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Steps in Creating Short Forms of IQ Tests 

(Quick, Dirty, and Not Recommended)

In order to develop the statistics for a short form, the reliability coefficient and intercorrelation of each subtest must be determined.

Step 1: Choose a Short Form

Create a table that lists the reliability of each chosen subtest along with the correlation matrix for those same subtests. For example, suppose you want a five-subtest short form for the WISC-III that uses Information (I), Vocabulary (V), Picture Completion (PC), Coding (Cd), and Block Design (BD) [the short form developed by Dumont and Faro]. The table below was created adapting information provided in the WISC-III manual. (The relevant columns are numbered 1 through 6 and the relevant rows are lettered A through F.)


1

2
3
4
5
6

r

A
.84
I
I
V
PC
Cd

B
.87
V
.70

C
.77
PC
.47
.45

D
.79
Cd
.21
.26
.18

E
.87
BD
.48
.46
.52
.27

F
4.14

1.86
1.17
.70
.27
4.00

Step 2: Determine the Sum of Reliabilities

Add the reliabilities in column 1 (rows A through E) to obtain the sum of the reliabilities. In this case the sum is equal to 4.14 (Column 1, row F).

Step 3: Determine the Sum of Intercorrelations

Add all of the intercorrelations. In this case they are equal to 4.00 (Column 6, row F).

Step 4: Determine the Multiplier and Additive

Using the number obtained in Step 3, obtain the Multiplier and the Additive for your subtest combinations from the appropriate tables linked below.

Table for Two-subtest short form

Table for Three-subtest short form

Table for Four-subtest short form

Table for Five-subtest short form

In the example above, we are making a five-subtest short form, so I would go to the Table for Five-subtest short form and look up the numbers associated with the value of 4.00. I find the correct Multiplier and Additive in the section that looks like:

3.79-3.96
1.4
30
3.97-4.15
1.4
31
4.16-4.35
1.4
32
4.36-4.56
1.3
35

The numbers are 1.4 and 31. To determine a deviation quotient for the proposed short form, add together the subtest scaled scores, multiply that sum by 1.4, and finally add 31 to the product.

In our example, substituting subtest scaled scores, the five subtests Short form would be:

(I+V+PC+Cd+BD)*1.4+31

(10+9+10+10+5)*1.4+31

(44)*1.4+31

61.6+31

Deviation Quotient = 92.6

 

Step 5: Determine the reliability of the short form by using the following formula

Reliability=

Sum of reliabilities + 2 (Sum of Intercorrelations) Number of Subtests + 2 (Sum of Intercorrelations)

For our example the reliability would be:

4.41 + 2(4.0) 5 + 2(4.0)
The reliability is .93.

Step 6: Determine the Standard Error of Measurement

Standard error of Measurement = Confidence level * Standard Deviation * Square Root (1-Reliability)

Confidence levels:

1.64 = 90% 1.96 = 95%
For our example:
1.96*15*Sqrt(1-.93) SEm=7.6

 


• Dumont, R. & Faro, C. (1993) WISC-III Short Form for Learning Disabled Children. Psychology in the Schools., 30, 212-219