3. (10 points)

Thirty Children are each randomly assigned to one of three remedial math skills training programs. Before entering the program, each child takes a standardized pretest (X). At the end of six months, a standardized achievement test (Y) is given to each of the children. The researchers wish to determine whether the training programs are equally effective or not. The data are presented below. In the column under Group; 1= Group1, 2=Group 2, 3=Group 3. In the column under Block is the pretest score and under the Column Y is the posttest score given after the remedial math program has been completed.

Group Block Y

1.00 29.00 61.00

1.00 37.00 73.00

1.00 26.00 54.00

1.00 32.00 63.00

1.00 31.00 62.00

1.00 37.00 76.00

1.00 39.00 72.00

1.00 39.00 80.00

1.00 33.00 73.00

1.00 36.00 72.00

2.00 39.00 79.00

2.00 34.00 66.00

2.00 34.00 76.00

2.00 39.00 84.00

2.00 36.00 73.00

2.00 39.00 75.00

2.00 34.00 66.00

2.00 29.00 85.00

2.00 34.00 62.00

2.00 26.00 79.00

3.00 41.00 78.00

3.00 36.00 66.00

3.00 29.00 56.00

3.00 33.00 61.00

3.00 42.00 70.00

3.00 33.00 65.00

3.00 32.00 59.00

3.00 42.00 80.00

3.00 39.00 65.00

3.00 36.00 64.00

1. Did running the analysis of covariance increase the precision/power of the experiment (hint examine MSerrors)