## ANCOVA (Analyses of covariance)

**ANCOVA is short for ANalysis of COVAriance. It is a statistical technique in which the distribution of the variance of a variable is explained by adjusting it to a grouping variable in combination with a continuous variable.**

**Introduction**

An ANCOVA is an extension of an ANOVA. In the ANOVA the subjects are grouped on one dimension and for every group the mean is computed. Performing an ANOVA compares the equality of these means. The details can be found on our webpage called ANOVA.

In an ANCOVA the classification of the objects (cases, respondents, subjects) is done in combination with a continuous variable. For instance, the satisfaction with the shopping centre in the neighbourhood can be measured on a scale ranging from 1 to 100 (the dependent variable). It might be interesting if men and women (the independent variable) value the shopping centre differently. According to the theory it is expected that elderly people value their neighbourhood higher than youngsters. Age seems to be a confounder and in the statistical analysis there is a need to take this into account by controlling the age effect.

Just a small comment: Be sure age is measured at a ratio scale. If it is measured at an ordinal scale, it can also be taken into account as a nominal variable. Now the analysis should be a MANOVA and not an ANCOVA.

**Examples of research questions for an ANCOVA**

The ANCOVA is applied for research questions like:

- Is there a difference between men and women in their appreciation for their shopping centre controlled for age?
- Do Americans live in bigger house than Europeans controlled by income?
- Is there a difference between Italy, the United Kingdom, Germany and Spain in the amount of CO
_{2}-emission controlled for concern size?

**The hypothesis for testing the ANCOVA**

In an ANOVA there is only one grouping variable. It means that there is only one dimension and on this dimension the means are compared. On an ANCOVA there is (at least) one test extra. In the output there is simply an extra line with the F-value, the degrees of freedom and the p-value.

To test the influence of the covariate, the test can be done twice. First do it without and then do it with the covariate. The change in the test values are due to the covariable.

**Requirements for an ANCOVA**

Characteristic for an ANCOVA is the comparing of the means of groups on at least one grouping variable in combination with a continuous variable.

The number of groups (the independent variable) has to be measured on one dimension with at least two values. If more dimensions or grouping variables are used, this is denoted as a MANCOVA. The number of groups is a variable on nominal level.

The dependent variable and the covariate should be a continuous variable. They must be continuous data, that is measured at an interval or ratio scale. If they are measured on ordinal level, there isn’t a widely used kind of analyses. The best way to deal with such a situation is treating the data as if they were measured on the interval level. Read more about this topic in our paper which test should be performed?