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Abstract:
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Before performing any statistical test that makes an assumption, it is often desirable to do a preliminary test to check the assumption. Several known tests for dose response employ isotonic regression and amalgamated means, including the chibar square test (nonparametric), the ebar square test (parametric with equal variances), and the Brown-Forsythe trend test (parametric with unequal variances, Roth 1983); all of them assume that the means are a monotonic function of dose. For one-sided alternatives, each of them has a known corresponding test for assessing the validity of the monotonicity assumption (one due to Roth 2005) that has no obvious two-sided analogue. We modify all three of the above one-sided tests to obtain appropriate two-sided tests for monotonicity in each setting (nonparametric, parametric with equal variances, and parametric with unequal variances).
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