1. Essentials of Marketing Research William G. Zikmund
Chapter 15:
Differences Between Groups
and Relationships Among Variables

2. Differences Between Groups
Contingency tables
Differences between two groups
Means
Proportions
Differences between three or more groups

3. two independent groups
Type of
Measurement
Differences between
two independent groups
Interval and
ratio
Independent groups:
t-test or Z-test

4. two independent groups
Type of
Measurement
Differences between
two independent groups
Ordinal
Mann-Whitney U-test

5. two independent groups
Type of
Measurement
Differences between
two independent groups
Nominal
Z-test (two proportions)
Chi-square test

6. Differences Between Groups
Contingency Tables
Cross-Tabulation
Chi-Square allows testing for significant differences between groups
“Goodness of Fit”

7. Chi-Square Test x² = chi-square statistics
Oi = observed frequency in the ith cell
Ei = expected frequency on the ith cell

8. Chi-Square Test x² = chi-square statistics
Oi = observed frequency in the ith cell
Ei = expected frequency on the ith cell

9. Chi-Square Test Ri = total observed frequency in the ith row
Cj = total observed frequency in the jth column
n = sample size

10. Degrees of Freedom
d.f.=(R-1)(C-1)

11. Degrees of Freedom
(R-1)(C-1)=(2-1)(2-1)=1

12. Awareness of Tire Manufacturer’s Brand
Men Women Total
Aware
Unaware

13. Chi-Square Test: Differences Among Groups Example

15. X2=3.84 with 1 d.f.

16. DIFFERENCE BETWEEN GROUPS WHEN COMPARING MEANS
Ratio scaled variables
t-test when groups are small
z-test when groups are large

17. Null Hypothesis About Mean Differences Between Groups

18. COMPARING TWO GROUPS WHEN COMPARING PROPORTIONS
Percentage comparisons
Sample proportion
Population proportion

19. Differences Between Two Groups when Comparing Proportions
The hypothesis is:
Ho: P1 = P2
may be restated as:
Ho: P1 - P2 = 0

20. Analysis of Variance m1 = m2 = m3
Hypothesis when comparing three groups
m1 = m2 = m3

21. RELATIONSHIPS AMONG VARIABLES
Correlation analysis
Bivariate regression analysis
Multiple regression analysis

22. Bivariate Regression
A measure of linear association that investigates a straight line relationship
Useful in forecasting

23. We are always acting on what has just finished happening
We are always acting on what has just finished happening. It happened at least 1/30th of a second ago.We think we’re in the present, but we aren’t. The present we know is only a movie of the past. Tom Wolfe in The Electric Kool-Aid Acid Test .

24. Multiple Regression Extension of bivariate regression
Multidimensional when three or more variables are involved
Simultaneously investigates the effect of two or more variables on a single dependent variable