Percentile Ranks for the Number of Digits Recalled Forward and Backward on the Wechsler Intelligence Scale for Children

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Percentile Ranks for the Number of Digits Recalled Forward and Backward on the Wechsler Intelligence Scale for Children, 4^th ed. (WISC-IV®) Derived from Data Presented in Table B.7, p. 267, Wechsler Intelligence Scale for Children 4^th ed.

John O. Willis Susan Morbey Ron P. Dumont

Rivier College Amherst, NH Fairleigh Dickinson University

Hale, Hoeppner, & Fiorello (2002) demonstrated the importance of separately examining data for digits repeated forward and digits repeated backward, and The Psychological Corporation has greatly increased the utility of the WISC-IV® Digit Span subtest by providing supplemental scaled scores for raw scores for Digits Forward and for Digits Backward (Wechsler, 2003, pp. 242-252). However, the raw scores upon which these scaled scores are based reflect both the number of digits recall forward and backward and the consistency with which the digits are recalled. The raw scores are based on 1- or 0-point scores for each of two trials for each length of digit span. Therefore, two children who both recalled, for example, five digits forward could have raw scores as different as 4 and 8 points if one child passed only one of the two trials for each length of digit span and the other consistently passed both trials.

The WISC-IV Manual (Wechsler, 2003, pp. 267) does provide "Cumulative Percentages of Standardization Sample (Base Rates) Obtaining Various Raw scores for Longest Digit Span Forward and Longest Digit Span Backward, by Age Group." Those data are based solely on the number of digits in the longest span recalled correctly, without regard to whether the child passed one or both trials at each length of span. The base rate data are useful, but somewhat cumbersome to report and explain in an evaluation report. Consequently, we have converted the WISC-IV® base-rate data for the number of digits recalled in the longest span recalled forward and the longest span recalled backward by the examinee (Wechsler, 2003, pp. 267) to percentile ranks, percentile ranges, and stanines. We have done this by first listing the cumulative percentages in reversed order, then calculating the percent of children for each length of digit span, and finally adding one-half of that percentage to the cumulative percentage for all shorter spans. These results, presented in the tables below (barring any arithmetic errors we may have made), are the same data presented in Table B.7 of the WISC-IV® Manual (Wechsler, 2003, pp. 267); they are simply presented as percentile ranks rather than base rates. We also converted the percentile ranks into equal-interval measures, found the midpoints between scores, and converted those back to percentile ranks to provide a range of percentile ranks for each length of digit span.

	Age 10	Forward	Percentile Rank	Percentile Range	Stanine
The first column lists the number of digits in	Span	Cum %	Percentile Rank	Percentile Range	Stanine
the longest span recall by the examinee. For example,	9	2.0	99	98 - 99	9
2 – 9 – 1 would be a span of 3 digits and 4 – 9 – 3 – 1	8	9.0	95	90 - 97	8
would be a span of 4 digits. The second column is the	7	33.5	79	68 - 88	7
cumulative percentage of children in the WISC-IV®	6	60.5	53	39 - 67	5
norming sample who recalled at least that many digits	5	83.0	28	18 - 39	4
(Table B.7 of the WISC-IV® Manual (Wechsler, 2003,	4	99.0	09	01 - 17	2
pp. 267). The final three columns give the percentile	3	100.0	01	01	1
rank, approximate range of percentile ranks, and stanine	2	100.0	0	01	1
for recalling at least that number of digits.	0	100.0	0	01	1

These spans are the number of digits recalled in the longest span recalled correctly: Table B.7 in the WISC-IV® Manual (Wechsler, 2003, p. 267), and in the "Process Analysis Total Raw Score to Base Rate Conversion" box in the lower right part of p. 2 of the WISC-IV® Record form (©The Psychological Corporation, 2003). These spans are the number of digits in the longest span recalled forward [(LDSF), maximum of 9] and backward [(LDSB) maximum of 8]. These data may be particularly useful if the Discrepancy Comparison between LDSF and LDSB (Table B.8 in the WISC-IV® Manual, Wechsler, 2003, p. 268) reveals a low base rate.

