ANALYSIS OF QUANTITATIVE DATAContingency table A summary format of the cross-
tabulation of two or more variables showing bivariate
quantitative data for variables in the form of percent-
ages across rows or down columns for the categories
of one variable.
Cross-tabulation The process of placing data for
two variables in a contingency table to show the
percentage or number of cases at the intersection of
variable categories.measured at any level of measurement, although
interval and ratio data must be grouped.
The bivarate contingency table is based on
cross-tabulation(i.e., tabulating two or more vari-
ables simultaneously). It is “contingent” because the
cases in each category of a variable are distributed
into each category of a second (or additional) vari-
able. The table distributes cases into the categories
of multiple variables at the same time and shows us
how the cases, by category of one variable, are “con-
tingent upon” the categories of other variables.
Constructing Percentaged Tables.Contingency
tables made up of the counts of a case are of limited
use because seeing patterns or variable relationships
with the counts of cases is difficult. By “standardiz-
ing” data, or turning them into percentages, we can
see patterns and relationships among variables more
easily even if the counts of cases vary greatly. It is
not difficult to construct a percentaged table, and
there are ways to make it look professional. We first
review the steps for constructing a table by hand.
The same principles apply if a computer makes the
table for you. We begin with the raw data (see data
from an imaginary survey in Example Box 2, Raw
Data and Frequency Distributions).
If you create a table by hand, you may find an
intermediate step between raw data and the table
useful (i.e., create a compound frequency distri-
bution [CFD]). It is similar to the frequency distri-
bution except that it is for each combination of the
values of two variables. For example, you want to
see the relationship between age and attitude about
the legal age to drink alcohol. Age is a ratio measure,
so you group it to treat the ratio-level variable as if
it were ordinal. In percentage tables, we group ratio-
or interval-level data to convert them into the ordi-
nal level. Otherwise, we might have 50 categories
for a variable and a table that is impossible to read.
The CFD has every combination of category.
Age has four categories and Attitude three, so there
are 3 4 12 rows. The steps to create a CFD are
as follows:
- Determine all possible combinations of vari-
able categories.
2. Make a mark next to the combination category
into which each case falls.
3. Add the marks for the number of cases in a
combination category.
If there is no missing information problem, add the
numbers of categories (e.g., all the “Agree”s, or all
the “61 and Older”s). In the example, missing data
are an issue. The four “Agree” categories in the CFD
add to 37 (20 10 4 3), not 38, as in the uni-
variate frequency distribution, because one of the
38 cases has missing information for age.
The next step is to set up the parts of a table (see
Figure 6) by labeling the rows and columns. The
independent variable usually is placed in the
columns, but this convention is not always followed.
Next, each number from the CFD is placed in a cell
in the table that corresponds to the combination of
variable categories. For example, the CFD shows
that 20 of the under-30-year-olds agree (top num-
ber) as does Figure 6 (upper left cell).
Figure 6 is a raw count or frequency table. Its
cells contain a count of the cases. It is easy to make
but very difficult to interpret because the rows or
columns can have different totals. What is of real
interest is the relative size of cells compared to
others.
Raw count tables can be converted into per-
centaged tables in three ways: percent by row, by
column, and by total. The first two are often used to
show relationships. The percent by total is almost
never used and does not reveal relationships easily.
Is it best to percentage by row or column?
Either can be appropriate. Here are the mechanics
of making a percentage table. When calculating col-
umn percentages, compute each cell’s percentage