# Multivariate Analysis of Covariate (MANCOVA)

What is MANCOVA?

MANCOVA is a statistical technique that is an extension of MANOVA that allows one to determine if there is a difference among groups after a new dependent variable (DV) is created by one or more covariate (Mertler & Reinhart, p. 145). “The effects of these covariates are then removed from the analysis, leaving one with a clearer picture of the true effects of the IV(s) on the multiple DVs” (p. 145). “A significant relationship between the set of DVs and the covariate or set of covariates should exist. In MANCOVA, if several covariates are being used, the amount of error reductions is determined by the magnitude of the multiple correlation between the new DV and the set of covariates” (Mertler & Reinhart, pp. 145-46).

What type of research questions are answered by MANCOVA?

MANCOVA addresses both multivariate and univariate analyses. For detailed sample questions please see page 146-147.

How does MANCOVA work?

The assumptions for MANCOVA must accommodate multiple DVs. Below are the assumptions for MANCOVA (Mertler & Reinhart, p. 147).

The observations within each sample and must be independent of each other.

The distributions of scores on the dependent variables must be normal in the populations from which the data were sampled.

The distributions of scores on the dependent variables must have equal variances.

Linear relationships must exist between all pairs of DVs, all pairs of covariates, and all DV- covariate pairs in each cell.

If two covariates are used, the regression planes for each group must be homogeneous or parallel. If more than two covariates are used, the regression hyperplanes must be homogeneous or parallel.

The covariates are reliable and are measured without error.

What is its measurements?

According to Mertler & Reinhart (2017), “the methods for testing assumptions are (1.) use histograms, box plots, and normal Q-Q plots to test normality. (2.) Kolmogorov-Smirnov test is used to examine the values for skewness and kurtosis when determining the statistical assessment of normality, and homoscedasticity is assessed by using Box’s test or Hartley’s F max test, Cochran’s test, or Levene’s test” (p. 148).

How is MANCOVA interpreted?

When writing up MANCOVA results, the narrative should address following (Mertler & Reinhart, p. 153):

Participant elimination and/or variable transformation.

Full MANCOCA results

Main effect for each IV and covariate on the combined DV

Main effect of the interaction between IVs

Univariate ANOVA results

Main effect for each IV and DV

Comparison of means to indicate which group differ on each DV

Are there different type of MANCOVAs?

“Factorial MANCOVA will test the main effect for each factor on the combined DV” (Mertler & Reinhart, p. 162).

How is it done in SPSS?

“To conduct the full Multivariate analysis, open the Multivariate dialog box by selecting: Analyze, General linear model, then Multivariate” Mertler & Reinhart, p. 157).

MANCOVA Discussion Questions

1: What are the two main reasons for including several covariates in an analysis?

2: What is the null hypothesis of MANCOVA that is being tested?

3: What happens if the null hypothesis is retained or rejected?

4: When is a Bonferroni type adjustment is appropriate to use while conducting MANCOVA?

5: A preliminary MANCOVA can be used to test what kind of assumption?

6: What are the steps to interpreting MANCOVA results?

7: What is the entire process for conducting MANCOVA?

8: In MANOVA and MANCOVA, when do you use Wilks’ Lambda when do you use Pillai’s Trace.

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