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- Title
- The Ubiquitous angle
- Related
- Journal of the Royal Statistical Society. Series A, Statistics in society, Vol. 168, No. 1, (2005), p.95-107
- DOI
- 10.1111/j.1467-985X.2004.00338.x
- Publisher
- Blackwell Publishing
- Date
- 2005
- Author/Creator
- Wood, Graham R
- Author/Creator
- Saville, David J
- Description
- 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’.
- Description
- 13 page(s)
- Subject Keyword
- 010400 Statistics
- Subject Keyword
- analysis-of-variance contrasts
- Subject Keyword
- correlation coefficient
- Subject Keyword
- F-test
- Subject Keyword
- independent samples t-test
- Subject Keyword
- linear algebra
- Subject Keyword
- linear models
- Subject Keyword
- p-value
- Subject Keyword
- regression
- Subject Keyword
- t-test
- Subject Keyword
- vector geometry
- Resource Type
- journal article
- Organisation
- Macquarie University. Dept. of Statistics
- Identifier
- http://hdl.handle.net/1959.14/145601
- Identifier
- ISSN:0964-1998
- Identifier
- mq-rm-2005002356
- Language
- eng
- Reviewed
Macquarie University ResearchOnline
