Introduction to Probability and Statistics for Engineers and Scientists

11.5Tests of Independence in Contingency Tables Having Fixed Marginal Totals 503

Population

Value 1 2 .. i. m Totals

1 N1,1 N2,1... Ni,1... Nm,1 N 1

2

..

.

jN1,j N2,j... Ni,j... Nm,j Nj

..

.

nN1,n N2,n... Ni,n Nm,n Nn

Totals M 1 M 2 ... Mi... Mm

Note thatNjdenotes the number of sampled members that have valuej.

EXAMPLE 11.5b A recent study reported that 500 female office workers were randomly
chosen and questioned in each of four different countries. One of the questions related to
whether these women often received verbal or sexual abuse on the job. The following data
resulted.

Country Number Reporting Abuse

Australia 28

Germany 30

Japan 51

United States 55

Based on these data, is it plausible that the proportions of female office workers who
often feel abused at work are the same for these countries?

SOLUTION Putting the above data in the form of a contingency table gives the following.

Country

1234 Totals

Receive abuse 28 30 58 55 171

Do not receive abuse 472 470 442 445 1,829

Totals 500 500 500 500 2,000

We can now test the null hypothesis by testing for independence in the preceding contin-
gency table. If we run Program 11.4, then the value of the test statistic and the resulting
p-value are

TS=19.51, p-value≈.0002