Everything about MANOVA and MANCOVA
MANOVA (multivariate analysis of variance): It is a type of multivariate analysis used to analyze data that involves more than one dependent variable at a time. MANOVA allows us to test hypotheses regarding the effect of one or more independent variables on two or more dependent variables. The obvious difference between ANOVA and the “Multivariate Analysis of Variance” (MANOVA) is the “M”, which stands for multivariate. In basic terms, MANOVA is an ANOVA with two or more continuous response variables. Like ANOVA, MANOVA has both the one-way flavor and a two-way flavor. The number of factor variables involved distinguishes the one-way MANOVA from a two-way MANOVA.
When comparing the two or more continuous response variables by the single factor, a one-way MANOVA is appropriate (e.g. comparing ‘test score’ and ‘annual income’ together by ‘level of education’). The two-way MANOVA also entails two or more continuous response variables, but compares them by at least two factors (e.g. comparing ‘test score’ and ‘annual income’ together by both ‘level of education’ and ‘zodiac sign’).
MANCOVA:
Multivariate analysis of covariance (MANCOVA): It is a statistical technique that is the extension of the analysis of covariance (ANCOVA). It is the multivariate analysis of variance (MANOVA) with a covariate(s).). In MANCOVA, we assess for statistical differences on multiple continuous dependent variables by an independent grouping variable, while controlling for a third variable called the covariate; multiple covariates can be used, depending on the sample size. Covariates are added so that it can reduce error terms and so that the analysis eliminates the covariates’ effect on the relationship between the independent grouping variable and the continuous dependent variables. ANOVA and ANCOVA, the main difference between the MANOVA and MANCOVA, is the “C,” which again stands for the “covariance.” Both the MANOVA and MANCOVA feature two or more response variables, but the key difference between the two is the nature of the IVs. While the MANOVA can include only factors, an analysis evolves from MANOVA to MANCOVA when one or more covariates are added to the mix.
