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A geometric examination of linear model assumptions
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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 ISSN 1369-1473.
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Official URL: http://dx.doi.org/10.1111/anzs.12042
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, Engineering and Medicine > Research Centres > Warwick Systems Biology Centre | ||||
| Journal or Publication Title: | Australian & New Zealand Journal of Statistics | ||||
| Publisher: | Wiley-Blackwell Publishing Ltd. | ||||
| ISSN: | 1369-1473 | ||||
| Official Date: | 23 September 2013 | ||||
| Dates: |
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| 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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