14-1 Statistically Adjusting the Data Variable Respecification Variable respecification involves the transformation of data to create new variables or modify existing variables. E.G., the researcher may create new variables that are composites of several other variables.

Analysis of Variance and Covariance

14-3 One-way Analysis of Variance Marketing researchers are often interested in examining the differences in the mean values of the dependent variable for several categories of a single independent variable or factor. For example: Do the various segments differ in terms of their volume of product consumption? Do the brand evaluations of groups exposed to different commercials vary? What is the effect of consumers' familiarity with the store (measured as high, medium, and low) on preference for the store?

14-4 Relationship Among Techniques Analysis of variance (ANOVA) is used as a test of means for two or more populations. The null hypothesis, typically, is that all means are equal. Analysis of variance must have a dependent variable that is metric (measured using an interval or ratio scale). There must also be one or more independent variables that are all categorical (nonmetric). Categorical independent variables are also called factors.

14-5 Statistics Associated with One-way Analysis of Variance F statistic. The null hypothesis that the category means are equal in the population is tested by an F statistic based on the ratio of mean square related to X and mean square related to error.

14-6 Illustrative Applications of One-way Analysis of Variance The department store is attempting to determine the effect of in-store promotion (X) on sales (Y). For the purpose of illustrating hand calculations, the data of Table 16.2 are transformed in Table 16.3 to show the store sales (Y ij ) for each level of promotion. The null hypothesis is that the category means are equal: H 0 : µ 1 = µ 2 = µ 3.

14-7 Illustrative Applications of One-way Analysis of Variance TABLE 16.3 EFFECT OF IN-STORE PROMOTION ON SALES Store Level of In-store Promotion No.HighMediumLow Normalized Sales _________________ _____________________________________________________

14-8 One-Way ANOVA: Effect of In-store Promotion on Store Sales Cell means Level of CountMean Promotion High (1) Medium (2) Low (3) TOTAL Source of Sum ofdfMean F ratio F prob. Variationsquaressquare Between groups (Promotion) Within groups (Error) TOTAL

14-9 SPSS Windows One-way ANOVA can be efficiently performed using the program COMPARE MEANS and then One-way ANOVA. To select this procedure using SPSS for Windows click: Analyze>Compare Means>One-Way ANOVA …