Serial 7s and Alphabet Backwards as Brief Measures of Information Processing Speed

Pergamon Archives of Clinical Neuropsychology, Vol. 11, No. 8, pp. 651-659, 1996 Copyright 9 1996 National Academy of Neuropsychology Printed in the USA. All fights reserved 0887-6177/96 $15.00 +.00 PH S0887-6177(96)00004-2 Serial 7s and Alphabet Backwards as Brief Measures of Information Processing Speed Mark A. Williams, Judith A. LaMarche, Ronald W. Alexander, Lisa D. Stanford, Elliot M. Fielstein, and Thomas J. Boll University of Alabama at Birmingham The construct and discriminant validity of Serial 7s and Alphabet Backwards as measures of information processing speed were examined. In Study 1, seven commonly used speeded neuropsychological measures, including Serial 7s and Alphabet Backwards, were subjected to factor analysis. Two factors emerged. Factor 1 was labeled visual-motor scanning speed. Factor 2 was labeled information processing speed and included Serial 7s and Alphabet Backwards. Study 2 compared 42 cardiac transplant candidates and 46 age, education, and IQ matched college student controls on Serial 7s and Alphabet Backwards. The cardiac patients were significantly slower on both Serial 7s and Alphabet Backwards but did not make more errors. These results suggest that Serial 7s and Alphabet Backwards can be used as brief and technically simple measures of information processing speed. Copyright 9 1996 National Academy of Neuropsychology The Serial 7s subtraction test and spelling words backwards (e.g., WORLD) have been widely used in the past as part of standard mental status examinations (e.g., Folstein, Folstein, & McHugh, 1975). Within this context, the patient's ability to complete these tasks and the number of errors made, have been the primary measures of interest. Using this approach, these tests have been useful in screening for dementia (Treves, Ragolsky- Gelernter, & Karczyn, 1990). More recently, serial subtraction tests and other reversed recitation procedures (e.g., saying the alphabet backward) have been included in neuropsychological test batteries as putative measures of complex attention and speed of information processing (e.g., LaMarche et al., 1994; Shum, McFarland, & Bain, 1990). Within this context, the time required to complete these tasks is the primary performance measure. Used as tests of information processing speed, Serial 7s and Alphabet Backwards may provide a brief alternative to other tests of information processing speed such as the Paced Auditory Serial Addition Test (PASAT; Gronwall & Sampson, 1974). The administration of Serial 7s and Alphabet Backwards requires no special equipment and takes relatively little time to administer. Therefore, these procedures lend themselves to being useful for the evaluation Address correspondence to: Mark A. Williams, Neuropsychology Laboratory, University of Alabama at Birmingham, 1521 1 lth Avenue South, Birmingham, Alabama 35294-4551. 651

652 M. A. Williams et al. of patients in various settings where testing equipment is not available or when extensive evaluation is not practical. Despite the common use of Serial 7s and Alphabet Backwards procedures as measures of information processing speed, the validity of these clinical procedures has not been adequately demonstrated. The present investigation was designed to examine the construct and discriminant validity of Serial 7s and Alphabet Backwards as measures of information processing speed. The first study used factor analysis to examine the relationship of Serial 7s and Alphabet Backwards to other timed tests that require speeded performance. The subjects were a heterogenous group of adult patients referred for neuropsychological evaluation. The second study evaluated the discriminant validity of Serial 7s and Alphabet Backwards by comparing the performance of a group of patients undergoing a comprehensive evaluation for heart transplantation to a group of college student controls. Studies have reported that as a group, cardiac transplant candidates show deficits in information processing speed, psychomotor speed, abstract reasoning, and memory (e.g., Bornstein, 1989; LaMarche et al., 1992). If Serial 7s and Alphabet Backwards are sensitive measures of information processing speed, this should be demonstrated by showing a relative deficit among the cardiac patients on these measures. Due to the previously demonstrated substantial correlations between tests of information processing speed and intelligence (e.g., Brittain, LaMarche, Reeder, Roth, & Boll, 1991), the cardiac transplant candidates and normal controls were matched on a measure of verbal intelligence as well as on the variables of age and education. This procedure allowed for the examination of the sensitivity of Serial 7s and Alphabet Backwards to reflect decreased information processing speed among the cardiac population after methodologically controlling for the influence of age, education, and premorbid intelligence. Method STUDY 1: CONSTRUCT VALIDITY OF SERIAL 7S AND ALPHABET BACKWARDS Subjects. The subjects were 346 adult patients referred for neuropsychological evaluation. All patients were tested through an outpatient clinic. Referral sources included neurological surgery, neurology, psychiatry, vocational rehabilitation, general medicine, and attorneys. Table 1 presents the distribution of diagnostic categories represented within this sample. To examine the relationship of Serial 7s and Alphabet Backwards within a sample not unduly influenced by grossly impaired patients, the current sample represents patients who were all able to complete Part B of the Trail Making Test in 180 seconds or less. This cutoff allows for inclusion of all patients except the most impaired and prevents inclusion of extreme outliers. Using normative data reported by Bornstein (1985) for the 20-39 age group, a score of 180 seconds translates to a Z score of 5.85. The mean age of the resulting sample was 34.49 (SD = 14.46). The mean education was 12.46 (SD = 2.82). Three hundred of the subjects were white, 45 were black, and 1 was self-identified as other. Measures and Procedures Each patient completed a comprehensive clinical neuropsychological battery assessing a broad range of cognitive functions. Timed tests that require speeded performance were extracted from the larger battery for the purpose of evaluating the construct validity of Serial 7s and Alphabet Backwards. This resulted in 12 separate measures being extracted from 7 tests.

