Encyclopedia of Sociology

ANALYSIS OF VARIANCE AND COVARIANCE

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CARLA B. HOWERY

ANALYSIS OF VARIANCE AND
COVARIANCE

Analysis of variance (ANOVA) and analysis of
covariance (ANACOVA) are statistical techniques
most suited for the analysis of data collected using
experimental methods. As a result, they have been
used more frequently in the fields of psychology
and medicine and less frequently in sociological
studies where survey methods predominate. These
techniques can be, and have been, used on survey
data, but usually they are performed within the
analysis framework of linear regression or the
‘‘general linear model.’’ Given their applicability
to experimental data, the easiest way to convey the
logic and value of these techniques is to first review
the basics of experimental design and the analysis
of experimental data. Basic concepts and proce-
dures will then be described, summary measures
and assumptions reviewed, and the applicability of
these techniques for sociological analysis discussed.

EXPERIMENTAL DESIGN AND ANALYSIS

In a classical experimental design, research sub-

jects are randomly assigned in equal numbers to

two or more discrete groups. Each of these groups

is then given a different treatment or stimulus and

observed to determine whether or not the differ-

ent treatments or stimuli had predicted effects on

some outcome variable. In most cases this out-

come variable has continuous values rather than

discrete categories. In some experiments there are

only two groups—one that receives the stimulus

(the experimental group) and one that does not

(the control group). In other studies, different

levels of a stimulus are administered (e.g., studies

testing the effectiveness of different levels of drug

dosages) or multiple conditions are created by

administering multiple stimuli separately and in

combination (e.g., exposure to a violent model

and reading pacifist literature).

In all experiments, care is taken to eliminate

any other confounding influences on subjects’

behaviors by randomly assigning subjects to groups.

As a result of random assignment, preexisting

differences between subjects (such as age, gender,

temperament, experience, etc.) are randomly dis-

tributed across groups making the groups equal in

terms of the potential effects of these preexisting

differences. Since each group contains approxi-

mately equal numbers of subjects of any given age,

gender, temperament, experience, etc., there

should be no differences between the groups on

the outcome variable that are due to these con-

founding influences. In addition, experiments are

conducted in standardized or ‘‘physically con-

trolled’’ situations (e.g., a laboratory), thus elimi-

nating any extraneous external sources of differ-

ence between the groups. Through random

assignment and standardization of experimental

conditions, the researcher is able to make the

qualifying statement ‘‘Other things being equal.. .’’

and assert that any differences found between

groups on the outcome measure(s) of interest are

due solely to the fact that one or more groups

received the experimental stimulus (stimuli) and

the other group did not.

Logic of analysis procedures. Analysis of vari-

ance detects effects of an experimental stimulus by

first computing means on the outcome variable

for the experimental and control groups and then

comparing those means. If the means are the