Question

9. Sum of Squares for the Difference Scores

A new form of cognitive therapy has been developed to treat the symptoms of depression. To determine the effectiveness of the treatment, depression scores were measured twice for each person in the sample - once before the therapy began (Pretest) and once after the therapy was completed (Posttest). The values below represent the Beck Depression Inventory scores for the two measurements (higher scores indicate higher levels of depression). Note that each row represents the two measurements from an individual.

IMPORTANT: In the computation of difference scores, please use the Posttest as your set of X2 values and the Pretest as your set of X1 values.

Pretest Posttest

26--------15

19--------17

26--------27

31--------30

15--------13

23--------20

24--------24

30--------31

17--------16

21--------19

26--------28

23--------20

26--------27

30--------28

18--------12

23--------22

26--------23

19--------15

29--------27

32--------33

20--------19

26--------25

32--------27

20--------15

26--------23

17--------18

27--------22

20--------20

What is the sum of squared deviations for the difference scores?

Answer 1

Pretest (X1)	Posttest(X2)	X1- X2	(X1- X2)2
26	15	11	121
19	17	2	4
26	27	-1	1
31	30	1	1
15	13	2	4
23	20	3	9
24	24	0	0
30	31	-1	1
17	16	1	1
21	19	2	4
26	28	-2	4
23	20	3	9
26	27	-1	1
30	28	2	4
18	12	6	36
23	22	1	1
26	23	3	9
19	15	4	16
29	27	2	4
32	33	-1	1
20	19	1	1
26	25	1	1
32	27	5	25
20	15	5	25
26	23	3	9
17	18	-1	1
27	22	5	25
20	20	0	0
		Total	318

Here

The sum of squared deviations for the difference scores is 318.