****** These are not the raw scores (points earned) used in Table A.8 in the WISC-IV® Manual (Wechsler, 2003, pp. 242-252), and in the "Process Analysis Total Raw Score to Scaled Score Conversion" box in the lower left part of p. 2 of the WISC-IV® Record form (©The Psychological Corporation, 2003). Those raw scores [maximum of 16 points forward (DSF), maximum of 16 points backward (DSB), total raw score maximum of 32 points] are based on the sums of 2s, 1s, and 0s. Those can be converted to scaled scores using Table A.8 in the WISC-IV® Manual (Wechsler, 2003, pp. 242-252).

Hale, J. B., Hoeppner, J. B., & Fiorello, C. A. (2002). Analyzing Digit Span components to assessment of attention processes. Journal of Psychoeducational Assessment, 20 (2), 128-143.

Kaplan, E., Fein, D., Kramer, J, Delis, D., & Morris, R. (1999). The WISC-III as a Process Instrument. San Antonio, TX: The Psychological Corporation. (WISC-III PI)

Wechsler, D. (2003). Wechsler Intelligence Scale for Children (4th ed.). San Antonio, TX: The Psychological Corporation. (WISC-IV)

The scaled score data in Table A.8 (Wechsler, 2003, pp. 242-252) reflect both memory span and consistency. The data below, derived from Table B.7 in the WISC-IV® Manual (Wechsler, 2003, p. 267) reflect only the span.

Age 6	Forward	Percentile Rank	Percentile Range	Stanine	Age 6	Backward	Percentile Rank	Percentile Range	Stanine
Span	Cum %	Percentile Rank	Percentile Range	Stanine	Span	Cum %	Percentile Rank	Percentile Range	Stanine
9	0.0	100	99	9
8	0.5	100	99	9	8	0.0	100	99	9
7	2.0	99	95 - 99	9	7	0.0	100	99	9
6	23.5	87	76 - 95	7	6	0.0	100	99	9
5	55.0	61	44 - 75	6	5	0.5	100	99	9
4	91.0	27	13 - 43	4	4	11.0	94	84 - 98	8
3	98.5	5	02 - 12	2	3	59.0	65	44 - 83	6
2	99.5	1	02	1	2	96.0	23	08 - 43	4
0	100.0	0	01	1	0	100.0	02	07	1

Age 7	Forward	Percentile Rank	Percentile Range	Stanine	Age 7	Backward	Percentile Rank	Percentile Range	Stanine
Span	Cum %	Percentile Rank	Percentile Range	Stanine	Span	Cum %	Percentile Rank	Percentile Range	Stanine
9	0.0	100	99	9
8	1.5	99	99	9	8	0.0	100	99	9
7	6.5	96	92 - 98	9	7	0.0	100	99	9
6	28.5	83	70 - 91	7	6	0.0	100	99	9
5	60.5	56	36 - 69	5	5	2.5	99	96 - 99	9
4	96.0	22	08 - 35	3	4	29.0	84	69 - 95	7
3	100.0	02	01 - 07	1	3	76.0	48	29 - 68	5
2	100.0	0	01	1	2	97.5	13	04 - 28	3
0	100.0	0	01	1	0	100.0	01	01 - 03	1

Age 8	Forward	Percentile Rank	Percentile Range	Stanine	Age 8	Backward	Percentile Rank	Percentile Range	Stanine
Span	Cum %	Percentile Rank	Percentile Range	Stanine	Span	Cum %	Percentile Rank	Percentile Range	Stanine
9	0.0	100	99	9
8	1.5	99	97 - 99	9	8	0.0	100	99	9
7	12.0	93	87 - 96	8	7	0.0	100	99	9
6	39.0	75	60 - 86	6	6	0.0	100	99	9
5	75.5	43	26 - 59	5	5	5.5	97	91 - 99	9
4	97.5	14	04 - 25	3	4	42.0	76	57 - 90	6
3	100.0	01	01 - 03	1	3	87.5	35	19 - 56	4
2	100.0	0	01	1	2	99.0	07	02 - 18	2
0	100.0	0	01	1	0	100.0	01	01

