Week 9: ANCOVA

Question 1

• What does ANCOVA stand for? What is a covariate? What is an extraneous variable?

Answer 1

ANCOVA = Analysis of Covariance
*An extension of ANOVA except when you compare groups, you take into account a covariate

Covariate = an extraneous variable (also referred to as a control or confounding variable)

Extraneous Variable = something you do not manipulate but can have an effect on your outcome (DV)

Question 2

• What do the numerator and denominator of an F ratio represent?

Answer 2

Variance between groups (mean square between)
F = ______________________________________
Variance within groups (mean square error)

Another way to look at it

  Signal       Variance explained by manipulation F = \_\_\_\_\_\_ = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
 Noise         Variance unexplained by manipulation

Question 3

• Why is a covariate important?

What influence does a covariate have?

Answer 3

Reduces the likelihood of Type II Error (finding no significant difference when there is a difference)

Reduces noise (a covariate controls an extraneous variable and helps make the manipulation of IV clear)
- adjusts the means of your IV based on the effects of covariate

Question 4

• IV, DV, and covariate: categorical or continuous?

Answer 4

Independent Variable = categorical

Dependent Variable = continuous

Covariate = continuous

Question 5

• What is the goal of an ANCOVA?

Answer 5

To reduce as much error (noise) with your covariate so that the manipulation of IV is more clear

Question 6

• What are the assumptions of an ANCOVA?

Answer 6

Independent observations
Normal distributions of DV
Homogeneity of Variance of DV - an important assumption- must be tested first

Question 7

• Why is the homogeneity of regression slopes an important assumption?

Answer 7

Homo (same) genetic (kind) of regression slopes assumption tells us if the relationship of your DV and covariate are the same in each group of the IV

If DV and covariate are not similar for each group (i.e. they do not have similar regression slopes), you violate the assumption.

Question 8

• What is an interaction?

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What happens when the interaction of your covariate and DV is p .05?

Answer 8

Interaction = relationship between 2 variables

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If f-test shows significant interaction (p .05) you do NOT violate homogeneity of regression of slopes
(The Same because it is not significantly different)

Question 9

• What does it mean when your homogeneity of regression slopes is violated? What error does it increase?

Answer 9

if homogeneity of regression slope is present, you can continue using ANCOVA

Do NOT use ANCOVA if homogeneity of regression slopes is violated - use ANOVA instead without using covariate

• covariate may not influence DV
• this violation can bias results increasing Type I error (finding a significant difference when in actuality there is no difference)

Question 10

• When should you continue to perform an ANCOVA?

Answer 10

if there is homogeneity of regression of slopes, determine whether groups in your IV are significantly different.
if so, do a Post Hoc Test for your IV