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260 Part IV: Building Strong Connections with Chi-Square Tests

Also, note that if you take the Z-test statistic for this example (from Figure
14-3), which is –1.41, and square it, you get 2.00, which is equal to the Chi-
square test statistic for the same data (last line of Figure 14-4). It’s also the
case that the square of the Z-test statistic (when testing for the equality of
two proportions) is equal to the corresponding Chi-square test statistic for
independence.

The Chi-square test and Z-test are equivalent only if the table is a two-by-two
table (two rows and two columns) and if the Z-test is two-tailed (the alterna-
tive hypothesis is that the two proportions aren’t equal, instead of using Ha:
One proportion is greater than or less than the other). If the Z-test isn’t two-
tailed, a Chi-square test isn’t appropriate. If the two-way table has more than
two rows or columns, use the Chi-square test for independence (because
many categories mean you no longer have only two proportions, so the Z-test
isn’t applicable).

The car accident–cellphone connection

Researchers are doing a great deal of study of Researchers also found out that the relative risk
the effects of cellphone use while driving. One was similar for drivers who differed in personal
study published in the New England Journal of characteristics, such as age and driving experi-
Medicine observed and recorded data in 1997 ence. (This finding means that they conducted
on 699 drivers who had cellphones and were similar tests to see whether the results were
involved in motor vehicle collisions resulting in the same for drivers of different age groups and
substantial property damage but no personal drivers of different levels of experience, and
injury. Each person’s cellphone calls on the day the results always came out about the same.
of the collision and during the previous week Therefore, age and the experience of the driver
were analyzed through the use of detailed bill- weren’t related to the collision outcome.)
ing records. A total of 26,798 cellphone calls
were made during the 14-month study period. The research also shows that “. . . calls made
close to the time of the collision were found to
One conclusion the researchers made was that be particularly hazardous (p < 0.001). Hands-
“. . . the risk of a collision when using a cell- free cellphones offered no safety advantage
phone is four times higher than the risk of a col- over hand-held units (p-value not significant).”
lision when a cellphone was not being used.” Note: The items in parentheses show the typi-
They basically conducted a Chi-square test to cal way that researchers report their results:
see whether cellphone use and having a col- using p-values. The p in both cases of parenthe-
lision are independent, and when they found ses represents the p-value of each test.
out the events were not, the researchers were In the first case, the p-value is very tiny, less
able to examine the relationship further using than 0.001, indicating strong evidence for a rela-
appropriate ratios. In particular, they found that tionship between collisions and cellphone use
the risk of a collision is four times higher for at the time. The second p-value in parentheses
those drivers using cellphones than for those was stated to be insignificant, meaning that it
who aren’t.

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