TABLE OF CONTENTS This chapter introduces the Analysis of Variance, briefly known as ANOVA. Both one-way and two-way ANOVA are discussed, and are illustrated with practical examples.
The analysis of variance, henceforth referred to as ANOVA, is the analysis of the variation in the outcomes of an experiment to assess the contribution of each variable to the total variation. ANOVA provides answers to questions such as "In a manufacturing plant, is the day shift really producing units with fewer defects than the swing and graveyard shifts?" Or, "Is one age group more productive than others in a department store?" ANOVA makes use of the F distribution which we discussed in Chapter 11. It allows us to compare several samples with a single test. It was developed by the British mathematician R. A. Fisher.
We use ANOVA in situations where we have a number of observed values, and these are divided among three or more groups. We want to know whether all these values belong to the same population, regardless of group, or we want to find out if the observations in at least one of the groups come from a different population. This determination is made by comparing the variation of values within groups and the variation of values between groups. The variation within groups is computed from the variation within groups of samples, whereas the variation between groups is computed from the variation among different groups of samples.
The F ratio is the variance between...
