Page 275 - Statistics II for Dummies

Chapter 14: Being Independent Enough for the Chi-Square Test 259

If you use the Z-test to see whether the proportion of male cellphone owners
is equal to the proportion of female cellphone owners, you’re really looking
at whether you can expect the same proportion of cellphone owners despite
gender (after you take the sample sizes into account). And that means you’re
testing whether gender (male or female) is independent of cellphone owner-
ship (yes or no).

If the proportion of female cellphone owners equals the proportion of male
cellphone owners, the proportion of cellphone owners is the same regardless
of gender, so gender and cellphone ownership are independent. On the other
hand, if you find the proportion of male cellphone owners to be unequal to
the proportion of female cellphone owners, you can say that cellphone use
differs by gender, so gender and cellphone ownership are dependent.
With the cellphone data, you have 45 males using cellphones (out of 100
males) and 55 females using cellphones (out of 100 females). The Minitab
output for the Chi-square test for independence (complete with observed and
expected cell counts, degrees of freedom, test statistic, and p-value) is shown
in Figure 14-4. The p-value for this test is 0.157, which is greater than the typi-
cal α level 0.05, so you can’t reject Ho.

Because the Chi-square test for independence and the Z-test tests are equiva-
lent when you have a two-by-two table, the p-value from the Chi-square test
for independence is identical to the p-value from the Z-test for two propor-
tions. If you compare the p-values from Figures 14-3 and 14-4, you can see
that for yourself.

Chi-Square Test: Gender, Cellphone
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts

Y N Total
M 45 55 100
50.00 50.00
0.500 0.500
Figure 14-4:
Minitab out- F 55 45 100
put testing 50.00 50.00
0.500 0.500
indepen-
dence of
Total 100 100 200
gender and
cellphone
Chi-Sq = 2.000, DF = 1, P-Value = 0.157
ownership.

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