General Uses of Analysis of Covariance (ANCOVA)
Analysis of Covariance (ANCOVA) is the inclusion of a continuous variable in addition to the variables of interest (i.e., the dependent and independent variable) as means for control. Because the ANCOVA is an extension of the ANOVA, the researcher can still can assess main effects and interactions to answer their research hypotheses. The difference between ANCOVA and ANOVA is that ANCOVA includes a covariate correlated with the dependent variable, adjusting the means on the dependent variable based on the covariate’s effects. Researchers can use covariates in various ANOVA-based designs, including between-subjects, within-subjects (repeated measures), and mixed (between- and within-subjects) designs. Thus, this technique answers the question: Did mean differences or interactive effects likely occur by chance after adjusting scores on the dependent variable for the effect of the covariate?
Increasing the Power of the F-Test in Experimental Designs
Tabachnick and Fidell (2013) review three general applications for an Analysis of Covariance include:
To increase the power of the F-test in experimental designs, researchers assign participants to treatment and control groups in an ANOVA-based design. Researchers can then use ANCOVA to eliminate unwanted variance in the dependent variable. This allows the researcher to increase test sensitivity. Adding reliable and necessary variables to these models typically reduces the error term. By reducing the error term, the sensitivity of the F-test also increases for main and interactive effects.
Equating Non-Equivalent Groups:
Another, though controversial, use of ANCOVA is to correct for initial group differences that exists on the dependent variable. Using this method, the researcher adjusts means on the dependent variable in an effort to correct for individual differences. This allows the researcher to adjust the means on the dependent variable to what they would have been should all of the participants scored equally on the covariate. Researchers commonly use this approach in non-experimental situations when they have not implemented random assignment.However, differences may have also have been due to other variables not measured or included as covariates.
- Adjustment of Means of Multiple Dependent Variables: This application is similar to the ones outlined above, but when the researcher is measuring multiple dependent variables, such as a Multivariate ANOVA (MANOVA). This application typically occurs when the researcher wants to assess the contribution of the various dependent variables by removing their effects from the analyses. This procedure is called a stepdown analysis.
The researcher can go about interpreting main effects and interactions as they typically would. The difference is that researchers first estimate the regression of the covariate on the dependent variable before partitioning the variance in scores into between-group and within-group. differences.; however, the error term is adjusted from the regression line derived from the covariate on the DV vs. running through the means in ANOVA designs.
References:
Tabachnick, B., & Fidell, L. (2013). Using multivariate statistics (6th ed.)Upper Saddle
River, NJ: Pearson.