Example #1 No Confounding
ANCOVA
Example #1 – “no confounding”
Two good ways to get a look at the data are to look at a graph and to look at separate ANOVAs for the DV and the Covariate
GRAPH
/SCATTERPLOT(BIVAR)=pract1 WITH perf1 BY group.
ONEWAY perf1 pract1 BY group
/STATISTICS DESCRIPTIVES.
DV (Performance) – looks like a mean difference with Tx > C
Covariate (Practice) – looks like no mean difference /
ANOVA results are consistent with the graphical results.
There is a significant DV mean difference between groups, but no significant difference on the covariate (i.e., no confounding).
For mathematical and interpretive reasons, it is advisable to work with the centered covariate
* mean practice taken from previous ANOVA.
compute pract1_cen = pract1 - 21.1891.
exe.
* this gets the ANCOVA with the IV-by-covariate interaction.
UNIANOVA perf1 BY group WITH pract1_cen
/EMMEANS=TABLES(group) WITH(pract1_cen=MEAN)
/PRINT=DESCRIPTIVE PARAMETER
/DESIGN=group pract1_cen group*pract1_cen.
/ 
The uncorrected mean difference from the ANOVA was 81.4298 – 69.9284 = 11.5014
The corrected mean difference from the ANCOVA was 82.56 – 68.849 = 13.715, when controlling at covariate mean = 21.1891
smaller error term means “more powerful NHST”
“no confounding” mean “no correction”
Example #2 – “augmenting confound”
The uncorrected mean difference from the ANOVA was
The corrected mean difference from the ANCOVA was , when controlling at covariate mean =
smaller error term means “more powerful NHST”
Example #3 – “interfering confound”
The uncorrected mean difference from the ANOVA was
The corrected mean difference from the ANCOVA was , when controlling at covariate mean =
smaller error term means “more powerful NHST”
Example #4– “no confounding” & “with interaction”
ANCOVA w/ Homogeneity of Regression Slope Assumption (Main effects model)
The uncorrected mean difference from the ANOVA was
The corrected mean difference from the ANCOVA was , when controlling at covariate mean =
smaller error term means “more powerful NHST”
Expectation/Assumption of group difference for different values of covariate
ANCOVA w/ interaction (Full model)
The uncorrected mean difference from the ANOVA was
The corrected mean difference from the ANCOVA was , when controlling at covariate mean =
smaller error term means “more powerful NHST”
Expectation/Assumption of group difference for different values of covariate
Example #5– “Augmenting confound” & “with interaction”
ANCOVA w/ Homogeneity of Regression Slope Assumption (Main effects model)
The uncorrected mean difference from the ANOVA was
The corrected mean difference from the ANCOVA was , when controlling at covariate mean =
smaller error term means “more powerful NHST”
Expectation/Assumption of group difference for different values of covariate
ANCOVA w/ interaction (Full model)
The uncorrected mean difference from the ANOVA was
The corrected mean difference from the ANCOVA was , when controlling at covariate mean =
smaller error term means “more powerful NHST”
Expectation/Assumption of group difference for different values of covariate
Example #6– “Interfering confound” & “with interaction”
ANCOVA w/ Homogeneity of Regression Slope Assumption (Main effects model)
The uncorrected mean difference from the ANOVA was
The corrected mean difference from the ANCOVA was , when controlling at covariate mean =
smaller error term means “more powerful NHST”
Expectation/Assumption of group difference for different values of covariate
ANCOVA w/ interaction (Full model)
The uncorrected mean difference from the ANOVA was
The corrected mean difference from the ANCOVA was , when controlling at covariate mean =
smaller error term means “more powerful NHST”
Expectation/Assumption of group difference for different values of covariate