STATISTICS • categorical independent variable – e.g., men versus women, control vs. experimental groups • continuous dependent variable – e.g, # times purchased, $ spent • comparisons of means – men 4.0, women 5.0 7/17/2016 Marketing Research 1 Basic strategy: • You have two groups and a mean (average) for each – e.g., men = 4.0, – women = 5.0 • How do you determine the strength of the covariation? 7/17/2016 Marketing Research 2 Examples Situation #1 Situation #2 M W W W M W M W M W M M MW 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Mean: M = 4, W = 5 Means: C = 4, W = 5 7/17/2016 Marketing Research 3 Comparison of means How do you test the covariation? 1. “inter-ocular” test – does it “hit you between the eyes?” – does it look big? 7/17/2016 Marketing Research 4 Comparison of means 2. t-test – use the numbers in the sample – scale by the “spread” [variance] – e.g., how many standard deviations apart? 7/17/2016 Marketing Research 5 Comparison of means: Graphically 7/17/2016 Marketing Research 6 Comparison of means: Graphically 7/17/2016 Marketing Research 7 Comparison of means 2. t-test – Formula: • X1 - X2 • S.D./sqrt of n [number of subjects] 7/17/2016 Marketing Research 8 Comparison of means 2. t-test (continued) – compare observed “t” – to t “critical” from table [A-4] • d.f. = n [number of subjects] - 1 • e.g., t [29] @ .05 = 1.699 [two tailed] • t [29] @ .025 = 2.045 [one tailed] – if t > t critical, difference in population 7/17/2016 Marketing Research 9 Comparison of means: Output 7/17/2016 Marketing Research 10 Unequal variances: The problem 7/17/2016 Marketing Research 11 Unequal variance: The solution • A useful rule of thumb is: – the difference in standard deviations is seldom a problem until one is more than twice the other. • In that instance, do a t-test using “separate” variance estimates. 7/17/2016 Marketing Research 12 The End 7/17/2016 Marketing Research 13