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A Chi-Square Approximation for the F Distribution

DOI: 10.4236/ojs.2018.81010, PP. 146-158

Keywords: Bartlett Correction, Homoscedasticity, Likelihood Ratio Statistic, One-Way ANOVA

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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.


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