Terminology: Regression, ANOVA, ANCOVA

In every field, it's essential to use the proper terminology in order to be understood and to inspire confidence. In statistics, some analyses can be described correctly in different ways. This can be viewed as liberating or as evidence of a sinister plot according to one's general outlook on life.

An example of this overlap in nomenclature occurs with

• regression,
• analysis of variance (ANOVA), and
• analysis of covariance (ANCOVA).

One simple rule states that

• if all predictors are numerical (quantitative), the analysis is called regression;
• if all predictors are categorical (qualitative), the analysis is called analysis of variance;
• if there are both qualitative and quantitative predictors, the analysis is called analysis of covariance.

Sometimes additional criteria are applied when both qualitative and quantitative predictors are used.

• If the focus is on the quantitative predictors, the analysis is often called regression.
• If the focus is on the qualitative predictors, the analysis is almost always called ANCOVA and the quantitative predictors are called covariates.

Most analysts would say the name ANCOVA should be used only when the model does not include interactions between the covariates and the factor of interest. Thus, a strict ANCOVA model is a "parallel slopes" model, so that the regression coefficients for the covariates are the same for all factor levels. When an author says that an ANCOVA model was fitted, assume no allowance was made for an interaction between the factor and covariates unless there is a statement to the contrary.

The name of the analysis is not always the the name of the computer program that performs it. Any ANOVA or ANCOVA can be performed by using an ordinary regression package if one is clever about constructing the proper sets of indicator variables. One can and should report that an ANOVA or ANCOVA was performed even when a regression program is used to do it.