Testing homogeneity of normal means with a simply ordered alternative and dependent observations

Lei, Xingye; Peng, Yingning; Wright, F. T.

doi:10.1016/0167-9473(94)00033-f

Cited by 3 publications

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“…1 Bartholomew's trend test Bartholomew's Ē2 k test [Bartholomew, 1959] for the simple ordered alternative H 1 : µ 1 ≤ µ 2 ≤ ... ≤ µ k |µ 1 < µ k in a fully randomised one-way layout with N (µ i , σ 2 ) (i = 1, ..., k) is a modification of the usual ANOVA F-test (which is sensitive to any heterogeneity between qualitative treatment levels), replacing the arithmetic mean estimators xi by the pool-adjacent-violators under order restriction (PAVA) estimates μi . This test belongs to the class of isotonic regression models, but for a single quantitative factor and not for a regression covariate or even dependent time series data (see the discussion for dependent data [Lei et al, 1995]). However, its use is severely limited by the lack of software (a permutative version is available in the CRAN package IsoGene [Lin et al, 2015]).…”

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Evaluation of Animal Carcinogenicity Studies: Cochran-Armitage Trend Test vs. Multiple Contrast Tests

Hothorn

Bretz²

2000

Biom. J.

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Typical animal carcinogenicity studies involve the comparison of several dose groups to a negative control. The uncorrected asymptotic Cochran‐Armitage trend test with equally spaced dose scores is the most frequently used test in such set‐ups. However, this test based on a weighted linear regression on proportions. It is well known that the Cochran‐Armitage test lacks in power for other shapes than the assumed linear one. Therefore, dichotomous multiple contrast tests are introduced. These build the maximum over several single contrasts, where each of them is chosen appropriately to cover a specific dose‐response shape. An extensive power study has been conducted to compare multiple contrast tests with the approaches used so far. Crucial results will be presented in this paper. Moreover, exact tests and continuity corrected versions are introduced and compared to the traditional uncorrected approaches regarding size and power behaviour. A trend test for any shape of the dose‐response relationship for either crude tumour rates or mortality‐ adjusted rates based on the simple Poly‐3 transformation is proposed for evaluation of carcinogenicity studies.

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