title: Deduced inference in the analysis of experimental data.
abstract: Any set of confidence interval inferences on J - 1 linearly independent contrasts on J means, such as the two comparisons μ1 - μ2 and μ2 - μ3 on 3 means, provides a basis for the deduction of interval inferences on all other contrasts, such as the redundant comparison μ1 - μ3. Deduced inference does not inflate the experimentwise error rate beyond the level associated with the set of direct statistical inferences from which it is deduced. This article shows that although deduced inference is not as precise as direct inference, it can be a useful alternative to the kind of post hoc analysis that often follows analyses of sets of linearly independent contrasts. The article also illustrates applications of deduced inference following analyses of factorial experiments, where the problems often associated with popular analysis strategies can be avoided if inferences on simple effect contrasts are deduced from confidence intervals on main and interaction effect contrasts.
authors.affiliation: University of New South Wales, Sydney, New South Wales 2052, Australia. k.bird@unsw.edu.au
authors.forename: Kevin D
authors.initials: KD
authors.lastname: Bird
mesh_terms: D000704:Analysis of Variance; D016001:Confidence Intervals; D016014:Linear Models; D013223:Statistics as Topic / Q000379:methods*