A Comparison of the X 2, −2 Log R, and Multinomial Probability Criteria for Significance Tests When Expected Frequencies are Small
作者： Judith-Anne W. Chapman
DOI: 10.1080/01621459.1976.10480959
关键词:
摘要: Abstract The exact multinomial, and χ2 probabilities for −2 log R have been compared. χ 2 are on average closer to the multinomial than corresponding probabilities. differences between usually smaller R. A pattern was observed among five types of significance levels, an explanation proposed.
sci-hub.se 参考文章(18)
Leon A. Hyer, Merle W. Tate, Significance Values for an Exact Multinomial Test and Accuracy of the Chi-Square Approximation, Final Report. ,(1969)
James K. Yarnold, The Minimum Expectation in X 2 Goodness of Fit Tests and the Accuracy of Approximations for the Null Distribution Journal of the American Statistical Association. ,vol. 65, pp. 864- 886 ,(1970) , 10.1080/01621459.1970.10481131
Donald Allan Darling, Theodore Wilbur Anderson, A Test of Goodness of Fit Journal of the American Statistical Association. ,vol. 49, pp. 765- 769 ,(1954) , 10.2307/2281537
Eric N. West, Oscar Kempthorne, A comparison of the chi2 and likelihood ratio tests for composite alternatives1 Journal of Statistical Computation and Simulation. ,vol. 1, pp. 1- 33 ,(1972) , 10.1080/00949657208810001
R. A. Fisher, The significance of deviations from expectation in a Poisson Series. Biometrics. ,vol. 6, pp. 17- 24 ,(1950) , 10.2307/3001420
Robert Radlow, Edward F. Alf, An Alternate Multinomial Assessment of the Accuracy of the χ2 Test of Goodness of Fit Journal of the American Statistical Association. ,vol. 70, pp. 811- 813 ,(1975) , 10.1080/01621459.1975.10480306
William G. Cochran, The $\chi^2$ Test of Goodness of Fit Annals of Mathematical Statistics. ,vol. 23, pp. 315- 345 ,(1952) , 10.1214/AOMS/1177729380
I. J. Good, T. N. Gover, G. J. Mitchell, Exact Distributions for χ2and for the Likelihood-Ratio Statistic for the Equiprobable Multinomial Distribution Journal of the American Statistical Association. ,vol. 65, pp. 267- 283 ,(1970) , 10.1080/01621459.1970.10481078
Douglas A. Zahn, Gail C. Roberts, Exact χ2 Criterion Tables with Cell Expectations One: An Application to Coleman's Measure of Consensus Journal of the American Statistical Association. ,vol. 66, pp. 145- 148 ,(1971) , 10.1080/01621459.1971.10482235
W. G. COCHRAN, The x2 distribution for the binomial and poisson series, with small expectations Annals of Human Genetics. ,vol. 7, pp. 207- 217 ,(1936) , 10.1111/J.1469-1809.1936.TB02140.X