Forfatter av avsnitt: Danielle J. Navarro and David R. Foxcroft

Faktoriell ANOVA

Over the course of the last few chapters we have done quite a lot. We have looked at statistical tests you can use when you have one nominal predictor variable with two groups (e.g., the t-test, chapter Sammenligning av to gjennomsnitt) or with three or more groups (e.g., in chapter Sammenligning av flere gjennomsnitt (enveis ANOVA)). The chapter on Korrelasjon og lineær regresjon introduced a powerful new idea, that is building statistical models with multiple continuous predictor variables used to explain a single outcome variable . For instance, a regression model could be used to predict the number of errors a student makes in a reading comprehension test based on the number of hours they studied for the test and their score on a standardised IQ test.

The goal in this chapter is to extend the idea of using multiple predictors into the ANOVA framework. For instance, suppose we were interested in using the reading comprehension test to measure student achievements in three different schools, and we suspect that girls and boys are developing at different rates (and so would be expected to have different performance on average). Each student is classified in two different ways: on the basis of their gender and on the basis of their school. What we would like to do is analyse the reading comprehension scores in terms of both of these grouping variables . The tool for doing so is generically referred to as factorial ANOVA. However, since we have two grouping variables , we often refer to the analysis as a two-way ANOVA, in contrast to the one-way ANOVAs that we ran in chapter Sammenligning av flere gjennomsnitt (enveis ANOVA).