TY - JOUR
T1 - The ubiquitous angle
AU - Wood, Graham R.
AU - Saville, David J.
PY - 2005
Y1 - 2005
N2 - 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'.
AB - 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'.
UR - http://www.scopus.com/inward/record.url?scp=12844261118&partnerID=8YFLogxK
U2 - 10.1111/j.1467-985X.2004.00338.x
DO - 10.1111/j.1467-985X.2004.00338.x
M3 - Article
AN - SCOPUS:12844261118
VL - 168
SP - 95
EP - 107
JO - Journal of the Royal Statistical Society. Series A: Statistics in Society
JF - Journal of the Royal Statistical Society. Series A: Statistics in Society
SN - 0964-1998
IS - 1
ER -