Age 9	Forward	Percentile Rank	Percentile Range	Stanine	Age 9	Backward	Percentile Rank	Percentile Range	Stanine
Span	Cum %	Percentile Rank	Percentile Range	Stanine	Span	Cum %	Percentile Rank	Percentile Range	Stanine
9	1.0	100	99	9
8	6.5	96	92 – 99	8	8	0.5	100	99	9
7	28.5	83	72 – 91	7	7	0.5	100	99	9
6	54.0	59	44 – 71	5	6	5.0	97	95 - 98	9
5	79.5	33	19 – 43	4	5	15.5	90	81 - 94	8
4	98.5	11	04 –18	2	4	58.5	63	44 - 80	6
3	100.0	01	03	1	3	92.0	25	13 - 43	4
2	100.0	0	01 – 03	1	2	98.5	05	02 - 12	2
0	100.0	0	01	1	0	100.0	01	01	1

Age 10	Forward	Percentile Rank	Percentile Range	Stanine	Age 10	Backward	Percentile Rank	Percentile Range	Stanine
Span	Cum %	Percentile Rank	Percentile Range	Stanine	Span	Cum %	Percentile Rank	Percentile Range	Stanine
9	2.0	99	98 - 99	9
8	9.0	95	90 - 97	8	8	0.0	100	99	9
7	33.5	79	68 - 88	7	7	1.0	100	99	9
6	60.5	53	39 - 67	5	6	7.0	96	92 - 98	9
5	83.0	28	18 - 39	4	5	26.0	84	72 - 91	7
4	99.0	09	01 - 17	2	4	64.5	55	36 - 71	5
3	100.0	01	01	1	3	94.5	21	09 - 35	3
2	100.0	0	01	1	2	99.0	03	01 - 08	1
0	100.0	0	01	1	0	100.0	01	01	1

Age 11	Forward	Percentile Rank	Percentile Range	Stanine	Age 11	Backward	Percentile Rank	Percentile Range	Stanine
Span	Cum %	Percentile Rank	Percentile Range	Stanine	Span	Cum %	Percentile Rank	Percentile Range	Stanine
9	2.0	99	98	9
8	6.0	94	82 - 97	8	8	1.0	100	99	9
7	27.5	57	46 - 81	5	7	3.0	98	97 - 99	9
6	63.0	32	23 - 45	4	6	9.0	94	90 - 96	8
5	87.0	13	08 - 22	3	5	29.5	81	67 - 89	7
4	99.5	04	01 - 07	1	4	72.0	49	34 - 66	5
3	100.0	0	01	1	3	94.0	17	10 - 32	3
2	100.0	0	01	1	2	99.0	04	02 - 09	1
0	100.0	0	01	1	0	100.0	01	01	1

Age 12	Forward	Percentile Rank	Percentile Range	Stanine	Age 12	Backward	Percentile Rank	Percentile Range	Stanine
Span	Cum %	Percentile Rank	Percentile Range	Stanine	Span	Cum %	Percentile Rank	Percentile Range	Stanine
9	2.0	99	98	9
8	8.5	95	90 - 97	8	8	1.50	99	99	9
7	37.5	77	65 - 89	6	7	5.00	97	95 - 97	9
6	68.0	47	34 - 64	5	6	12.00	92	87 - 94	8
5	90.5	21	13 - 33	3	5	36.50	76	65 - 86	6
4	99.0	05	02- 12	2	4	70.00	47	34 - 64	4
3	100.0	01	01	1	3	92.50	19	10 - 33	3
2	100.0	0	01	1	2	99.50	04	01 - 09	2
0	100.0	0	01	1	0	100.00	01	01	1

