**ANCOVA
(Analysis of Covariance)**

** **

1 Continuous Dependent Variable with
normal distribution

2 (or more) Categorical or Continuous
Independent Variables with normal distribution

*y
=** a * x _{1} + b * x_{2} + c *
x_{3} +…m * x_{n} + b*

The independent and dependent variable structures for
Multiple Regression, factorial ANOVA, and ANCOVA tests are similar. ANCOVA is
differentiated from the other two in that it is used when the researcher wants
to neutralize the effect of a continuous independent variable in the
experiment. The researcher may simply not be interested in the effect of a
given independent variable when performing a study.

Another situation where ANCOVA should be applied is when an
independent variable has a strong correlation with the dependent variable, but
does not interact with other independent variables in predicting the dependent
variable’s value. ANCOVA is used to neutralize the effect of the more powerful,
non-interacting variable. Without this intervention measure, the effects of
interacting independent variables can be clouded.

HCI Example:

Nass and Lee [8] perform a
study of the effect of various Text-to-Speech (TTS) interfaces on user
behavior. In the study, subjects view information about 5 books on a retail web
site. In addition, they listen to TTS reviews for each book and answer questions
about the book reviewer. The researchers manipulate the TTS in each condition
so that it either sounds like the speech of an extroverted person or
introverted person. Extrovert speech is characterized by higher and more
diverse pitch, a faster rate, and louder volume.

The researchers postulate subjects will find the book
reviewer more credible if the TTS interface personality of the audio review
reflects their own personality style. When analyzing the results, the
researchers believe the subject’s gender also has a bearing on the subject’s
assessment of the book reviewer. They use ANCOVA to control the effect of
gender, which allows them to just compare the subject’s extrovert/introvert
preference to the TTS extrovert/introvert style. The team also conducts a
factorial ANOVA test to see if the results differ from ANCOVA, and they do not.
Because both results were the same, gender did not actually have a bearing on
subject behavior.

ANCOVA is actually not the best statistical test for the
Nass and Lee experiment.i [1]A
better test would have been two-way ANOVA. Two-way ANOVA has a utility that
allows the researcher to check if the
independent variables interact to predict the dependent variable. Further, an
auxiliary technique is available to neutralize the effect of a variable in
two-way ANOVA if unwanted interaction exists. ANCOVA is applied correctly when
the neutralized independent variable is measured on a continuous scale. In the
Nass and Lee experiment, gender, a categorical variable, is neutralized, so
ANCOVA is not the proper instrument.

[1] From conversation with Michael Peascoe at University of Minnesota Statistical Consulting Clinic.