# ANCOVA

## Adjust the outcome for covariates when comparing independent groups

The analysis of covariance (ANCOVA) is a statistical test used to control for the effects of a confounding variable (covariate) on the relationship or association between a predictor and outcome variable. With ANCOVA, the covariate is measured at a continuous level. The predictor variable can represent independent groups or levels of a categorical variable. The outcome is continuous with ANCOVA.

Just like with other independent group comparisons, there are certain statistical assumptions that must be met before an ANCOVA is employed:

1. The covariate and outcome variables should meet the

2. There should be

3.

4. The strength and direction of the association between the covariate and the outcome variable must be similar in each independent group. This assumption is known as

Just like with other independent group comparisons, there are certain statistical assumptions that must be met before an ANCOVA is employed:

1. The covariate and outcome variables should meet the

**assumption of normality**.2. There should be

**homogeneity of variance**between the independent groups.3.

**The covariate should****not be correlated at higher than .80 to the outcome**. If so, a different covariate should be chosen.4. The strength and direction of the association between the covariate and the outcome variable must be similar in each independent group. This assumption is known as

**homogeneity of regression**. Thus, your covariate variable needs to be precise and accurate enough to properly control for the variance associated with the relationship between the predictor and outcome variable when using ANCOVA.The figure below depicts the use of ANCOVA. The difference between independent groups on a continuous outcome is being adjusted for with a continuous covariate.

### The steps for conducting ANCOVA 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 continuous outcome variable to highlight it.

6. Click on the

7. Click on the "grouping" or categorical predictor variable to highlight it.

8. Click on the

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

10. Click on the

11. Click on the

12. In the

13. Click on the "grouping" or categorical predictor variable to highlight it.

14. Click on the

15. Click on the

16. Click on the

17. Click

18. Click

2. Click

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

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

**.**__U__nivariate5. Click on the continuous outcome variable to highlight it.

6. Click on the

**arrow**to move the variable into the**box.**__D__ependent Variable:7. Click on the "grouping" or categorical predictor variable to highlight it.

8. Click on the

**arrow**to move the variable into the**box.**__F__ixed Factor(s):9. Click on the continuous covariate variable to highlight it.

10. Click on the

**arrow**to move the variable into the**box.**__C__ovariate(s):11. Click on the

**button.**__O__ptions12. In the

**Estimated Marginal Means**, look in the**box.**__F__actor(s) and Factor Interactions:13. Click on the "grouping" or categorical predictor variable to highlight it.

14. Click on the

**arrow**to move the variable into the**Display**box.__M__eans for:15. Click on the

**C**box to select it.__o__mpare main effects16. 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 ANCOVA

1. Look in the

If the

If the

2. Look in the

If the

If the

3. Look at the

If the

If the

4. If the covariate was significant, and the "grouping" or predictor variable was significant, then researchers have evidence that there was a statistically significant difference between the groups or levels when controlling for the covariate.

If the covariate is significant, but the "grouping" or predictor variable is not, then the ANCOVA has shown evidence that it does not adjust the association.

If the covariate is not significant, but the "grouping" or predictor variable is significant, then the covariate does not adjust the association between the predictor and outcome variable.

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

*p*-value is**LESS THAN .05**, then researchers have violated this assumption and should check for outliers or run non-parametric tests.If the

*p*-value is**MORE THAN .05**, then researchers have met the assumption and continue with the analysis.2. Look in the

**Tests of Between-Subjects Effects**, under the**Sig.**column. These are the*p*-values that are interpreted. Look first at the row denoting the covariate variable.If the

*p*-value is**LESS THAN .05**, then the covariate significantly adjusts the association between the predictor and outcome variable.If the

*p*-value is**MORE THAN .05**, then the covariate does**NOT**adjust the association between the predictor and outcome variable.3. Look at the

*p*-value associated with the "grouping" or categorical predictor variable.If the

*p*-value is**LESS THAN .05**, then there was a statistically significant difference between the groups or levels of the variable.If the

*p*-value is**MORE THAN .05**, then there was**NOT**a statistically significant difference between the groups or levels of the variable.4. If the covariate was significant, and the "grouping" or predictor variable was significant, then researchers have evidence that there was a statistically significant difference between the groups or levels when controlling for the covariate.

If the covariate is significant, but the "grouping" or predictor variable is not, then the ANCOVA has shown evidence that it does not adjust the association.

If the covariate is not significant, but the "grouping" or predictor variable is significant, then the covariate does not adjust the association between the predictor and outcome variable.

Click on the

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

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