Serial 7s and Alphabet Backwards 653 TABLE 1 Distribution of Diagnostic Categories Represented Within the Sample Diagnosis N Traumatic Brain Injury 125 Cerebrovascular Accident 52 Learning Disabled Adults 50 Primary Psychiatric Disorder 35 Mild Head Injury 28 Cerebral Tumor 10 Hydrocephalus 8 Progressive Dementia 6 Toxic Exposure 6 Systemic Lupus 6 Other a 20 alncludes nonneurological and nonpsychiatric vocational rehabilitation referrals and mixed medical patients (e.g., fibromyalgia, fatigue syndrome, chronic pain, possible seizure disorder). Testing was performed by trained psychometrists, medical psychology graduate students, and post-doctoral fellows who all followed standardized administration procedures. Serial 7s. Subjects were asked to subtract 7 from 100 in a serial fashion. For each subtraction error made, subjects were promptly provided with the correct answer and instructed to continue the subtraction procedure beginning with the corrected response. Time to complete the task was recorded in seconds. Number of errors was recorded as a measure of accuracy. A performance index score was computed by dividing each patient's response time by their number of correct responses (14 maximum). This resulted in a score reflecting the average number of seconds required to obtain each correct answer (performance index score). The performance index score provides the advantage of examining time taken to complete the task in the context of performance accuracy. This approach has been used previously in reporting normative data on speeded tests (e.g., PASAT; Brittain, LaMarche, Reeder, Roth, & Boil, 1991). Alphabet Backwards. Subjects were asked to recite the alphabet backwards as quickly as possible. For each error made, subjects were promptly given the correct response and instructed to continue the backward recitation procedure beginning with the corrected item. Time to complete the task was recorded in seconds and number of errors made was recorded as a measure of accuracy. A performance index score was computed for alphabet backwards by dividing each patient's performance time by their number of correct responses (maximum of 26). Symbol Digit Modalities Test (SDMT; Smith, 1973). Both the written and oral forms were given with the written component being completed first. The performance score consisted of the total number of correct responses obtained for each trial in 90 seconds. Trail Making Test (TMT," Boll, 1978). Parts A and B were administered. The performance measure consisted of the time taken to complete each task. Grooved Pegboard Test (GPT; Matthews & Klove, 1964). Two trials of this test were administered, the first with the patients' dominant hand and the second with the nondominant hand. Time required to complete each trial was the perfolinance measure.

