Fisher’s F-ratio illustrated graphically

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Allen, Rory. 2018. Fisher’s F-ratio illustrated graphically. The Mathematical Gazette, 102(553), pp. 50-62. ISSN 0025-5572 [Article]

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Official URL: https://doi.org/10.1017/mag.2018.7

Abstract or Description

This paper aims to make Fisher’s F-ratio more easily understood by representing it graphically, using model comparison. In the graph, the null and experimental models are plotted with the number of parameters on the horizontal axis and goodness of fit to data on the vertical axis. The value of F appears as the ratio between the slopes of two lines in the diagram. The diagram gives rise in an obvious way to the “Occam line”, which is shown to embody the principle of parsimony. There is an organic relationship between the F-ratio and the Occam line, such that the plot point representing the experimental hypothesis lies below the Occam line if, and only if, the F-ratio is greater than one. The paper also shows using a simple geometrical argument that the natural measure of effect size when using the F-ratio is adjusted R-squared, and argues that its ANOVA counterpart, epsilon-squared, is superior to the commonly used omega-squared measure.

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Article

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https://doi.org/10.1017/mag.2018.7