You have more than two groups and a mean (average) for each ◦ e.g., young = 4.0, ◦ middle aged = 5.0, ◦ older = 4.5 How do you determine the strength of the covariation? Marketing Research 7/17/2016 2 ◦ Decomposes “variance” into: treatment effects other factors unexplained factors ◦ Compares data to group means Subtracts each data point from group mean Squares it Keeps a running total of “Sum of Squares” Marketing Research 7/17/2016 3 ◦ The Sums of Squares are then: Divided by the number of groups (To get an estimate “per group”) “Mean Squares” MSSr = SSr / df (variance per group) MSSr / MSSu = F Total variance “explainable” ◦ F compared to F crit [dfn, dfd] ◦ if F > F crit, difference in population Marketing Research 7/17/2016 4 ◦ One way ANOVA investigates: ◦ Main effects factor has an across-the-board effect e.g., age or involvement Marketing Research 7/17/2016 5 Study of movie profits ◦ Dependent variable: Gross revenue in dollars [continuous] ◦ Independent variables: Sex [categorical] Violence ◦ Examine predictors of profitability: Sex, violence, interaction (sex * violence) Marketing Research 7/17/2016 6 5 4 No sex Sex 3 2 Low High VIOLENCE LEVEL Marketing Research 7/17/2016 7 5 4 No sex Sex 3 2 Low VIOLENCE LEVEL High Marketing Research 7/17/2016 8 ◦ A TWO-WAY ANOVA investigates: ◦ INTERACTIONS effect of one factor depends on another factor e.g., larger advertising effects for those with no experience importance of price depends on income level and involvement with the product Marketing Research 7/17/2016 9 5 4 No sex Sex 3 2 Low High VIOLENCE LEVEL Marketing Research 7/17/2016 10 Study of movie profits ◦ Dependent variable: Gross revenue in dollars [continuous] ◦ Independent variables: Sex [categorical] Violence ◦ Examine predictors of profitability: Sex, violence, interaction (sex * violence) Marketing Research 7/17/2016 11 Tests of Between-Subjects Effects Dependent Variable: Total Gross Type III Sum Source of Squares Corrected Model 43744.364 a Intercept 952785.362 SEX 35467.649 VIOLENCE 10228.369 SEX * VIOLENCE 21.589 Error 995088.361 Total 1991539.265 Corrected Total 1038832.725 df 3 1 1 1 1 381 385 384 Mean Square 14581.455 952785.362 35467.649 10228.369 21.589 2611.780 F 5.583 364.803 13.580 3.916 .008 Sig. .001 .000 .000 .049 .928 a. R Squared = .042 (Adjusted R Squared = .035) Marketing Research 7/17/2016 12 Marketing Research 7/17/2016 13