654 M. A. Williams et al. Word Fluency (WF; Benton & Hamsher, 1983). Subjects were asked to verbally produce as many words as they could beginning with the letters C, F, and L. Sixty seconds were allowed to produce word associations to each letter. The performance measure consisted of the total number of words produced for the three letters. Paced Auditory Serial Addition Test (PASAT; Gronwall & Sampson, 1974). Subjects completed the first two trials of the PASAT. Performance measures consisted of the mean time per correct response for each trial (index score) as well as the total number of errors made across the two trials. Results and Discussion Two separate factor analyses (oblimin and varimax) were conducted on the scores from the 12 measures. Due to the substantial overlap in variance among factors produced from these variables, oblique rotation is more appropriate than orthogonal rotation (Tabachnick & Fidell, 1989). However, orthogonal rotations are more commonly found in the literature and for the sake of comparibility to other factor analytic studies (e.g., Shum et al., 1990; Picano, Klusman, Hornbostel, & Moulton, 1992) orthogonal rotated factor analysis proves useful. The factor analysis yielded a two-factor solution which accounted for 59% of the total variance. The oblimin and varimax rotated factor analyses produced identical factor structures. Table 2 presents results from both factor analyses. The first factor accounted for 46% of the variance. Factor loadings above 0.50 with factor 1 were found for both the oral and written version of the SDMT, parts A and B of the TMT, and the GPT. Previous varimax rotated factor analytic studies have obtained a similar factor labeled visual-motor scanning speed (e.g., Shum et al., 1990; Picano et al., 1992). A second factor, which accounted for 13% of the variance, received factor loadings above 0.50 from the Serial 7s index score, the Alphabet Backwards index score, and from the PASAT. This factor can be interpreted as reflecting information processing speed. The Word Fluency test failed to load on either factor above the 0.50 level. These findings, obtained from a heterogenous group of patients, are consistent with those presented by Shum et al. (1990) obtained on a sample of closed head injured patients. In a factor analytic study of eight tests of attention, these authors demonstrated that of the timed tests they evaluated, two factors emerged. The first factor (visual-motor scanning) consisted TABLE 2 Varimax and Oblimin Rotated Factor Matrices for Selected Speeded Neuropsychologicai Measures: Patient Sample (N = 346) Varimax Rotation Oblimin Rotation Variable Fact 1 Fact 2 Fact 1 Fact 2 SDMT (written) -0.82-0.32-0.82-0.12 SDMT (oral) -0.78-0.38-0.75-0.21 Trail Making Test (part A) 0.70 0.19 0.70 0.02 Trail Making Test (part B) Grooved Pegboard (dominant) 0.63 0.80 0.47 0.12 0.56 0.84 0.34-0.09 Grooved Pegboard (nondominant) Serial 7s (index score) 0.77 0.09 0.07 0.58 0.83-0.07-0.14 0.62 Alphabet Backwards (index score) 0.19 0.71 0.01 0.73 PASAT Trial 1 (index score) 0.16 0.82-0.05 0.86 PASAT Trial 2 (index score) PASAT Total Errors 0.16 0.35 0.70 0.83-0.02 0.15 0.72 0.82 Word Fluency -0.24-0.39-0.15-0.36

Serial 7s and Alphabet Backwards 655 of Digit Symbol, Letter Cancellation, SDMT, and TMT. They labeled the second factor sustained selective processing that consisted of the time taken to complete serial 13s, serial 7s, and the Stroop Test interference score. Shum et al. (1990) findings are consistent with the two-factor structure demonstrated within our sample using similar measures. Method STUDY 2: DISCRIMINANT VALIDITY OF SERIAL 7S AND ALPHABET BACKWARDS Subjects. The patient group consisted of 42 individuals suffering from end-stage cardiac disease which qualified them for participation in a comprehensive evaluation program for consideration of heart transplantation. As part of the evaluation program, each patient underwent a battery of neuropsychological tests. This group consisted of 19 men and 23 women. The mean age was 27.98 (SD = 5.66). Twenty-eight of the subjects were white and 14 were black. The control group consisted of 46 college student volunteers who received credit in their introductory psychology course for their participation. The mean age of this group was 25.50 (SD = 6.9). There were 13 men and 33 women. Thirty-one of the subjects were white, 14 were black, and 1 subject was self-identified as other. The two groups were matched on the variables of age, education, and vocabulary T-scores from the Shipley Institute of Living Scale (SILS). Table 3 provides a summary of demographic variables. Measures and Procedures The cardiac patients completed Serial 7s, Alphabet Backwards, and the SILS as part of a comprehensive neuropsychological test battery. Control subjects were recruited specifically to participate in a normative study on Serial 7s and Alphabet Backwards. In both cases, identical test instructions and procedures were used. Test administration was conducted by TABLE 3 Demographic Characteristics of Patient and Control Groups Group Cardiac Patients Controls (n = 42) (n = 46) t p Age (years) Mean 27.98 25.50 SD 5.66 6.90 Education (years) Mean 13.52 13.11 SD 1.85 1.52 SILS Vocabulary T-Score Mean 44.43 47.54 SD 10.74 7.81 Gender Male 19 (45%) 13 (28%) Female 23 (55%) 33 (72%) Race White 28 (67%) 31 (68%) Black 14 (33%) 14 (30%) Other 0 I (2%) 1.83 0.07 1.15 0.25 1.57 0.12

