In some experiments where we use ANOVA some of the unexplained variability (i.e. the error) is due to some additional variable (called a covariate) which is not part of the experiment. If we can somehow remove the effect of this variable, we could reduce the error variance thus enabling us to get a more accurate picture of the true effect of the independent variable. This is the main goal of Analysis of Covariance (ANCOVA).
Example 1: A school system is exploring four methods of teaching reading to their children, and would like to determine which method is best. It selects a random sample of 40 children and randomly divides them into four groups, using a different teaching method for each group. The reading score of each of the children after a month of training is given in Figure 1.
Before doing the analysis one of the researchers postulated that the scores of the children would be influenced by the income of their families, speculating that children from higher income families would do better on the reading tests no matter which teaching method was used, and so this factor should be taken into account when trying to determine which teaching method to use. The family income (in thousands of dollars) for each of the children in the study is also given in Figure 1. Based on the data, is there a significant difference between the teaching methods?
Figure 1 – Data for Example 1