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Fisher's F-ratio illustrated graphically

Published online by Cambridge University Press:  08 February 2018

Rory Allen
Rory Allen*
Affiliation:
Department of Psychology, Goldsmiths, University of London, London SE14 6NW

Extract

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Calculating Fisher's F-ratio is a key step in a number of statistical procedures involving null hypothesis significance testing. This is particularly so in the case of ANOVA (analysis of variance) in its several forms, but even multiple regression includes a test of significance of the overall model which employs an F-ratio. The present paper aims at making the basic ideas behind this common statistic more comprehensible by providing a visual counterpart to, and justification for, its algebraic definition.

As an example of how the definition works, consider the following very simple set of data comprising an independent variable consisting of three groups, where the values of the dependent variable are 1, 2, 3 for the first group, 4, 5, 6 for the second group and 7, 8, 9 for the third group. The groups could represent three drug treatments, and the numbers, a measure of clinical outcome for each of nine participants. One might represent this set of data as a row vector thus: (1, 2, 3, 4, 5, 6, 7, 8, 9).

Information

Type
Articles
Information
The Mathematical Gazette , Volume 102 , Issue 553 , March 2018, pp. 50 - 62
Copyright
Copyright © Mathematical Association 2018 

References

1. Mewhort, D. J. K., A comparison of the randomization test with the F test when error is skewed, Behavior Research Methods 37(3) (2005) pp. 426–435.Google Scholar
2. Mewhort, D. J. K., Johns, B. T. and Kelly, M., Applying the permutation test to factorial designs, Behavior Research Methods 42(2) (2010) pp. 366–372.Google Scholar
3. Albers, C. and Lakens, D., Biased sample size estimates in a priori power analysis due to the choice of the effect size index and follow-up bias (submitted for publication).Google Scholar
4. Okada, K., Is omega squared less biased? A comparison of three major effect size indices in one-way ANOVA, Behaviormetrika 40(2) (2013) pp. 129–147.Google Scholar