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A Chi-Square Approximation for the <i>F</i> Distribution
Beijing Education Examinations Authority, Beijing, China
Department of Mathematics and Statistics, York University, Toronto, Canada
- 1 Beijing Education Examinations Authority, Beijing, China
- 2 Department of Mathematics and Statistics, York University, Toronto, Canada
Open Journal of Statistics·Volume 08 (2018)·Pages 146–158·Published 25 January 2018·DOI10.4236/ojs.2018.81010
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Abstract
F distribution is one of the most frequently used distributions in statistics. For example, it is used for testing: equality of variances of two independent normal distributions, equality of means in the one-way ANOVA setting, overall significance of a normal linear regression model, and so on. In this paper, a simple chi-square approximation for the cumulative distribution of the F -distribution is obtained via an adjusted log-likelihood ratio statistic. This new approximation exhibits remarkable accuracy even when the degrees of freedom of the F distribution are small.
KeywordsBartlett CorrectionHomoscedasticityLikelihood Ratio StatisticOne-Way ANOVA
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