656 M. A. Williams et al. trained medical psychology graduate students, psychometrists, and a postdoctoral fellow in clinical neuropsychology. Shipley Institute of Living Scale (SILS; Zachary, 1986). The Shipley Institute of Living Scale is a commonly used brief measure of intelligence. The scale consists of a 40-item multiple choice vocabulary test and a 20-item test of abstraction and conceptual reasoning. Due to the relative insensitivity of the vocabulary subtest to mild to moderate brain dysfunction (Phay, 1990), only this subtest was used as an estimate of intellectual functioning. Results and Discussion The two groups were compared on each of the dependent measures using independent t tests. Group means, SDs, and significance levels are listed in Table 4. On Serial 7s, the cardiac patients displayed a slower performance time compared to the control group, t(86) = 2.53, p = 0.013. The patient group did not, however, make significantly more errors than the control group. Consistent with these results was the finding of a significant group difference on the Serial 7s performance index score (total time/# correct), t(86) = 2.50, p = 0.014. Due to the lack of homogeneity of group variances, a nonparametric procedure was used to assess for group differences on the time measure for Serial 7s. Using a one-tailed test, the Mann-Whitney U test resulted in a significant group difference as well (p = 0.047). On Alphabet Backwards, the cardiac patient group performed more slowly than the control group, t(86) = 2.59, p = 0.011. Again, however, the groups did not differ significantly on the number of errors made. Examination of the Alphabet Backwards performance index score showed significant group differences, t(86) = 2.68, p = 0.009. A Pearsons correlation procedure was performed to examine the relationship between education, Serial 7s, Alphabet Backwards, and the SILS vocabulary test. The results are displayed in Table 5. As expected, moderate correlations (-0.40 to -0.50) were found between the tests of information processing speed and the SILS vocabulary T-score. Whereas the correlation between Serial 7s and Alphabet Backwards was moderate and statistically significant for the control group (r = 0.58), the correlation between these tests within the cardiac patient group was smaller and not statistically significant (r = 0.35). This weak correlation is likely due in large part to the excessive variability found among the patient group on Serial 7s. Education failed to correlate significantly with Serial 7s (r = -0.24) and Alphabet Backwards (r = -0.15) for the patient group as well as for the control group (r = -0.20 and TABLE 4 Mean Scores and t Test Results Cardiac Patients Controls (n = 42) (n = 46) M (SD) M (SD) t p Serial 7s Time 112.41 (103.74) Errors 2.79 (2.93) Index score 13.54 (17.70) Alphabet Backwards Time 90.91 (60.90) Errors Index score 3.05 4.17 (3.09) (3.04) 70.96 2.33 (38.20) (1.94) 2.53 0.87 0.01 0.38 6.74 (4.93) 2.50 0.01 63.94 (34.09) 2.58 0.01 2.43 2.79 (1.96) (1.64) 1.12 2.68 0.27 0.01

Serial 7s and Alphabet Backwards 657 TABLE 5 Correlations Between Education, Serial 7s, Alphabet Backwards, and SILS Vocabulary T-Scores Patients Controls Alphabet Shipley Alphabet Shipley Serial 7s Backward Vocab Serial 7s Backward Vocab Education -0.24-0.15 0.51 * * -0.20-0.09 0.06 Serial 7s 0.35-0.40* 0.58** -0.42* Alphabet Backwards -0.50** -0.45** *p < 0.01; **p < 0.001 (one-tailed). r = -0.09, respectively). These weak correlations likely reflect the influence of restricted range within the education variable. By design, college student controls were used and patients were selected to match to this restricted educational range in order to methodologically control for educational influences. It seems reasonable to expect that given a broader educational range that Serial 7s and Alphabet Backwards performance would be significantly related to educational background as has been consistently reported for other measures of information processing speed (e.g., Brittain et al., 1991). Visual inspection of the correlation coefficients obtained between education, Serial 7s, and Alphabet Backwards suggests a tendency for Alphabet Backwards to be less related to educational background than Serial 7s for both the patient and control groups. However, nonindependent t tests between the coefficient pairs revealed no statistically significant differences between Serial 7s-education and Alphabet Backwards-education coefficient pairs for both the patient group, t(39) = 0.57, p > 0.25, and for the control group, t(43) = -0.80, p > -0.20. (t tests were performed on Fisher transformed r's; see Howell, 1982, p. 201). CONCLUSIONS These studies provide support for the construct and discriminant validity of Serial 7s and Alphabet Backwards as brief measures of information processing speed. When Serial 7s and Alphabet Backwards were subjected to factor analysis along with other commonly used speeded performance measures, two factors emerged. The first factor, visual-motor scanning speed, included the Symbol Digit Modalities Test (written and oral), the Trail Making Test (Parts A and B), and the Grooved Pegboard Test. The second factor, information processing speed, included Serial 7s, Alphabet Backwards, and the Paced Auditory Serial Addition Test. This factor structure is consistent with that reported in previous factor analytic studies (e.g., Shum et al., 1990). The discriminant validity of Serial 7s and Alphabet Backwards was demonstrated by showing that cardiac transplantation candidates, matched on the variables of age, education, and intelligence with a control group, were substantially slower than the controls. The cardiac patients, however, did not make more response errors, suggesting that performance accuracy (number of errors) on Serial 7s and Alphabet Backwards is a less sensitive indicator of cognitive disruption than is speed of performance. This pattern of results, in which speed of information processing is reduced without an increase in performance errors, has been reported from several studies which have examined attentional processing among patients who have sustained severe closed-head injuries (e.g., Brouwer & van Wolfelaar, 1985; Ponsford & Kinsella, 1992). It appears that reduced information processing speed is a much more common deficit resulting from higher cortical dysfunction than are deficits in

