ANCOVA (Analysis of Covariance)
1 Continuous Dependent Variable with normal distribution
2 (or more) Categorical or Continuous Independent Variables with normal distribution
y = a * x1 + b * x2 + c * x3 +Öm * xn + 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 variableís 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.
Nass and Lee  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 subjectís gender also has a bearing on the subjectís assessment of the book reviewer. They use ANCOVA to control the effect of gender, which allows them to just compare the subjectís 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 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.
 From conversation with Michael Peascoe at University of Minnesota Statistical Consulting Clinic.