Covariance is a measure of how much two variables change together and how strong the relationship is between them. Analysis of covariance is a general linear model which blends ANOVA and regression. It evaluates whether population means of a dependent variable are equal across levels of a categorical independent variable, while statistically controlling for the effects of other continuous variables that are not of primary interest. There are known as covariates. There, when the analysis of covariance takes place, we adjust the dependent variable means to what they would be if all groups were equal on the covariates.
Analysis of covariance can be used to increase statistical power by reducing the within group error variance. For one to completely understand this concept, it is necessary to understand the test used to evaluate differences between groups, the F-test. This test is computed by the following:
F = MSbetween/MSwithin
I this value is a larger than the critical value, we conclude that there is a significant difference between groups. Unexplained variance includes error variance, as well as the influence of other factors. When we control for the effect of covariance on the dependant variable, we remove it from the denominator making F larger, thereby increasing your power to find a significant effect if one exists.