Discriptive

Statistics for Managers Using SPSS

Chapter 11

Chi-SquareTest of Independence

Chap 11-1

Goals

After completing this topic, you should be able to:

 

Construct contingency tables Display the observed counts, expected counts, and the relevant percentages in the table

 Perform a 2 test of association/independence

Chap 11-2

Contingency Tables

Contingency Tables



Used to classify sample observations according to two or more characteristics Also called a cross-tabulation or crossclassification table.



Chap 11-3

Example: 2 x 2 Contingency Table

 Research Question: Is there a significant relationship between gender and on-line shopping preference?

On-line shopping preference

Yes Male Gender Female Total 12 24 36 No 108 156 264 Total 120 180 300

Chap 11-4

2 test of association



This is a measure of association between two categorical variables (nominal vs nominal; ordinal vs ordinal; nominal vs ordinal)

H0: There is no relationship between two categorical variables H1: There is a relationship between the two categorical variables

Chap 11-5

Test of Hypothesis

Ho: No relationship between gender and on-line shopping preference H1: There is a relationship between gender and on-line shopping preference α = 0.05 Decision rule: Reject Ho of p-value < 0.05 State the 2 test statistics or p-value

Chap 11-6

Contingency Table Example

(continued)

Sample results organized in a contingency table:

sample size = n = 300: On-line shopping Preference Gender Female

120 Females, 12 prefer on-line shopping

180 Males, 24 prefer on-line shopping

Yes

12

No

108 120

Male

24

36

156

264

180

300

Chap 11-7

The Chi-Square Test Statistic

The Chi-square test statistic is:

( fo  fe )2 2   fe all cells



where: fo = observed frequency in a particular cell fe = expected frequency in a particular cell if H0 is true 2 for the 2 x 2 case has 1 degree of freedom

(Assumed: each cell in...