The ubiquitous angle

Graham R. Wood, David J. Saville*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    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'.

    Original languageEnglish
    Pages (from-to)95-107
    Number of pages13
    JournalJournal of the Royal Statistical Society. Series A: Statistics in Society
    Issue number1
    Publication statusPublished - 2005


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