Page 321 - Statistics for Dummies

Chapter 19: Two-Way Tables and Independence

A limitation of a joint distribution is that you can’t fairly compare two groups
to each other (for example pet campers versus non–pet campers) because the
joint distribution puts more weight on larger groups. The next section shows
how to fairly compare the groups in a two-way table.
Comparing groups with conditional
distributions
You need a different type of distribution other than a joint distribution to
compare the results from two groups (for example comparing opinions of pet
campers versus non–pet campers). Conditional distributions are used when
looking for relationships between two categorical variables; the individuals
are first split into the groups you want to compare (for example, pet campers
and non–pet campers); then the groups are compared based on their opinion
on a pet section (yes, no). In the following sections, I explain how to calculate
and graph conditional distributions. 305
Calculating conditional distributions
To find conditional distributions for the purpose of comparison, first split the
individuals into groups according to the variable you want to compare. Then
for each group, take the cell count (the number of individuals in a particular
cell) divided by the marginal total for that group. Do this for all the cells in
that group. Now repeat for the other group, using its marginal total as the
denominator and the cells within its group as the numerators. (See the earlier
section “Figuring the totals” for more about marginal totals.) You now have
two conditional distributions, one for each group, and you fairly compare the
results for the two groups.
For the pet camping survey data example (earlier in this chapter), you
compare the opinions of two groups: pet campers and non–pet campers;
in statistical terms you want to find the conditional distributions of opinion
based on the pet camping variable. That means you split the individuals
into the pet camper and non–pet camper groups, and then for each group,
you find the percentages of who supports and opposes the new pet section.
Table 19-7 shows these two conditional distributions in table form (working
off Table 19-3).

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