Essentials

146 ESSENTIALS OF STATISTICSTable 7.1 An Example of an Interaction ContrastDON’T FORGETWhen Will I Use the Statisticsin this Chapter?You are measuring one outcome (i.e.,dependent) variable on a quantitativescale (or looking at one such variableat a time), and you are comparinggroups along two or more dimensionsor factors (any of the factors can representexisting populations, or experimentaltreatments or conditions).PlaceboDrugMales 36 28Females 40 22The contrast just tested is called aninteraction contrast. If it is significant,we can say that the drug interacts withgender, in that the effect of the drug,relative to a placebo, changes fromone gender to another. Depending onthe nature and the size of the interactionwe might recommend that thedrug be used only with females.Interactions can be very interestingboth practically and theoretically. Thesimplest kind of interaction is the twoby two (symbolized as 2 2) interaction,as in the example above (twodrug conditions and two genders). Interactions, however, can get more complicated(e.g., three drug conditions by two genders), and when they do, a simple linearcontrast will not be sufficient. To handle these more complex cases you willneed an extension of the ANOVA procedure you learned in Chapter 5. This extension,called factorial ANOVA (for reasons soon to be made clear) is the subjectof this chapter.THE FACTORIAL DESIGNThe one-way ANOVA is called one-way because there is only one independentvariable, also called a factor, that distinguishes the groups. If the groups differedalong two factors, a two-way ANOVA could probably be applied to the results.(The dependent variable should have been measured on an interval or ratio scale.If more than one dependent variable is to be used in the same analysis you wouldneed a multivariate analysis of variance [MANOVA]. In this book we will onlydeal with univariate ANOVAs—i.e., one DV at a time.) To illustrate how two factorscan be combined in one experiment we offer the following example.Suppose you are the principal of a large school and you want to improve readingscores. In comparison to the traditional method for teaching reading, you