The Accuracy of the Abbreviated Stanford-Binet Intelligence Scale
- Author:
Fowler D. Brooks, Assistant Professor of Education,
Johns Hopkins University
Whenever it is impassible or impracticable to give all the tests of the Stanford-Binet at each age level tested, an abbreviated scale, formed by omitting two tests at each age, may be used.1
How accurate is this abbreviated scale? One way of answering this question is to compare individuals’ IQ’s on the complete scale with their IQ’s derived by considering only the starred tests. This procedure involves, of course, the assumption that an individual taking the complete scale would have the same “passes” and “failures” on the starred tests as he would have had, if he had been given only the starred tests. We do not know how much error is involved in this assumption, but we are inclined to believe that it is not significant. We doubt if any appreciable suggestion or incentive comes from the unstarred tests which would enable the ‘’ examinee ” to do better on the starred ones. Any difference in accuracy of the long form over the abbreviated form is probably due to the relative general difficulty of the starred and unstarred tests. At any rate, our procedure is subject to error to the extent that this assumption does not hold.
We have data from 575 individuals, chronological ages 6 to 17 years inclusive, who were given the Stanford-Binet scale. Their record blanks were then rescored, the two unstarred tests being omitted and the starred ones being given the appropriate values. The two sets of IQ’s were then compared.
The group as a whole is below normal, the average IQ being 90. The IQ’s of the older children are less than those of the younger ones, as may be seen in Table I, the average IQ’s being 96 at ages 6 to 11, and 83 at ages 12 to 17. Furthermore, the distributions at the younger ages are skewed at the higher IQ’s, at the middle ages are normal, and at the older ages are skewed at the lower IQ’s. The distribution for the entire group shows an undue proportion of lower IQ’s being in distinct contrast with that given by Terman for 905 unselected children, ages 5 to 14 years.
1 Each test of the abbreviated scale is indicated on the record booklets by an asterisk.
Table I MEANS AND STANDARD DEVIATIONS OF STANFORD BINET IQ’S OF PUPILS OF EACH AGE GROUP FROM SIX TO SEVENTEEN YEARS. Age Number of Mean IQ S.D.
Cases 6 13 107.1 16.8 7 50 99.0 12.8 8 60 97.1 16.6 9 69 95.2 19.2 10 47 88.4 14.1 11 69 95.4 21.0 12 55 87.4 17.9 13 67 84.4 17.7 14 54 82.2 12.9 15 33 78.5 16.5 16 45 79.4 15.5 17 13 79.3 17.6 Total 575 89.7 18.7
Our results show that the abbreviated scale is very accurate, that IQ’s from it are from 2 to 4 points less accurate than those from the complete form, and that the median short-form IQ is less than that on the complete form. These facts are shown in Tables II and III from which it appears that abbreviated IQ’s differ from the complete-form IQ’s by amounts varying from ?33 to +31 points, the twenty-five percentiles of the differences range from
Table II THE RANGE, THE FIRST, SECOND, AND THIRD QUARTILIES, AND THE Q OF THE DIFFERENCES BETWEEN IQ’S ON THE STANFORD BINET AND ABBREVIATED STANFORD BINET SCALES Differences between Stanford-Binet IQ’S and IQ’S on Abbreviated StanfordBinet Scale Age N Range Qx Qa Q Median 6 13 ?21 to 31 ?1.75 .50 2.63 ?2.50 7 50 ?16 to 10 ?3.79 .80 2.30 ?2.25 8 60 ?33 to 7 ?5.25 2.00 3.63 ?2.29 9 69 ?18 to 13 ?3.79 1.96 2.88 ?1.64 10 47 ?17 to 14 ?3.31 2.85 3.08 ? .30 11 69 ?10 to 10 ?3.44 1.31 2.38 ?1.69 12 55 ?15 to 4 ?4.87 1.28 3.08 ?2.64 13 67 ? 9 to 5 ?3.54 1.75 2.65 ? .83 14 54 ? 8 to 9 ?4.87 1.10 2.99 ?3.00 15 33 ?13 to 3 ?3.58 .75 2.17 ?1.36 16 45 ?14 to 8 ?4.92 .88 2.90 ?2.17 17 13 ? 7 to 3 ?6.37 .92 3.65 ?1.50 12 13
around ?6 to ?3 points and the seventy-five percentiles from .5 to nearly 3 points. Considering signs, the range of the middle fifty per cent of the differences is from 4 to 7 points of IQ; hut disregarding signs it is from 2!/2 to 6 points.
Table III the range, the first, second, and third quartiles, and THE Q OF THE DIFFERENCES BETWEEN IQ’S ON THE STANFORD BINET AND ABBREVIATED STANFORD BINET SCALES?DISREGARDING SIGNS Differences ?Age N Median Qi Q? Q 6 13 3.50 1.75 7.75 3.00 7 50 4.00 1.94 5.63 1.85 8 60 3.50 2.15 5.60 1.73 9 69 3.43 1.79 4.75 1.48 10 47 3.05 1.25 4.21 1.48 11 69 2.50 1.43 4.72 1.65 55 3.17 1.81 4.89 1.54 67 2.63 1.60 4.41 1.41 14 54 3.46 1.77 5.38 1.81 15 33 2.41 1.28 3.71 1.22 16 45 3.46 1.73 5.94 2,11 17 13 2.50 1.08 6.38 2.65
The relative standings of individuals on the abbreviated scale are essentially the same as on the complete scale, the ten correlations between “long?” and “short-form” IQ’s at all ages from 7 to 16 being uniformly high and positive, ranging from .93 to .98 and averaging .96 (See Table IV).
Table IV CORRELATION BETWEEN IQ’S FROM STANFORD BINET AND ABBREVIATED STANFORD BINET SCALES ?Age N Pearson r 7 50 .931 8 60 .930 9 69 .965 10 47 .962 11 69 .984 12 55 .976 13 67 .977 14 54 .971 15 33 .966 16 45 .946
Is the magnitude of the differences in IQ on the two scales related to the degree of intelligence? Are the IQ’s of the brighter, average, or duller individuals affected most by the omission of two tests at each age? The correlations (Table V) give some evidence that the omitted tests have greater effect upon the IQ’s of the brighter pupils than upon those of the duller ones since the average of the coefficients is .35.
Table V CORRELATION BETWEEN IQ AND THE AMOUNT OF DIFFERENCE BETWEEN STANFORD BINET AND ABBREVIATED STANFORD BINET IQ’S Age N Pearson r 7 50 .097 8 60 .311 9 69 .150 10 47 .443 11 69 .460 12 55 .501 13 67 .044 14 54 .413 15 33 .601 16 45 .453 Mean .347
Conclusions. Our data on 575 individuals indicate the following : 1. The abbreviated Stanford-Binet scale gives IQ’s from 2 to 4 points less accurate than those from the complete scale. 2. Abbreviated IQ’s average somewhat less than those from the complete scale.
3. Individuals’ relative standings (or ranks) are nearly the same on both scales the average of the correlations computed for each chronological age from seven to sixteen years being .96.
4. There is a slight tendency for the abbreviated scale to be less accurate with the brighter individuals, the average correlations of IQ with differences between “long?” and “short-form” IQ’s being .35.
5. Accordingly the abbreviated scale is almost as accurate as the complete scale, whether it be used to determine an individual’s IQ or the relative mental standings of a group.
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