Multiple Comparisons among Means-A Review

Abstract

The problems inherent in making a number of simultaneous inferences about a set of sample means centre around the degree of protection against Type I errors afforded by the test in use. The various viewpoints and the better known techniques for solving the problems are discussed and other, less well‐known, methods are introduced, particularly that due to Duncan with its basis in the Bayesian approach. The use of the methods is exemplified by the results of a trial on a large number of treatments and the need for the multiple comparisons methods is clearly shown. Results of a new simulation shed light on the operating characteristics of many of the tests discussed and recommendations are made as to the best techniques to use in various circumstances.

Talus fabric, clast morphology, and botanical Indicators of Slope Processes on the Chaos Crags (California Cascades), U.S.A.

“…When several means are compared with t tests, the probability of obtaining a false significant difference between data sets is high (Thomas, 1973), and for a data set of eight means, this error probability is about 50 % (Steel and Torrie, 1960). Thus, t tests were validated with Duncan's Multiple Range (DMR) and with Scheffé's F tests (Duncan, 1955;Scheffé, 1953).…”

Comparisons of Treatments After an Analysis of Variance in Ecology

“…Multiple comparisons have been reviewed by statisticians (e.g., O'Neill and Wetherill1971, Thomas 1973, Miller 1981, Stoline 1981, Games et al 1983, Hochberg and Tamhane 1987 and have been discussed in articles in many fields, e.g., agronomy (Chew 1976, Baker 1980, animal production and veterinary science (Gill 1973, Waldo 1976, Cox 1980, entomology (Jones 1984, Perry 1986, medicine (Rosen andHoffman 1978, Salsburg 1985), plant pathology (Madden et al 1982), and psychology (Jaccard et al 1984, Klockers andSax 1986). These papers have examined either the relative merits of different UMCPs or whether UMCPs should be used at all, leading to a more general discussion of the use-fulness of statistical hypothesis testing (e.g., Jones and Matloff 1986).…”

Pairwise multiple comparison procedures: A review.

“…The present review is intended to alert psychological researchers to some of the more promising PMC procedures currently available. Somewhat dated but still instructive reviews of multiple comparison procedures in general can be found in Dunnett (1970), Miller (1966Miller ( , 1977, O'Neill and Wetherill (1971), Spjotvoll (1974), andThomas (1973).…”