The ubiquitous angle

Graham R. Wood and David J. Saville

Journal of the Royal Statistical Society Series A, 2005, vol. 168, issue 1, 95-107

Abstract: Summary. Previously we used the geometry of n‐dimensional space to derive the paired samples t‐test and its p‐value. In the present paper we describe the ‘ubiquitous’ application of these results to single degree of freedom linear model hypothesis tests. As examples, we derive the p‐ and t‐values for the independent samples t‐test, for testing a contrast in an analysis of variance and for testing the slope in a simple linear regression analysis. An angle θ in n‐dimensional space is again pivotal in the development of the ideas. The relationships between p, t, θ, F and the correlation coefficient are also described by using a ‘statistical triangle’.

Date: 2005
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https://doi.org/10.1111/j.1467-985X.2004.00338.x

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