# MANCOVA

## Account for increased Type I error when comparing independent groups on multiple adjusted outcomes

**MANCOVA**is often employed to account for what is called "

**increased experimentwise error rates**" when

**testing multiple hypotheses concurrently and adjusting several outcome values at the same time with a covariate**. Essentially, with each mutually exclusive analysis between the categorical predictor variable and the adjusted outcome, the chances of

**committing a Type I error increase**substantially. If the

**statistical assumptions**of a MANCOVA can be met, it is a much more powerful inferential statistic that can yield both main and interactional effects while controlling for a covariate.

The figure below depicts the use of MANCOVA. The differences between independent groups are being adjusted for by a covariate when assessing multiple continuous outcomes.

### The steps for conducting MANCOVA in SPSS

1. The data is entered in a between-subjects fashion.

2. Click

3. Drag the cursor over the

4. Click

5. Click on the first continuous outcome variable to highlight it.

6. Click on the

7. Repeat Steps 5 and 6 until all of the continuous outcome variables are in the

8. Click on the categorical predictor variable that represents independent groups or levels.

9. Click on the

10. Click on the continuous covariate variable to highlight it.

11. Click on the

12. Click on the

13. Click on the categorical predictor variable in the

14. Click on the

15. Click on the

16. In the

17. Click

18. Click

2. Click

**.**__A__nalyze3. Drag the cursor over the

**drop-down menu.**__G__eneral Linear Model4. Click

**.**__M__ultivariate5. Click on the first continuous outcome variable to highlight it.

6. Click on the

**arrow**to move the variable into the**box.**__D__ependent Variables:7. Repeat Steps 5 and 6 until all of the continuous outcome variables are in the

**box.**__D__ependent Variables:8. Click on the categorical predictor variable that represents independent groups or levels.

9. Click on the

**arrow**to move the variable into the**box.**__F__ixed Factor(s):10. Click on the continuous covariate variable to highlight it.

11. Click on the

**arrow**to move the variable into the**box.**__C__ovariate(s):12. Click on the

**Options**button.13. Click on the categorical predictor variable in the

**box to highlight it.**__F__actor(s) and Factor Interactions:14. Click on the

**arrow**to move the variable into the**box.**__D__isplay Means for:15. Click on the

**C**box to select it.__o__mpare main effects16. In the

**Display**table, click on the**,**__D__escriptive statistics**,**__E__stimates of effect size**O**, and__b__served power**boxes to select them.**__H__omogeneity tests17. Click

**Continue**.18. Click

**OK**.### The steps for interpreting the SPSS output for MANCOVA

1. Look in the

If it is

If it is

2. Look in the

If it is

If it is

3. Look in the

If it is

If it is

4. Look in the

If it is

If it is

5. Look in the

If it is

If it is

6. Look in the

If a

If a

7. Look in the

If a

If a

8. Scroll down to the

9. Look in the

If a

If a

**Box's Test of Equality of Covariance Matrices**, in the**Sig.**row. This is the*p*-value that is interpreted.If it is

**LESS THAN .05**, then researchers have violated the assumption of homogeneity of covariance and should not interpret the outputs further.If it is

**MORE THAN .05**, then researchers can continue with the analysis and have met the assumption of homogeneity of covariance.2. Look in the

**Levene's Test of Equality of Error Variances**table, in the**Sig.**column. This is the p-value that is interpreted.If it is

**LESS THAN .05,**then researchers have violated the assumption of homogeneity of variance and should not interpret the outputs further.If it is

**MORE THAN .05**, then researchers can continue with the analysis and have met the assumption of homogeneity of variance.3. Look in the

**Multivariate Tests**table, under the**Sig.**column, for the row that has the continuous covariate variable's name and**Pillai's Trace**. This is the*p*-value that is interpreted.If it is

**LESS THAN .05**, then researchers have evidence that the covariate adjusts values of the outcome.If it is

**MORE THAN .05**, then Researchers do not have evidence that the covariate adjusts the outcome. No further interpretation is needed. Report the*p*-value.4. Look in the

**Multivariate Tests**table, under the**Sig.**column, for the row that has the categorical predictor variable's name and**Pillai's Trace**. This is the*p*-value that is interpreted.If it is

**LESS THAN .05**, then researchers have evidence of a significant main effect when controlling for the covariate.If it is

**MORE THAN .05**, then researchers do not have evidence of a significant effect when controlling for the covariate. No further interpretation is needed. Report the*p*-value.5. Look in the

**Levene's Test of Equality of Error Variances**table, under the**Sig.**column, for each outcome variable that has a*p*-value testing the assumption of homogeneity of variance.If it is

**LESS THAN .05**, then researchers have violated the assumption and should not continue with the analysis.If it is

**MORE THAN .05**, then researchers can continue with the analysis and interpretation.6. Look in the

**Tests of Between-Subjects Effects**table, under the**Sig.**column, for the row denoting the continuous covariate variable. These are the*p*-values that are interpreted for each individual covariate. These should be interpreted only if there is a significant main effect for the covariate in the**Multivariate Tests**table.If a

*p*-value for one of the outcome variables is**LESS THAN .05**, then there was a significant main effect among the independent groups or levels for the covariate. If researchers find this significant main effect, they need to run post hoc analyses to explain the effect.If a

*p*-value for one of the outcome variables is**MORE THAN .05**, then there was**NOT**significant main effect among the independent groups or levels for the covariate.7. Look in the

**Tests of Between-Subjects Effects**table, under the**Sig.**column, for the row denoting the categorical predictor variable. These are the*p*-values that are interpreted for each individual outcome variable. These should be interpreted if there is a significant main effect in the**Multivariate Tests**table.If a

*p*-value for one of the outcome variables is**LESS THAN .05**, then there was a significant main effect among the independent groups or levels of that outcome. If researchers find this significant main effect, they need to run post hoc analyses to explain the effect.If a

*p*-value for one of the outcome variables is**MORE THAN .05**, then there was**NOT**significant main effect amongst the independent groups or levels of that outcome.8. Scroll down to the

**Estimated Marginal Means**section of the output. Look in the**Estimates**table. These are the adjusted means and standard errors of the outcome for each group or level of the categorical variable.9. Look in the

**Pairwise Comparisons**table, under the**Sig.**column. These are the post hoc*p*-values that are interpreted.If a

*p*-value is**LESS THAN .05**, then there was a significant difference in the adjusted means between the independent groups or levels of the categorical predictor variable on the outcome.If a

*p*-value is**MORE THAN .05**, then there was**NOT**a significant difference in the adjusted means between the independent groups or levels of the categorical predictor variable on the outcome.Click on the

**Download Database**and**Download Data Dictionary**buttons for a configured database and data dictionary for MANCOVA.**Click on the****Validation of Statistical Findings**button to learn more about bootstrap, split-group, and jack-knife validation methods.## Statistician Services for Professionals

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