Wood, Graham and Saville, David J. (2013) A geometric examination of linear model assumptions. Australian & New Zealand Journal of Statistics , Volume 55 (Number 3). pp. 285-303. doi:10.1111/anzs.12042

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Abstract

From a geometric perspective, linear model theory relies on a single assumption, that (‘corrected’) data vector directions are uniformly distributed in Euclidean space. We use this perspective to explore pictorially the effects of violations of the traditional assumptions (normality, independence and homogeneity of variance) on the Type I error rate. First, for several non-normal distributions we draw geometric pictures and carry out simulations to show how the effects of non-normality diminish with increased parent distribution symmetry and continuity, and increased sample size. Second, we explore the effects of dependencies on Type I error rate. Third, we use simulation and geometry to investigate the effect of heterogeneity of variance on Type I error rate. We conclude, in a fresh way, that independence and homogeneity of variance are more important assumptions than normality. The practical implication is that statisticians and authors of statistical computing packages need to pay more attention to the correctness of these assumptions than to normality.

Item Type:	Journal Article
Divisions:	Faculty of Science > Centre for Systems Biology
Journal or Publication Title:	Australian & New Zealand Journal of Statistics
Publisher:	Wiley-Blackwell Publishing Ltd.
ISSN:	1369-1473
Official Date:	23 September 2013
Dates:	Date Event 23 September 2013 Published
Volume:	Volume 55
Number:	Number 3
Page Range:	pp. 285-303
DOI:	10.1111/anzs.12042
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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