ANCOVA

Question 1

What are possible consequences of including covariates related to the dependent variable in the analysis?

Answer 1

1. reduction of bias.

2. reduction of error variance.

Question 2

What is the hypothesis of an ANCOVA analysis?

Answer 2

H0: uk = u for every k; H1 not H0.

Question 3

What is the syntax for an ANCOVA analysis?

Answer 3

UNIANOVA Y BY A with X 
/METHOD = SSTYPE(3)
/INTERCEPT = INCLUDE
/EMMEANS = TABLES(A) WITH (X=MEAN)
/PRINT = ETASQ DESCIPTIVE PARAMETER HOMOGENEITY 
/CRITERIA = ALPHA (0.05) 
/DESIGN = X A

Question 4

What is the linear formula for an ANCOVA?

Answer 4

Yi2 = uy + a’2 + bw (Xi2 - ux) + e

Question 5

What are the assumptions for the ANCOVA?

Answer 5

the same assumptions as ANOVA but

4. covariate measured before experimental manipulation.
5. covariate measured without measurement error.
6. relation between X and Y is linear.
7. no interaction between X and A (homogeneity of regression slopes).

Question 6

What is the syntax for testing regression slopes?

Answer 6

UNIANOVA Y BY A with X 
/METHOD = SSTYPE(3) 
/INTERCEPT = INCLUDE 
/EMMEANS = TABLES(A) WITH (X=MEAN) 
/PRINT = ETASQ PARAMETER HOMOGENEITY 
/CRITERIA = ALPHA (0.05) 
/DESIGN = A X A*X