MANCOVA (Multivariate Analysis of Covariance) is the multivariate equivalent to ANCOVA (Analysis of Covariance). MANCOVA indicates whether there are statistically significant differences in group means. The main distinction between MANOVA and multiple analysis of covariance (MANCOVA) is the inclusion of interval independents as covariates. These covariates are control variables that minimize model error and guarantee the greatest fit. After accounting for the covariate, MANCOVA analyses the mean differences between groups for a linear combination of dependent variables, for example, assessing the output difference by age group after accounting for educational background.
Researchers can use MANCOVA similarly to MANOVA. Researchers can choose the dependent variable in the dependent variable box and the factor variable in the fixed factor box in the multivariate choice window. Additionally, the covariate that was utilized for adjustment needs to be specified by researchers. For instance, educational qualification might be chosen as the covariate when comparing the output (productivity) differences by age group (after accounting for educational attainment).
The “C,” which again stands for “covariance,” is the key distinction between the MANOVA and the MANCOVA. The MANOVA and the MANCOVA have two or more response variables, but the IVs’ characteristics are the main distinction between the two. While the MANOVA can only include factors, when one or more covariates are included, the analysis moves from a MANOVA to a MANCOVA.
- Minimum of four elements are required for a one-way MANCOVA: two or more groupings (levels or factors) of one independent variable, two or more dependent variables, and one or more covariates. The bilateral MANCOVA contains two independent variables.
Covariates / Covariance Defined #
A measure of the correlation between two random variables is covariance. Like variance, covariance reveals how two variables fluctuate collectively rather than just how one variable varies. One of these two variables may be a covariate. Any factor influencing how your independent variables interact with your dependent variable is a factor.
ANOVA, MANOVA and MANCOVA #
The first distinction between an ANOVA and a MANOVA or MANCOVA is that an ANOVA only has one dependent variable, but a MANOVA or MANCOVA both contain numerous dependent variables. Typically, an ANOVA contrasts two or more independent sets of responses for a continuous variable, usually three or more groups.
A MANOVA and MANCOVA, on the other hand, both feature numerous dependent variables, albeit there are variations between the two as well. The number of independent variables distinguishes a MANOVA from a MANCOVA. A MANOVA, like an ANOVA, examines multiple dependent variables among independent groups using just one independent variable (usually a categorical variable that represents independent groups). Similar to a MANOVA, a MANCOVA also allows for many independent variables (covariates).