TITLE:
A Chi-Square Approximation for the F Distribution
AUTHORS:
L. Jiang, Augustine Wong
KEYWORDS:
Bartlett Correction, Homoscedasticity, Likelihood Ratio Statistic, One-Way ANOVA
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.1,
February
24,
2018
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.