Analysis of Covariance
(ANCOVA)

This experiment was suggested by Poitras-Martin, Danielle, & Steve, Gerald, L. (1977). Psychological education: A skills-oriented approach. Journal of Counseling Psychology, 24, 153-157. Data was taken from Roger E. Kirk's Experimental Design: Procedures for the Behavioral Sciences.

Example

Two approaches to learning problem-solving strategies were investigated. A total of 30 6th-grade students were randomly assigned to on of the two approaches and a control group (3 total groups). The first treatment condition (Treatment 1) involved participating in five sessions per week during three consecutive weeks with a mentor. The second treatment condition (Treatment 2) involved participating in involved watching films and working with a peer five sessions per week during three consecutive weeks. The same amount of time was required for both treatment group 1 and 2. The students in the control group did not receive any form of training. All students were measured on the associated thinking before the experimented started. At the conclusion of the experiment, five problem situations were presented, and the students were instructed to write down as many solutions to each one as they could. The dependent was the number of solutions proposed, summed across the five problems. The following data were obtained.

Treatment 1

 

Treatment 2

 

Control

Solutions

Associate Thinking

 

Solutions

Associate Thinking

 

Solutions

Associate Thinking

11

21

 

11

21

 

7

21

12

23

 

14

24

 

18

26

19

25

 

10

21

 

16

25

13

23

 

9

20

 

11

21

17

23

 

12

23

 

9

22

15

24

 

13

24

 

10

23

17

24

 

10

23

 

13

25

14

20

 

8

21

 

14

24

13

22

 

14

25

 

12

24

16

24

 

11

24

 

12

23

[Download Data]

Running SPSS

 

Testing for Assumption of Regression Lines

Go to the Model Option and select the Custom radio button. Then move each factor and covariate over to the right box. Finally build your interaction term (highlight both the factor and covariate terms) and move them over to the right side.

Output for Examining the Homogeneity of Regression Lines

 

Major Analysis

Go back to the Model Option and select the Full Factorial radio button.

Go to Options and select what options you would like to calculate. Don't forget to move the factor over into the right box (Display Means for:)--this gives you the adjusted means.

SPSS Output

 

You will need to run a Post Hoc. I suggest that you do all pairwise comparisons (3 analyses) using Bonferroni adjustment to protect against an inflated Type I error rate. I just use the Data option of Selecting Cases if .. command.

The following command selects groups 1 and 2 (ne=not equate)


Results

An analysis of covariance (ANCOVA) was used to examine differences between the two treatment groups and the control group on number of solutions after controlling for associative thinking. The data were screened for missing data, outliers, and normality. There were no missing data or outliers detected. The distribution appeared normally distributed.  The means and standard deviations for both the number of solutions and the associative thinking, and adjusted means are reported in the following table.

 

Solutions

 

Associative Thinking

 

 

 

Group

M

SD

 

M

SD

 

Adjusted M

Treatment  1

14.70

2.54

 

22.90

1.52

 

14.78

Treatment 2

11.20

2.04

 

22.60

1.71

 

11.67

Control

12.20

3.26

 

23.40

1.71

 

11.65

In a test of the interaction between the grouping conditions and the covariant (i.e., associative thinking), there was not a statistically significant interaction suggesting that the assumption of homogeneity of regression lines was tenable, F (1, 20) =.02,  p=.89. The assumption of equality of error variance was satisfied, F = 1.39,  p=.27. Results of the ANCOVA indicated that there was a statistically significant difference for the adjusted number of solutions means between the groups, F (1, 26) =11.73,  p<.001, partial eta squared = .47. Post hoc follow up analyses examining all pairwise comparisons using a Bonferroni adjustment suggested that treatment 1 was higher than both treatment group 2 (F = 19.47,  p<.001) and the control group (F = 15.25,  p=.001). There was not a difference between treatment group 2 and the control group (F = .007,  p=.93).

Summary

The results suggest that working with a mentor for five weeks will have a significant impact on problem-solving skills.