# One-way ANCOVA

ANCOVA (Analysis of Covariance) tests for equality of means for several univariate groups, adjusted for covariance with another variate. ANCOVA can be compared with ANOVA, but has the added feature that for each group, variance that can be explained by a specified "nuisance" covariate (x) is removed. This adjustment can increase the power of the test substantially.

The program expects two or more pairs of columns, where each pair (group) is a set of correlated x-y data (means are compared for y, while x is the covariate). The example below uses three pairs (groups) a, b and c.

The Plot tab presents a scatter plot and linear regression lines for all the groups. The ANOVA-like summary table contains sum-of-squares etc. for the adjusted means (between-groups effect) and adjusted error (within-groups), together with an *F* test for the adjusted means. An *F* test for the equality of regression slopes (as assumed by the ANCOVA) is also given. In the example, equal adjusted means in the three groups can be rejected at *p<0.05. equality="" of="" slopes="" can="" not="" be="" rejected="">p*=0.74).

The Groups tab gives the summary statistics for each group (mean, adjusted mean and regression slope).

Assumptions include similar linear regression slopes for all groups, normal distributions, similar variance and sample sizes.

**Missing data**: x-y pairs with either x or y missing are disregarded.