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Part V: Statistical Studies and the Hunt for a Meaningful Relationship
To conduct a hypothesis test for a relationship between two categorical vari-

ables (when each variable has only two categories, like yes/no or male/
female), you either do a test for two proportions (see Chapter 15) or a Chi-
square test (which is covered in my book Statistics II For Dummies, also pub-
lished by Wiley). If one or more of your variables have more than two
categories, such as Democrats/Republicans/Other, you must use the Chi-
square test to test for independence in the population.
Be mindful that you may run across a report in which someone is trying to
give the appearance of a stronger relationship than really exists, or trying to
make a relationship less obvious by how the graphs are made. With pie charts,
the sample size often is not reported, leading you to believe the results are
based on a large sample when they may not be. With bar graphs, they stretch
or shrink the scale to make differences appear larger or smaller, respectively.
(See Chapter 6 for more information on misleading graphs of categorical data.)
Checking Independence and
Describing Dependence
The main reason researchers collect data on two categorical variables is to
explore possible relationships or connections between the variables. For
example, if a survey finds that more females than males voted for the incum-
bent president in the last election, then you conclude that gender and voting
outcome are related. If a relationship between two categorical variables has
been found (that is, the results from the two groups are different), then stat-
isticians say they’re dependent.
However, if you find that the percentage of females who voted for the incum-
bent is the same as the percentage of males who voted for the incumbent,
then the two variables (gender and voting for the incumbent) have no rela-
tionship and statisticians say those two variables are independent. In this sec-
tion, you find out how to check for independence and describe relationships
found to be dependent.
Checking for independence
Two categorical variables are independent if the percentages for the second
variable (typically representing the results you want to compare, such as
support or oppose) do not differ based on the first variable (typically repre-
senting the groups you want to compare, such as men versus women). You
can check for independence with the methods that I cover in this section.

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