Age 13	Forward	Percentile Rank	Percentile Range	Stanine	Age 13	Backward	Percentile Rank	Percentile Range	Stanine
Span	Cum %	Percentile Rank	Percentile Range	Stanine	Span	Cum %	Percentile Rank	Percentile Range	Stanine
9	3.5	98	96	9
8	14.5	91	84 - 96	8	8	1.0	99	99	9
7	47.0	69	58 - 82	6	7	7.0	96	94 - 98	9
6	75.5	39	25 - 55	4	6	19.5	87	81 - 93	7
5	94.0	15	07 - 24	3	5	41.5	70	57 - 80	6
4	99.5	03	01 - 06	1	4	78.5	40	25 - 56	5
3	100.0	01	01	1	3	97.5	12	06 - 24	3
2	100.0	01	01	1	2	99.5	02	01 - 05	1
0	100.0	01	01	1	0	100.0	01	01	1

Age 14	Forward	Percentile Rank	Percentile Range	Stanine	Age 14	Backward	Percentile Rank	Percentile Range	Stanine
Span	Cum %	Percentile Rank	Percentile Range	Stanine	Span	Cum %	Percentile Rank	Percentile Range	Stanine
9	3.5	98	96	9
8	15.5	91	84 - 95	8	8	0.5	100	99	9
7	45.0	70	57 - 83	6	7	7.0	96	94 -98	9
6	73.0	41	30 - 56	5	6	19.0	87	81 - 93	7
5	90.0	19	13 - 27	3	5	42.0	70	57 - 80	6
4	99.0	06	03 - 12	2	4	76.5	41	27 - 56	5
3	100.0	01	01 - 02	1	3	96.5	14	06 - 26	3
2	100.0	0	01	1	2	100.0	02	01 - 05	1
0	100.0	0	01	1	0	100.0	0	01	1

Age 15	Forward	Percentile Rank	Percentile Range	Stanine	Age 15	Backward	Percentile Rank	Percentile Range	Stanine
Span	Cum %	Percentile Rank	Percentile Range	Stanine	Span	Cum %	Percentile Rank	Percentile Range	Stanine
9	6.0	97	95 - 99	9
8	19.0	88	79 - 94	7	8	2.0	99	98 - 99	9
7	56.5	62	47 - 78	6	7	10.5	94	88 - 97	8
6	81.0	31	19 - 46	4	6	31.0	79	70 - 87	7
5	96.5	11	06 - 18	3	5	53.0	58	44 - 69	5
4	100.0	02	01 - 05	1	4	82.0	33	19 - 43	4
3	100.0	0	01	1	3	98.0	10	03 - 18	2
2	100.0	0	01	1	2	100.0	01	01 - 02	1
0	100.0	0	01	1	0	100.0	0	01	1

Age 16	Forward	Percentile Rank	Percentile Range	Stanine	Age 16	Backward	Percentile Rank	Percentile Range	Stanine
Span	Cum %	Percentile Rank	Percentile Range	Stanine	Span	Cum %	Percentile Rank	Percentile Range	Stanine
9	10.5	95	91 - 99	8
8	25.0	82	72 - 90	7	8	2.5	99	97 - 99	9
7	61.0	57	41 - 71	5	7	11.5	93	88 - 96	8
6	82.5	28	19 - 40	4	6	25.5	82	75 - 87	7
5	95.5	11	06 - 18	3	5	46.0	64	49 - 74	6
4	99.0	03	02 - 05	1	4	82.0	36	21 - 48	4
3	100.0	01	01	1	3	98.0	10	04 - 20	2
2	100.0	0	01	1	2	100.0	01	01 - 03	1
0	100.0	0	01	1	0	100.0	0	01	1

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