Adult Age and Digit Symbol Substitution Performance: A Meta-Analysis

William J. Hoyer, Robert S. Stawski, Christina Wasylyshyn, and Paul VerhaeghenSyracuse University

This article reports the results of a meta-analysis of the effects of age, education, and estimated year ofmeasurement on scores from the Wechsler Adult Intelligence Scale and the Wechsler Adult IntelligenceScale—Revised Digit Symbol Substitution Test. Analysis of effect sizes for age reported in 141 studiespublished between 1986 and 2002 indicated a mean standardized difference of –2.07. Age accounted for86% of the variance in a regression model using age, education, and year submitted as predictors of DigitSymbol scores. There was no association between years of education or year submitted and Digit Symbolscores for younger adults or older adults.

One of the most widely used instruments for describing theperformance of younger and older adults in cognitive aging studiesis the Digit Symbol Substitution Test (DSST) from the WechslerAdult Intelligence Scale (WAIS; Wechsler, 1955) and the Wech-sler Adult Intelligence Scale—Revised (WAIS–R; Wechsler,1981). The DSST has two properties that make it a valuable toolfor aging research. First, the DSST seems to serve as a robustmarker for describing sample characteristics in studies of agedifferences. Age–DSST correlations of between –.46 and –.77 aretypically reported (e.g., Birren, 1965; Birren & Morrison, 1961;Doppelt & Wallace, 1955; Kaufman, Reynolds, & McLean, 1989;Royer, Gilmore, & Gruhn, 1981; Salthouse, 1992). Second, scoreson the DSST have been shown to exhibit strong correlations withmeasures that in some way involve perceptual speed (Laux &Lane, 1985; Lindenberger & Baltes, 1997; Salthouse, 2000; Sli-winski & Buschke, 1999), and perceptual speed or processingspeed is known to be a large source of the variance in manyage–performance relations (e.g., Birren, 1965; Cerella, 1990; Mad-den, 2001; Salthouse, 1996).

The DSST consists of a look-up table showing pairs of digitsand hieroglyphic-like symbols and rows of boxes with a digit inthe top section and an empty space in the bottom section of eachbox. A participant’s score is the number of empty boxes completedin 90 s. The DSST is easily administered, and the procedures foradministration and scoring of the test leave relatively little roomfor variation. Because the format and test materials for the DSSThave remained unchanged (Wechsler, 1955, 1981), the DSST dataalready available in studies published during the past 16 years

provide an ideal base for a comprehensive meta-analysis of therelations between age and DSST scores and for exploring possiblerelations between DSST scores and years of education and years ofmeasurement (estimated using year submitted for publishedmanuscripts).

In regard to possible relations between DSST scores and edu-cational level, the available data, all from nonaggregated data sets,suggest no relationship (Birren & Morrison, 1961; Salthouse,1992). It would be useful to show that age–DSST relations areindependent of years of formal education across a broad range ofstudy samples. Although there are no reports directly examiningthe relationship between age-related declines in DSST scores andyears of measurement, Schaie (1994) reported relatively stableperformance for measures of perceptual speed for cohorts bornbetween 1907 and 1966 and tested between 1956 and 1991. How-ever, this finding stands somewhat in contrast to analyses by Flynn(1987) and Raven (2000) indicating secular increases in intelli-gence test scores. Flynn reported gains of between 5 and 25 pointsin IQ scores during the past 50 years in secondary analyses of largedata sets taken from different countries. Raven described substan-tial secular increases in scores on the Raven’s Progressive Matri-ces (RPM) during the past 20 years, although RPM scores takenprior to 1979 were found to be stable across testing occasions. Inlight of the generally strong relations between intelligence andperceptual speed reported in the literature (e.g., Postuma, de Geus,& Boomsma, 2001; Salthouse, 1996; Sliwinski & Buschke, 1999;Verhaeghen & Salthouse, 1997; Zimprich & Martin, 2002), itwould be useful to know whether there have been secular increasesin DSST scores in recent years.

