Analysis of covariance (ANCOVA) is an analysis technique that is applied to two variables in order to determine the strength of relationship between the two variables. This determines how the variables change together. This data analysis technique employs a general linear model. This means that is combines the analysis of variance as well as regression analysis to one data set. One of the variables to be tested has to be an independent variable while the other variable needs to be a dependent variable. The analysis determines the variance of the means of the dependent variable as compared to the independent variable on all levels. Means are compared while at the same time controlling the effects of a continuous variable (covariates) (Berman, 2010).
These variables can predict the outcome of a study. It can also be defined as the control variable that acts as a secondary variable. It affects the relationship between an independent and dependent variable which when carrying out an ANCOVA are of primary interest. Analysis of covariance is used to find significant difference between groups of data by reducing the within-group error variance. This is mainly because ANCOVA allows one to eliminate error variances from a dependent variable. The error variance is one that cannot be predicted from an independent variable (Berman, 2010).
ANCOVA analysis is based on four major assumptions. These assumptions assist with the explanation of the results of the analysis.
The first assumption is of randomness and independent sampling. This implies that the data collected or the data being analyzed must be selected randomly from the desired population of study. In addition, the data collected must be independent of each other. If the data is not randomly and independently sampled the results of the analysis will be inaccurate:
The second assumption is normality. This implies that the dependent variable to be analyzed should be normally distributed within the population of study. This is especially the case when the sample size of the study is small. If the dependent variable is not normally distributed or skewed, the analysis is invalid (Milliken & Johnson, 2002).
The third assumption is homogeneity of variance. This implies that the variance of the dependent variable must be equal for all levels of the independent variable and covariates. If homogeneity of variance does not exist then the analysis is invalid.
The fourth assumption is the homogeneity of regression. This implies that it is assumed that regression is homogenous. This means that the correlation (or slope of line) between the dependent variable and the covariates is equal for all levels of the independent variable. In a data set where the independent variable and the control variable have a significant relationship. If this is the case then the results of an ANCOVA is invalid. This is mainly because misinterpretations of the data may occur due to bias (Milliken & Johnson, 2002).
Conducting an ANCOVA:
In order to conduct an ANCOVA a number of tests have to be carried out on the data. Three main tests are carried out on the variables in order to determine whether an ANCOVA can be carried out.
The first test that should be carried out is the multicollinearity test. This is a phenomenon where two control variables are highly correlated. Therefore, this test examines the control variables. If a control variable shows significant relationship to another control variable (the correlation is tested at 0.5 or above) then one of the control variables should be removed. This is mainly because both control variables are redundant since they will affect the dependent variable to the same degree (Milliken & Johnson, 2002).
The second test is the test for homogeneity of variance. This test is in line with assumption three that has been made above. This can be done using the Levene's test. If the value of P<0.05 then the groups are not homogenous (Milliken & Johnson, 2002).As discussed earlier, the assumption implies that the variance of the dependent variable must be equal for all levels of the independent variable and covariates. If homogeneity of variance does not exist then the analysis is invalid (Berman, 2010).
The third test the test for homogeneity of regression. This test is in line with assumption four made above. As discussed earlier the correlation (or slope of line) between the dependent variable and the covariates is equal for all levels of the independent variable. Thus, this has to be tested in order to determine whether the regression is homogenous. In a data set where the independent variable and the control variable have a significant relationship. If this is the case then the results of an ANCOVA is invalid. This is mainly because misinterpretations of the data may occur due to bias (Berman, 2010).
In conclusion, if the dataset passes all three tests then the ANCOVA analysis can be carried out using any data analysis techniques such as SPSS, STATA, or Microsoft Excel. However, there are a number of further tests if the results obtained show significant main effects. In addition, the power considerations of adding a covariate increase the statistical power of the analysis of variance. It also reduces the degree of freedom.
Berman, S. (2010). Analysis of covariance: a comprehensive expository text. [S.l.], Xlibris Corp.
'Linear Models In Statistics 2nd Edition Is The Essential Introduction To The Theory And Application Of Linear Models Now In A Valuable New Edition' 2008, M2presswire, Newspaper Source, EBSCOhost, viewed 22 September 2012.
Milliken, G. A., & Johnson, D. E. (2002). Analysis of covariance. Boca Raton [u.a.], Chapman & Hall/CRC.