Significantly InsignificantFTests
- 1 February 2003
- journal article
- Published by Taylor & Francis in The American Statistician
- Vol. 57 (1) , 27-32
- https://doi.org/10.1198/0003130031108
Abstract
P values near 1 are sometimes viewed as unimportant. In fact, P values near 1 should raise red flags cautioning data analysts that something may be wrong with their model. This article examines reasons why F statistics might get small in general linear models. One-way and two-way analysis of variance models are used to illustrate the general ideas. The article focuses on the intuitive motivation behind F tests based on second moment arguments. In particular, it argues that when the mean structure of the model being tested is correct, small F statistics can be caused by not accounting for negatively correlated data or heteroscedasticity; alternatively, they can be caused by an unsuspected lack of fit. It is also demonstrated that large F statistics can be generated by not accounting for positively correlated data or heteroscedasticity.Keywords
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