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Differential Ability Scales (DAS)


Confidence Intervals

The DAS face sheet offers a good opportunity to record scores as confidence bands rather than as single points. The small cross bars on the vertical lines under the subtests and clusters make it easy to mark off precise score ranges. For the cluster scores and GCA or Special Nonverbal Composite, the confidence band is already provided when you look up the score, so all that is needed is an X or heavy cross bar at the score, smaller cross bars at the ends of the confidence interval, and a heavy, vertical line between the smaller cross bars as shown in Figure 1.

Figure 1.

For individual subtests, the process requires an extra step to compute the confidence interval. When you look up the Ability Score for the student’s raw score, you find the Standard Error of Measurement (SEm) or 68% confidence interval in parentheses to the right of the Ability Score. Multiply the SEm by 1.65 (1 2/3) for a 90% confidence interval or by 1.96 (2) for a 95% confidence band. In the example in Figure 2, a Raw Score of 4 on Item Set 4-16 yields an Ability Score of 60 with an SEm of 6. The 90% confidence band for an SEm of 6 is 10 [1.65 x 6 = 9.90 » 10 or 1 2/3 x 6 = 6 12/3 = 10]. The 95% confidence band for the SEm of 6 is 12 [1.96 x 6 = 11.76 » 12 or 2 x 6 = 12.]

Figure 2.

When you look up the T score for the Ability Score, also look up the T score for the Ability Score minus the confidence interval and the T score for the Ability Score plus the confidence interval. In our example, you would look up the T Scores for 60 and for 60 ± 10 or for 50, 60, and 70. You would make an X at 60, draw cross bars at 50 and 70, and draw a heavy, vertical line between the cross bars. For the examiner’s convenience, Table 9 shows 90% and 95% confidence intervals for SEm values from 1 through 20.

 

Table 9   90% & 95% Confidence Intervals

Confidence Intervals

SEm

90%

95%

1

2

2

2

3

4

3

5

6

4

7

8

5

8

10

6

10

12

7

12

14

8

13

16

9

15

18

10

17

20

11

18

22

12

20

24

13

22

26

14

23

28

15

25

30

16

27

32

17

28

34

18

30

36

19

32

38

20

33

40

A "psychograph" (Wechsler's term) with 90% or 95% confidence bands encourages both examiner and reader to think of scores as intervals, not as single points. The confidence bands reinforce the requirements not to interpret insignificant differences between test scores and to be sure to pay attention to significant differences between scores.

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