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Comparisons of Treatments After an Analysis of Variance in Ecology
Author(s) -
Day R. W.,
Quinn G. P.
Publication year - 1989
Publication title -
ecological monographs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.254
H-Index - 156
eISSN - 1557-7015
pISSN - 0012-9615
DOI - 10.2307/1943075
Subject(s) - statistics , variance (accounting) , sample size determination , ecology , statistical hypothesis testing , monte carlo method , type i and type ii errors , nonparametric statistics , parametric statistics , mathematics , statistical power , econometrics , multiple comparisons problem , biology , accounting , business
The statistical literature on tests to compare treatments after the analysis of variance is reviewed, and the use of these tests in ecology is examined. Monte Carlo simulations on normal and lognormal data indicate that many of the tests commonly used are inappropriate or inefficient. Particular tests are recommended for unplanned multiple comparisons on the basis of controlling experimentwise type I error rate and providing maximum power. These include tests for parametric and nonparametric cases, equal and unequal sample sizes, homogeneous and heterogeneous variances, non—independent means (repeated measures or adjusted means), and comparing treatments to a control. Formulae and a worked example are provided. The problem of violations of assumptions, especially variance heterogeneity, was investigated using simulations, and particular strategies are recommended. The advantages and use of planned comparisons in ecology are discussed, and the philosophy of hypothesis testing with unplanned multiple comparisons is considered in relation to confidence intervals and statistical estimation.