658 M. A. Williams et al. focusing or sustaining attention (Ponsford & Kinsella, 1992). The specific cause of these patients' information processing slowing requires further examination. For example, while specific neurological deficits may be responsible, other etiologies need to be examined as well. These include the nonspecific effects of severe illness, emotional disruption, and medication effects. Although Serial 7s and Alphabet Backwards show promise for being useful as brief measures of information processing speed, there is a need for the collection of normative data on individuals from a broader age and education range than is reported in the control group in this study. Because of the moderate correlations found between measures of information processing speed and IQ scores, it will be important to design the collection process across a range of IQ scores as has been done with other tests of information processing speed (Brittain et al., 1991). Serial 7s has been criticized in the past due to its sensitivity to practice effects (Ronsen & Fox, 1986). Our results found performance variability among the patient group to be substantially higher on Serial 7s compared to Alphabet Backwards. It may be that a smaller number of persons have had experience with saying the alphabet backwards relative to performing serial subtraction tasks and therefore Alphabet Backwards may be less influenced by history effects. Although in this sample Alphabet Backwards was not found to be significantly less related to educational background relative to Serial 7s, the trend was in this direction. It is hypothesized that in a sample not as restricted in educational range as was our own, that Alphabet Backwards would be found to be significantly less tied to education than is Serial 7s; however, this awaits further evaluation. Moore, Pierce, and Graybill (1980), reported that in a college student sample, Serial 6s, 8s, and 9s were similar in difficulty to Serial 7s. Further comparative studies examining the relative difficulties of different serial subtraction tests are needed. Serial 7s and Alphabet Backwards were chosen for evaluation in this article due to the substantial frequency in which they are used in clinical practice. Other simple tasks, however, show face validity as being useful measures of information processing speed. These include serial addition tasks (e.g., counting forward by 4s) and other backward recitation tasks (e.g., reverse recitation of days of the week or months of the year). Although continued psychometric research is needed, preliminary data from this study suggest that Serial 7s and Alphabet Backwards are time efficient and technically simple measures of information processing speed. REFERENCES Benton, A. L., & Hamsher, K. (1983). MultilingualAphasia Examination. Iowa City, IA: AJA Associates. Boll, T. J. (1978). Diagnosing brain impairment. In B. Wolman (Ed.), Diagnosis of mental disorders: A handbook (pp. 601-674). New York: Plenum Press. Bornstein, R. A. (1985). Normative data on selected neuropsychological measures from a non-clinical sample. Journal of Clinical Psychology, 41, 651-659. Bornstein, R. A. (1989). Neuropsychological impairment in candidates for cardiac transplantation. Journal of Clinical and Experimental Neuropsychology, 11, 364. Brittain, J. L., LaMarche, J. A., Reeder, K. P., Roth, D. L., & Boll, T. J. (1991). Effects of age and IQ on paced auditory serial addition task (PASAT) performance. The Clinical Neuropsychologist, 5, 163-175. Brouwer, W. H., & van Wolfelaar, P. C. (1985). Sustained attention and sustained effort after closed-head injury: Detection and 0.10 Hz heart rate variability in a low event rate vigilance task. Cortex, 21, 111-119. Folstein, M. E, Folstein, S. E., & McHugh, P. R. (1975). "Mini-mental state": A practical method for grading the cognitive state of patients for the clinician. Journal of Psychiatric Research, 12, 189-196. Gronwall, D. M. A., & Sampson, H. (1974). The psychological effects of concussion. Auckland, New Zealand: Auckland University Press. Howell, D. C. (1982). Statistical methods for psychology. Boston: Duxbury Press.

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