ANCOVA is a procedure of analysis of variance procedure where the effects of the covariates (extraneous variables) are eliminated from the data of the dependent variable before analysis of ANOVA is carried out. ANCOVA permits the control of the linear effect of extraneous variables unwanted in a study (Bradley, 2009).
ANCOVA Utilizes regression analysis to eliminate the effect of extraneous variables in the analysis. ANCOVA is used to enhance the precision of group comparisons through accounting for variation on the prognostic variables. In the analysis for imbalances in the prognostic variables, ANCOVA is also used to adjust the comparisons between the groups (Bowers, 2008).
ANCOVA is also used in the comparison of two and more linear regression lines as a method of comparing Y variables among groups. ANCOVA is also used to statistically control for deviation in Y variables caused by variations in the X variable. In ANCOVA analysis, two types of null hypothesis are tested. The first hypothesis that is tested is the hypothesis that the slopes of two regression lines are identical. If this hypothesis is not accepted, then the second null hypothesis that the Y intercepts of two or more regression lines are identical is tested (McDonald, 2009).
ANCOVA analysis can also be used in the comparison of more than two regression lines, and if these regression lines have, a similar slope it is possible to carry out a planned comparison of the Y intercepts. The first step in performing ANCOVA is the generation of the regression line. The next step is the comparison of the slopes of the regression line. Testing of the null hypothesis that the slopes of the regression lines are the same is carried out (Campbell, 2010).
The final step of ANCOVA analysis is comparing the Y intercept. If the slopes of the regression line differ significantly, this step is not possible because the regression lines cross each other at some point. If the slopes of the regression lines are significantly different, the ANCOVA analysis is complete, and the hypothesis is that the slopes are different is accepted (McDonald, 2009).
If the slopes of the regression lines do not differ significantly, the next step in ANCOVA analysis is drawing a regression line via each group of points with all the regression lines having a common slope. The common slope is the weighted average of all the slopes for the groups in the analysis (Bowers, 2008).
The final step in ANCOVA analysis is the testing of the null hypothesis that the Y intercepts of all the regression lines with a similar slope are all the same. Since these lines are parallel, accepting that these lines are significantly different at the Y intercept means that the lines are different each point (McDonald, 2009).
Reference
Bradley, H., (2009). Analysis of covariance ANCOVA. Retrieved from
http://srmo.sagepub.com/view/encyclopedia-of-measurement-and-statistics/n18.xml
Bowers D. (2008). Medical statistics from scratch an introduction for health
Professionals. New York: John Wiley & Sons.
Campbell, M., (2010). Medical statistics: a textbook for the health sciences. New York: John
Wiley & Sons.
McDonald, J. H. (2009). Handbook of biological statistics. Sparky house publishing,
Baltimore, Maryland.
