Scenario Analysis & Discussion Question

QSO 510 Module Eight 1

Module Seven compared several population means through a statistical procedure called analysis of variance (ANOVA). Module Eight introduces contingency tables to summarize categorical data and a chi-square test for the independence of two categorical sets of data. The previous modules of this course considered data that is quantitative and measurable. This module examines count data that falls into categories, or classes. Count data can be summarized with the use of contingency tables. A contingency table displays counts for two variables measured on a nominal level of measurement. You may recall that nominal data is count data with no natural order to the categories. For example, a business school dean may categorize accounting graduates by gender and whether or not they have passed the certified public accountant (CPA) examinations. That data is summarized in the following contingency table:

Gender Passed CPA Exam

Did Not Pass CPA Exam

Total

Male 7 3 10

Female 12 2 14

Total 19 5 24

Related to contingency tables is the chi-square test of independence for two categorical variables. Consider the following examples:

 The manager of a chemical plant that produces fertilizer operates two shifts, a day

shift and an evening shift. A chi-square may be used to verify that productivity of

fertilizer is independent of the shift on which it was manufactured.

 A human resources manager may survey employees regarding their satisfaction with

the benefits offered by the company. Employees surveyed are paid hourly or salaried

and their satisfaction is categorized as satisfied, neutral, or dissatisfied. The manager

may use a chi-square test to verify that employee satisfaction with the benefits offered

is independent of the type of pay for these employees.

 The head of the traffic department in a large city may be concerned about the use of

cell phones in motor vehicles and its effect on the number of accidents in the city. A

chi-square test may show that cell phone use in a vehicle is independent or has no

effect on the accident rate in that city.

 A manufacturer of athletic shoes receives materials required to make the shoes from

four suppliers. Athletic shoes are categorized as acceptable or unacceptable. The

2 QSO 510 Module Eight

company’s quality control manager may use a chi-square test to determine whether

the acceptability of the athletic shoes is related to the supplier of the component

materials.

Hypotheses that accompany a chi-square test of independence include a null hypothesis of independence between two categorical variables and an alternative hypothesis that a relationship exists between the two categorical variables. As Module Eight will show, the chi- square test is useful for establishing the independence of two variables that cannot be quantified and measured, nor analyzed by the traditional correlation coefficient.