MORE COMPARISONS OF MEANS

1. MORE COMPARISONS OF MEANS • 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

2. Hypothesis Tests Related to Differences Black Box sig. tests p. value = .001 H0: µ1 = µ2 = µ3

3. Hypothesis Tests Related to Differences .001 1.0 Disagree Agree Conditional probability P (Sample Data | Null is True) Level of agreement between Null and sample data sig. tests p. value = .001 H0: µ1 = µ2 = µ3

4. u1 u2 u3 u1 u2 u3 u1 u2 u3 Hypothesis Tests Related to Differences Looking at the averages for each box size (u1, u2, u3), do we believe that these 3 types sell the same? Hmmm, is there anything else that we might like to know about each group of sales data? Consider the potential sales volume of three different sizes of the same Cheerios cereal. Okay, so is the same (or lack of) difference occurring in the next set of comparison? What about the variance? Let’s look and see. With the variance in sales (across stores), are the three different comparisons the same? Why or why not? What about this third set of comparisons? Lets get rid of the “Black Box” sig. tests p. value = .001 H0: µ1 = µ2 = µ3

5. ANOVA • 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

6. ANOVA • 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. ANOVA (continued) • One way ANOVA investigates: • Main effects • factor has an across-the-board effect • e.g., age • or involvement Marketing Research

8. Example • 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

9. Example Marketing Research

10. 5 4 No sex Sex 3 2 Low High Main effect: Sex VIOLENCE LEVEL Marketing Research

11. Example Marketing Research

12. 5 4 No sex Sex 3 2 Low High Main effect: Violence VIOLENCE LEVEL Marketing Research

13. ANOVA • 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

14. Example Marketing Research

15. 5 4 No sex Sex 3 2 Low High Interaction: Sex by Violence VIOLENCE LEVEL Marketing Research

16. Example • 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

17. SPSS Output • Interpret the results Marketing Research

18. The End Marketing Research