Social Research Methods: Qualitative and Quantitative Approaches

ANALYSIS OF QUANTITATIVE DATA

Statistical control is a central idea used in

many advanced statistical techniques. A measure of

association such as the correlation coefficient only

suggests a relationship. Until you consider control

variables, the bivariate relationship might be spuri-

ous. This is why researchers are cautious in inter-

preting bivariate relationships until they have

considered control variables.

After you introduce control variables, you see

the net effectof an independent variable, that is, the

effect of the independent variable “net of,” or in

spite of, the control variable. We briefly look at two

ways to introduce control variables: trivariate per-

centaged tables and multiple regression analysis.

The Elaboration Model of
Percentaged Tables
Constructing Trivariate Tables.To meet the con-
ditions needed for causality, we want to “control
for” or see whether an alternative explanation elim-
inates a causal relationship. If an alternative expla-
nation accounts for a relationship, then the bivariate
relationship may be spurious. We operationalize
alternative explanations as third or control variables.
You can consider such third variables by sta-
tistically introducing control variables in trivariate
or three-variable tables. Trivariate tables differ only
slightly from bivariate tables. In a sense, they con-
sist of multiple bivariate tables. A trivariate table
consists of a separate bivariate table of the inde-
pendent and dependent variables created for each
category of the control variable. The multiple tables
of your independent and dependent variable, one
for each control variable category, are its partials.
The tables partial out the effects based on the con-
trol variable. The number of partials depends on the
number of categories in the control variable. Partial
tables look just like bivariate tables, but they use a
subset of the cases. Only cases with a specific value
on the control variable are in the partial. Thus, you
can combine the partials to restore the initial bivari-
ate table without a control variable.
Trivariate tables have three limitations. First,
they are difficult to interpret if a control variable has
more than four categories. Second, control variables
can be at any level of measurement, but you must

group interval-level or ratio-level control variables

(i.e., convert them to the ordinal level). Finally, the

total number of cases is a limiting factor because

the cases are divided among cells in partials. The

number of cells in the partials equals the number of

cells in the bivariate relationship multiplied by the

number of categories in the control variable. For

example, a control variable has three categories, and

a bivariate table has 12 cells, so the partials have

3  12 36 cells. An average of five cases per cell

is recommended, so 5  36 180 cases at mini-

mum are required.

Like bivariate table construction, a trivariate

table begins with a CFD but a three-way instead of

a two-way CFD. An example of a trivariate table

with “gender” as a control variable for the bivari-

ate relation in Table 1 is shown in Table 5.

As with the bivariate tables, each combination

in the CFD represents a cell in the final (here the

partial) table. Each partial table has the variables in

an initial bivariate table. For three variables, three

bivariate tables are logically possible. In the

example of Table 5, the combinations are (1) gen-

der by attitude, (2) age group by attitude, and (3)

gender by age group. The partials are set up on the

basis of the initial bivariate relationship. The inde-

pendent variable in each is age group, the depen-

dent variable is attitude, and gender is the control

variable. Thus, the trivariate table consists of a pair

of partials, each showing the age/attitude relation-

ship for a given gender.

Your theory and understanding of the social

world suggest both the hypothesis in the initial

bivariate relationship and which variables might be

alternative explanations (i.e., the control variables).

As with bivariate tables, the CFD provides the

raw count for cells (partials here). You convert them

Partials In contingency tables for three variables,

tables between the independent and dependent vari-

ables for each category of a control variable.

Net effect The result of one variable (usually inde-

pendent) on another (usually dependent) after the

impact of control variables that affects both has been

statistically removed.