Understanding the t-test as a variance ratio test, and why t-squared = F.

Allen, Rory. 2008. Understanding the t-test as a variance ratio test, and why t-squared = F.. Technical Report. Academia.edu, On line. [Report]

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Abstract or Description

This unpublished report explains why the t-test is statistically equivalent to a variance ratio test, on the same basis as Fisher's F-test used in the analysis of variance, and shows why in the case of two groups the F statistic reduces to the square of the t statistic, and why the formula for t takes the form it does in cases where the variance in the groups has to be calculated separately for the two groups (the Behrens-Fisher problem).

Since writing this paper, I have developed these ideas into a radical new approach to statistical hypothesis testing, based on model comparison. This is set out in detail in my book, Statistics and Experimental Design for Psychologists: a model comparison approach, published in October 2017 and now available on Amazon. The book’s website, which has a sample chapter and a complete set of worked examples free to download, is at: http://www.worldscientific.com/worldscibooks/10.1142/q0019

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Report (Technical Report)



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Date Deposited:

14 Dec 2012 11:49

Last Modified:

29 Apr 2020 15:49



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