R. G. D. Steel

Bio: R. G. D. Steel is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 21053 citations.

Pseudoreplication and the Design of Ecological Field Experiments

Abstract: Pseudoreplication is defined. as the use of inferential statistics to test for treatment effects with data from experiments where either treatments are not replicated (though samples may be) or replicates are not statistically independent. In ANOVA terminology, it is the testing for treatment effects with an error term inappropriate to the hypothesis being considered. Scrutiny of 176 experi- mental studies published between 1960 and the present revealed that pseudoreplication occurred in 27% of them, or 48% of all such studies that applied inferential statistics. The incidence of pseudo- replication is especially high in studies of marine benthos and small mammals. The critical features of controlled experimentation are reviewed. Nondemonic intrusion is defined as the impingement of chance events on an experiment in progress. As a safeguard against both it and preexisting gradients, interspersion of treatments is argued to be an obligatory feature of good design. Especially in small experiments, adequate interspersion can sometimes be assured only by dispensing with strict random- ization procedures. Comprehension of this conflict between interspersion and randomization is aided by distinguishing pre-layout (or conventional) and layout-specifit alpha (probability of type I error). Suggestions are offered to statisticians and editors of ecological j oumals as to how ecologists' under- standing of experimental design and statistics might be improved.

On territorial behavior and other factors influencing habitat distribution in birds

Abstract: This example is provided so that non-theorists may see actual applications of the theory previously described. The Dickcissel sex ratio is employed as an indirect index of suitability. A sex ratio index was found to be correlated positively with density. This is consistent with the hypothesis that territorial behavior in the males of this species limits their density. This study provides a valid example of how the problem can be approached and offers a first step in the eventual identification of the role of territorial behavior in the habitat distribution of a common species.

Comparisons of Treatments After an Analysis of Variance in Ecology

Abstract: 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 consid- ered in relation to confidence intervals and statistical estimation.

Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analyses of Variance and Covariance

Abstract: The effects of violating the assumptions underlying the fixed-effects analyses of variance (ANOVA) and covariance (ANCOVA) on Type-I and Type-II error rates have been of great concern to researchers and statisticians. The major effects of violation of assumptions are now well known, after nearly four decades of research. Early summaries and reviews by Hey (1938), Garret and Zubin (1943), Grant (1944), and Gourlay (1955) and more recent reviews by Bradley (1963), Atiqullah (1967), Elashoff (1969) and Scheffe (1959, Ch. 10) can be extended and updated with recent research which provides closure to an area of active inquiry. (For a review of the effects of violation of the assumptions of the randomeffects ANOVA-a subject not reviewed here-the reader is directed to Scheffe, 1959, pp. 334-337 and Box & Anderson, 1962.) Asking whether ANOVA and ANCOVA assumptions are satisfied is not idle curiosity. The assumptions of most mathematical models are always false to a greater or lesser extent. The relevant question is not whether ANOVA assumptions are met exactly, but rather whether the plausible violations of the assumptions have serious consequences on the validity of probability statements based on the standard assumptions. Applied statistics in education and the social sciences experienced a largely unnecessary hegira to non-parametric statistics during the 1950s. Increasingly during the 1950s and early 1960s the fixed-effects, normal theory ANOVA was replaced by such comparable nonparametric techniques as the Wilcoxon test, Mann-Whitney U-test, Kruskal-Wallis one-way ANOVA, and the Friedman two-way ANOVA for ranks (Siegel, 1956). The flight to non-parametrics was unnecessary principally because researchers asked "Are normal theory ANOVA assumptions met?" instead of "How important are the inevitable violations of normal theory ANOVA assumptions?"