ANOVA Problems with Simple Numbers

Abstract

This article shows how to construct simple numerical exercises in balanced and unequally replicated one-way analysis of variance (ANOVA) (and experimental design) such that the estimated effects and residual standard deviations are preassigned whole numbers. Methods for generating single samples and simple linear regressions with exact estimates are already available (see Edwards 1959, Searle and Firey 1980, Posten 1982, and Read and Riley 1983). In this article the basic method of Read and Riley is extended to one-way ANOVA. For small numbers of treatments and replications and small residual standard deviations, tables of basic data are supplied that greatly expedite the construction of ANOVA layouts; the same methods may easily be applied, and the tables extended, to generate exercises involving larger numbers if required. The sets of estimated effects are essentially arbitrary, and so the significance or insignificance of main effects, or of contrasts thereof, can be illustrated by data sets designed for the purpose. This facility is a new and helpful aid to instruction.

Key Words:

• Constructing one-way ANOVA's
• Simple calculations