facoltà di Giurisprudenza”, Università di Cagliari.
K.E. HAN, P.J. CATALANO, P. SENCHAUDHURI, C. MEHTA (2004), Exact analysis of dose-response for multiple correlated binary outcomes, “Biometrics”, 004,60, pp. 216-24.
C. HIROTSU (1986), Cumulative chi-squared statistic as a tool for testing goodness-of-fit, “Biometrika”, 73, pp. 165-173.
E.L. LEHMANN (1953), The power of rank tests, “The Annals of Mathematical Statistics”, 24, 1, pp. 23-43.
G. LETI (1965), Sull’entropia, su un indice del Gini e su altre misure dell’eterogeneità di un collettivo, “Metron”, XXIV, pp. 1-4.
M.D. LORENZ (1905), Methods of measuring the concentration of wealth, “Journal of the American Statistical Association”, 70, pp. 209-219.
T.M. LOUGHIN (2004), A Systematic Comparison of Methods for Combining P-Values from Independent Tests, “Computational Statistics and Data Analysis”, 47, pp. 467-485.
T.M. LOUGHIN, P.N. SCHERER (1998), Testing for Association in Contingency Tables with Multiple Column Responses, “Biometrics”, 54, pp. 630-637.
T. LUMLEY (1996), Generalized estimating equations for ordinal data: a note on working correlation structures. “Biometrics”, 52, pp. 354-361.
D. NETTLETON, T. BANERJEE (2001), Testing the equality of distributions of random vectors with categorical components, “Computational Statistics and Data Analysis”, 37, pp. 195-208.
G.P. PATIL, C. TAILLIE (1982), Diversity as a concept and its measurement (with discussion), “Journal of the American Statistical Association”, 77, pp. 548-567.
F. PESARIN (1994), Goodness-of-fit testing for ordered discrete distributions by resampling techniques, “Metron”, LII, pp. 57-71.
F. PESARIN (2001), Multivariate Permutation Test With Application to Biostatistics. Wiley, Chichester.
F. PESARIN, L. SALMASO (2006), Permutation tests for univariate and multivariate ordered categorical data, “Australian Journal of Statistics”, 35, pp. 315-324.
E.C. PIELOU (1975), Ecological Diversity, Wiley, New York.
E.C. PIELOU (1977), Mathematical Ecology, Wiley, New York.
A. RÉNYI (1966), Calculus des probabilitès, Dunod, Paris.
C.E. SHANNON (1948), A mathematical theory of communication, “Bell System Technological Journal”, 27, 379-423, pp. 623-656.
M.J. SILVAPULLE, P.K. SEN (2005), Constrained Statistical Inference, Inequality, Order, and Shape Restrictions. Wiley, New York.
J.F. TROENDLE (2002), A likelihood ratio test for the nonparametric Behrens-Fisher problem. “Biometrical Journal”, 44, 7, pp. 813-824.
Y. WANG (1996), A likelihood ratio test against stochastic ordering in several populations. “Journal of the American Statistical Association”, 91, pp. 1676-1683.
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