Page 315 - Statistics for Dummies

Chapter 19: Two-Way Tables and Independence
data earlier in this chapter (each question will be handled in the following
sections, respectively):
✓ What percentage of the campers are in favor of a pet section?
✓ What percentage of the campers are pet campers who support a pet
section?
✓ Do more non–pet campers support a pet section, compared to pet campers?
The answers to these (and any other) questions about the data come from
finding and working with the proportions, or percentages, of individuals
within certain parts of the table. This process involves calculating and examin-
ing what statisticians call distributions. A distribution in the case of a two-way
table is a list of all the possible outcomes for one variable or a combination of
variables, along with their corresponding proportions (or percentages).
For example, the distribution for the pet camping variable lists the percent-
ages of people who do and do not camp with pets. The distribution for the 299
combination of the pet camping variable (yes, no) and the opinion variable
(support, oppose) lists the percentages of: 1) pet campers who support a pet
section; 2) pet campers who oppose a pet section; 3) non–pet campers who
support a pet section; and 4) the non–pet campers who oppose a pet section.
For any distribution, all the percentages must sum to 100%. If you’re using pro-
portions (decimals), they must sum to 1.00. Each individual has to be some-
where, and he can’t be in more than one place at one time.
In the following sections, you see how to find three types of distributions, each
one helping you to answer its corresponding question in the preceding list.
Singling out variables with
marginal distributions
If you want to examine one variable at a time in a two-way table, you don’t
look in the cells of the table, but rather in the margins. As seen in the earlier
section “Figuring the totals,” the marginal totals represent the total number
in each row (or column) separately. In the two-way table for the pet camping
survey (refer to Table 19-3), you see the marginal totals for the pet camping
variable (yes/no) in the right-hand column, and you find the marginal totals
for the opinion variable (support/oppose) in the bottom row.
If you want to make comparisons between two groups (for example, pet
campers versus non–pet campers), however, the results are easier to inter-
pret if you use proportions instead of totals. If 350 people were surveyed,
visualizing a comparison is easier if you’re told that 60% are in Group A and
40% are in Group B, rather than saying 210 people are in Group A and 140 are
in Group B.

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