In this study, we report the results of a meta-analysis of theeffects of age, education, and year of measurement (estimatedfrom year submitted for published manuscripts) on DSST perfor-mance using all pertinent data published in Psychology and Agingand the Journals of Gerontology (all subsections) between 1986and 2002. That there is a large number of studies reporting DSSTscores for younger and older adults and that the format of theWAIS and WAIS–R versions of the DSST has remained un-changed (until recently; see Wechsler, 1997) makes it an idealdependent variable for assessing age–performance relations as afunction of educational characteristics of the samples and yearsubmitted.

William J. Hoyer, Robert S. Stawski, Christina Wasylyshyn, and PaulVerhaeghen, Department of Psychology and Center for Health and Behav-ior, Syracuse University.

This research was supported by National Institute on Aging GrantAG-11451. We thank Serge Onyper and Silvie Semenec for assistance witha preliminary data collection and Ulman Lindenberger for comments on anearlier draft.

An Excel spreadsheet listing the studies providing data for the meta-analysis and the effect sizes for each of the samples is available fromWilliam J. Hoyer.

Correspondence concerning this article should be addressed to WilliamJ. Hoyer, Department of Psychology, 430 Huntington Hall, SyracuseUniversity, Syracuse, NY 13244-2340. E-mail: wjhoyer@syr.edu

Psychology and Aging Copyright 2004 by the American Psychological Association, Inc.2004, Vol. 19, No. 1, 211–214 0882-7974/04/$12.00 DOI: 10.1037/0882-7974.19.1.211

211

Method

Sample of Studies

All volumes of Psychology and Aging and the Journals of Gerontology(all subsections)1 published between 1986 and 2002 were hand searchedfor articles reporting mean raw scores for the WAIS or WAIS–R DSST(the standard paper-and-pencil version). Articles reporting at least onesample of younger adults (with a mean age below 30 years) and one sampleof “healthy” older adults (with a mean age above 60 years) were included.Scores derived from samples with participants reported to have dementiawere excluded. For longitudinal studies and for studies reporting multipleadministrations of the DSST to the same participants, only scores from thefirst administration of the test were included. A total of 141 studiesreporting data from 3,731 younger adults and 3,876 older adults satisfiedthese inclusion–exclusion criteria; 99 of the studies were in Psychologyand Aging, 40 were in Journal of Gerontology: Psychological and SocialSciences, and 2 were in Journal of Gerontology: Medical Sciences. MeanDSST scores and means and ranges for age and education for the youngerand older samples are reported in Table 1.

Statistical Analysis Procedures

A standard effect size analysis was performed to determine the age effecton DSST scores (Hedges & Olkin, 1983). For each combination of scoresfor younger adults and older adults, the mean standardized difference forthe size of the age effect was determined. The mean standardized differ-ence was calculated as the mean score for older adults minus the meanscore for younger adults, divided by the pooled standard deviation. Ifmeans and standard deviations were not reported, inferential statistics wereused to calculate the mean standardized difference, if possible; 46 of the141 effect sizes were extracted from t or F tests. To test whether the meanstandardized difference for the size of the age effect can be represented asa single value (the overall effect size), we calculated a homogeneitystatistic, Qt (Hedges & Olkin, 1983, pp. 154–156). If Qt, which is achi-square statistic distributed with k � 1 degrees of freedom (where kequals the number of effect sizes), exceeds the critical value, furtheranalysis of possible moderator variables is indicated.

Results

Figure 1 shows mean DSST scores by age. The averaged effectsize (d) for age was –2.07, the lower bound of the 95% confidenceinterval was –2.12, and the upper bound of the 95% confidenceinterval was –2.03. The overall effect size was heterogeneous,Qt(141) � 511.18. A hierarchical regression analysis (weighted bysample size) was performed on raw DSST scores, to examine

