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 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.
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 Analyze.
3. Drag the cursor over the General Linear Model drop-down menu.
4. Click Univariate.
5. Click on the continuous outcome variable to highlight it.
6. Click on the arrow to move the variable into the Dependent Variable: box.
7. Click on the "grouping" or categorical predictor variable to highlight it.
8. Click on the arrow to move the variable into the Fixed Factor(s): box.
9. Click on the continuous covariate variable to highlight it.
10. Click on the arrow to move the variable into the Covariate(s): box.
11. Click on the Options button.
12. In the Estimated Marginal Means, look in the Factor(s) and Factor Interactions: box.
13. Click on the "grouping" or categorical predictor variable to highlight it.
14. Click on the arrow to move the variable into the Display Means for: box.
15. Click on the Compare main effects box to select it.
16. Click on the Descriptive statistics, Estimates of effect size, Observed power, and Homogeneity tests boxes to select them.
17. Click Continue.
18. Click OK.
2. Click Analyze.
3. Drag the cursor over the General Linear Model drop-down menu.
4. Click Univariate.
5. Click on the continuous outcome variable to highlight it.
6. Click on the arrow to move the variable into the Dependent Variable: box.
7. Click on the "grouping" or categorical predictor variable to highlight it.
8. Click on the arrow to move the variable into the Fixed Factor(s): box.
9. Click on the continuous covariate variable to highlight it.
10. Click on the arrow to move the variable into the Covariate(s): box.
11. Click on the Options button.
12. In the Estimated Marginal Means, look in the Factor(s) and Factor Interactions: box.
13. Click on the "grouping" or categorical predictor variable to highlight it.
14. Click on the arrow to move the variable into the Display Means for: box.
15. Click on the Compare main effects box to select it.
16. Click on the Descriptive statistics, Estimates of effect size, Observed power, and Homogeneity tests boxes to select them.
17. Click Continue.
18. Click OK.
The steps for interpreting the SPSS output for ANCOVA
1. Look in the 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.
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.
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