The result indicates a high correlation between education levels and preferences
about smoking in public places (p¼ 0 :001).
Note:An SAS program would include these instructions:
DATA;
INPUT EDUCAT POLICY COUNT;
CARDS;
115
1244
1323
143
2115
2 2 100
2330
245
3115
3240
3310
3 4 10;
PROC FREQ;
WEIGHT COUNT;
TABLES EDUCAT*POLICY/CHISQ;
Statistical decisions based on Pearson’s chi-square statistic make use of the
percentiles of the chi-square distribution. Since chi-square is a continuous
distribution and categorical data are discrete, some statisticians use a version
of Pearson’s statistic with acontinuity correction, calledYates’ corrected chi-
square test, which can be expressed as
Xc^2 ¼X
i;jðjxijeijj 0 : 5 Þ^2
eijStatisticians still disagree about whether or not a continuity correction is
needed. Generally, the corrected version is more conservative and used more
widely in the applied literature.
So far, the test for the comparison of two proportions and the test for
independence have been presented in very di¤erent ways; fortunately, they are
not that di¤erent. For example, if we apply the test of independence to a 2 2
table where data came from two binomial samples, say a case–control study,
we get same chi-square statistic as if we applied the chi-square test to com-
pare the two proportions against a two-sided alternative. In other words,
the chi-square test—presented as a comparison of observed versus expected
frequencies—applies regardless of the sampling mechanism. For example, we
can use the chi-square test to compare several proportionssimultaneouslyusing
data from several binomial samples (see Example 6.13). [In this type of prob-
226 COMPARISON OF POPULATION PROPORTIONS