Multivariate analysis of covariance (MANCOVA) is a statistical technique that is the extension of analysis of covariance (ANCOVA). Basically, all these techniques are like the multivariate analysis of covariance (MANCOVA). Multivariate analysis of variance (MANOVA), Analysis of covariance (ANCOVA), etc. are a family of analysis of variance (ANOVA). T-test is used to compare the means of two groups. When groups are more than two, then we use the ANOVA. In ANOVA, we use one dependent variable with more than two groups. If we want to compare more than two groups with two or more than two dependent variables, then it is the case of MANOVA. When we add a covariate in MANOVA, then it is the case of Multivariate analysis of covariance (MANCOVA). Covariate is added to the MANCOVA so that it can reduce error terms. In MANCOVA we can add more than one covariate—it depends on the sample size.
Assumptions in multivariate analysis of covariance (MANCOVA):
In multivariate analysis of covariance (MANCOVA), all assumptions are the same as in MANCOVA, but one more additional assumption is related to covariate. The following are the assumptions of MANCOVA:
1.Normal distribution: In multivariate analysis of covariance (MANCOVA), the dependent variable should be normally distributed within each group.
2.Homogeneity of variances: In multivariate analysis of covariance (MANCOVA), homogeneity of variances is assumed or it is assumed that the variance of all groups is equal.
3.Multivariate normality: Multivariate analysis of covariance (MANCOVA) is very sensitive with the outlier. In the case of multivariate analysis of covariance (MANCOVA), multivariate normality is required.
4.Level and Measurement of the Variables: In multivariate analysis of covariance (MANCOVA), dependent and covariate variables should continue as metric variables. In multivariate analysis of covariance (MANCOVA), grouping variables should be nominal.
Key concepts and terms in multivariate analysis of covariance (MANCOVA):
Box’s M test: In multivariate analysis of covariance (MANCOVA), Box’ M test is used to know the equality of covariance between the group. Null hypothesis in multivariate analysis of covariance (MANCOVA) is that observed covariance matrices of the dependent variable are equal across the groups.
Hotelling’s Trace: In multivariate analysis of covariance (MANCOVA), multivariate test simultaneously tests each factor effect on the dependent groups. Hotelling’s trace is a multivariate test that is used in the case of two dependent variables.
Wilks’ lambda: Wilk’s lambda is also a multivariate test. In multivariate analysis of covariance (MANCOVA), Wilk’s lambda is used when the dependent variable has more than two groups.
Levene’s test: In multivariate analysis of covariance (MANCOVA), we assume that the dependent variable has the same variance as all the groups. Levene’s test tests this assumption in multivariate analysis of covariance (MANCOVA).
Eta square: In multivariate analysis of covariance (MANCOVA), Eta-squared is the proportion of the total variability in the dependent variables accounted for by the variation in the independent variables.
Power: In multivariate analysis of covariance (MANCOVA), Power shows the probability of correctly rejecting the false null hypothesis.
Covariate: Covariate is basically a control variable in multivariate analysis of covariance (MANCOVA), which is uncorrelated with the independent variables and correlated with the dependent variables. Covariate is used to reduce the error term.
Multivariate analysis of covariance (MANCOVA) in SPSS: The following steps have to be performed for multivariate analysis of covariance (MANCOVA):
1.Run SPSS and open the “data file.”
2.Click on the “analysis” menu and select the multivariate from the general linear model.
3.Select the “dependent,” “independent” and “covariate” variable from the list.
4.Click on “option” and select the option that you want.
5.Click on “ok.”
MANCOVA Resources
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