chapter 12 readings

What is ANCOVA?

A statistical method that combines ANOVA and regression by controlling for the effect of one or more covariates.

What is a covariate?

A continuous variable that is related to the dependent variable and statistically controlled in the analysis.

Why is ANCOVA used?

To reduce error variance and increase statistical power by accounting for variance attributable to covariates.

In what situations is ANCOVA particularly useful?

When comparing group means while adjusting for baseline differences on a related variable.

What is an example of ANCOVA use?

Comparing post-test scores between treatment groups while controlling for pre-test scores.

How does ANCOVA improve analysis?

By adjusting group means to account for differences in the covariate, leading to more accurate comparisons.

How does ANCOVA adjust the estimate of error?

It removes variance associated with the covariate from the within-group error term.

What happens to the F-ratio after adjustment?

It typically increases, making the test more powerful if the covariate is relevant.

What is the effect of including an irrelevant covariate?

It can reduce statistical power and add unnecessary complexity.

What does ANCOVA adjust?

The group means of the DV to account for the effect of the covariate.

In an ANCOVA example comparing reading scores across programs, what might be a covariate?

Pre-intervention reading ability or IQ score.

What is the adjusted mean?

The group mean after removing the influence of the covariate.

What are the core assumptions of ANCOVA?

1. Independence of observations

2. Normality

3. Homogeneity of variance

4. Linearity between DV and covariate

5. Homogeneity of regression slopes

What does homogeneity of regression slopes mean?

The relationship between the covariate and the DV is the same across all groups.

How do you test for homogeneity of regression slopes?

Include an interaction term between the covariate and group in the model; if significant, the assumption is violated.

What to do if this assumption of homogeneity is violated?

Avoid ANCOVA or use a model that accounts for the interaction between the covariate and the group.

What is the effect size commonly used in ANCOVA?

Partial eta squared (η²p)

What does a large η²p indicate in ANCOVA?

A substantial proportion of variance in the DV is accounted for by the IV after adjusting for the covariate.

How does covariate inclusion affect effect size interpretation?

It helps isolate the unique contribution of the IV to the DV.

What plot helps visualize the covariate's effect?

A scatterplot with regression lines for each group.

What output should you interpret in SPSS ANCOVA?

The adjusted means, covariate significance, IV significance, and effect sizes.

How do you test regression slope homogeneity in SPSS?

Include a group × covariate interaction and check if it’s statistically significant.

Why is slope homogeneity critical in ANCOVA?

Violated slopes mean covariate adjustments are not valid across groups.

What does a non-significant interaction imply? homogeneity

The regression slopes are equal — assumption met.

Can ANCOVA be used in mixed designs?

Yes, to adjust for covariates in designs with both repeated and independent factors.

What is a covariate in a mixed design?

A continuous variable that influences the DV across both repeated and between-group factors.

How are covariates applied in mixed models?

They can be used to control baseline or pre-test differences across all conditions.

What does a significant covariate mean?

The covariate significantly explains part of the variance in the DV.

When should you include a covariate?

When it is theoretically justified and strongly related to the DV.

What happens if the covariate is not linearly related to the DV?

The ANCOVA assumptions are violated; results may be biased.

What is over-adjustment in ANCOVA?

Including covariates that are consequences of the IV or unrelated to the DV.

What part of variance is adjusted by ANCOVA?

The portion explained by the covariate, removed from the error term.

What is the difference between adjusted and unadjusted means?

Adjusted means account for covariate influence; unadjusted do not.

What is the role of regression in ANCOVA?

Regression is used to estimate and control the influence of the covariate.

Can ANCOVA help with baseline imbalance in randomized trials?

Yes, by statistically equalizing groups on initial measures.

What does ANCOVA assume about covariates and IVs?

Covariates should not be affected by the IV; they must be independent.