Final answer:
ANCOVA reduces error variance by including a covariate in the analysis to adjust for its effects on the dependent variable. By adjusting for these effects, ANCOVA makes the analysis more accurate and reduces the residual error variance.
Step-by-step explanation:
ANCOVA, or Analysis of Covariance, is a statistical technique that combines both ANOVA (Analysis of Variance) and regression analysis. It reduces error variance by including a covariate, which is a continuous variable, in the analysis. By including a covariate, ANCOVA adjusts for the effects of the covariate on the dependent variable, making the analysis more accurate and reducing the residual error variance.
For example, let's say we want to compare the test scores of three different schools, but we know that the students' socioeconomic status also affects their test scores. By including socioeconomic status as a covariate in the ANCOVA analysis, we can remove the effects of socioeconomic status on the test scores, reducing the error variance and allowing us to make more accurate comparisons between the schools.
In summary, ANCOVA reduces error variance by including a covariate in the analysis to adjust for its effects on the dependent variable.