possible moderators of the heterogeneity. In the first step (Model1), age, years of education, and year submitted for the study wereentered simultaneously as predictors of DSST scores (k � 242). Inthe second step (Model 2), we explored whether the slopes for age,for years of education, and for year submitted differed as a func-tion of age group. In Model 2, the three two-way interaction termsfor these factors were added as predictors of DSST scores. Theunstandardized B, standardized beta, and the t values for each ofthe predictors in the two regression models are reported in Table 2.The overall effect of Model 1, the three-parameter model, onDSST scores was significant, F(3, 238) � 446.37, MSE � 20.93,R2 � 0.85. The coefficients were significant for age ( p � .001)and years of education ( p � .019), and the coefficient for yearsubmitted was not significant (t � 1). The overall effect of Model2, the six-parameter model, on DSST scores was also significant,F(6, 235) � 224.72, MSE � 20.85, R2 � 0.85. The fit for Model2 was no better than the fit for Model 1, �R2 � 0.002, F(3, 235) �1.31. In Model 2, only the coefficient for age ( p � .002) wassignificant. The absence of interaction terms suggested that theslopes for age and years of education for the two age groups werenot different. It is important to note that the Nonsignificant Age(within groups) � Age Groups interaction (t � 1.70) suggests thatthe slopes of the age–DSST relation were not different between thetwo age groups and that the age–DSST relation is not an artifact ordistortion associated with using extreme groups. The regressionslope, –0.46 items per year (Model 1), was consistent with thevalue of the slope of –0.47 reported by Salthouse (1992) and theslope of –0.43 reported by Emmerson, Dustman, Shearer, andTurner (1989) using a symbol digit test.

Figure 2 shows the relation between DSST scores and educa-tion, and Figure 3 shows the relation between DSST scores andyear submitted. The plots show the data from the 242 samples thatwere used in the regressions. The differences in the distributions ofyears of education between the samples of younger adults andolder adults were quite striking and are shown in histogram formin Figure 4. As reported in Table 2, there was no relationship

1 This journal was called Journal of Gerontology prior to and includingVolume 41 (1986). The subsections of the Journals of Gerontology in-cluded in the search were Biological Sciences, Medical Sciences, Psycho-logical Sciences, and Social Sciences.

Table 1Means and Ranges for Measures of the Characteristics of the Research Participants

Measure No. of studies

Younger adults Older adults

M Range M Range

Age (years, unweighted) 139 21.4 18.1–30.7 69.5 60.7–78.9Age (years, weighted by n) 139 21.6 69.8Education (unweighted) 117 13.9 12.0–16.7 15.2 11.7–17.9Education (weighted by n) 117 14.1 15.3Digit symbol (unweighted) 138 69.3 51.2–82.7 48.2 38.8–66.8Digit symbol (weighted by n) 138 69.8 48.6

Note. The age groups consisted of 3,731 younger adults and 3,876 older adults. Education � number of yearsof formal education. Digit symbol � score on Wechsler Adult Intelligence Scale or Wechsler Adult IntelligenceScale—Revised Digit Symbol Substitution subtest.

212 BRIEF REPORTS

between DSST scores and years of education when differencesbetween age groups were taken into account (Model 2).

Another weighted least squares regression analysis was per-formed to determine whether the effect sizes for DSST scores werepredicted by the size of the difference in age or education betweenage groups. The overall effect of the regression model on DSSTscores was significant, F(2, 117) � 5.23, MSE � 15,845, R2 �0.08. The coefficient for the age difference was significant (t �–3.18, p � .002), indicating that the strength of the age–DSSTrelation was related to the size of the chronological age differencesfor the groups. The coefficient for difference in years of educationwas not significant (t � 1).

Discussion

The aim of this study was to assess the magnitude of the ageeffect in DSST scores by applying meta-analytic methods to the

data reported in age-comparative studies published in Psychologyand Aging and the Journals of Gerontology during the past 16years. The magnitude of the effect of age on DSST scores obtainedfrom 141 age comparisons was substantial (d � –2.07). Thisfinding confirms the high correlations between age and DSSTscores reported in standardization studies (e.g., Birren & Morrison,1961; Kaufman et al., 1989; Wechsler, 1997) and in large nonag-gregated data sets with digit symbol and symbol digit measures(e.g., Royer et al., 1981; Salthouse, 1992, 2000).

Although the biobehavioral processes underlying age effects onDSST scores are not well understood (e.g., Laux & Lane, 1985;Piccinin & Rabbitt, 1999; Salthouse, 1992, 2000), the results of thepresent study indicate unequivocally that the speed of carrying out

Table 2Summary Statistics for Two Regression Models

Predictor B � t

Model 1 (R2 � .85)

Age �0.46 �0.95 �33.09*Education 0.62 0.07 2.37*Year submitted �0.01 �0.00 �0.61

Model 2 (R2 � .85)

Age �0.65 �1.34 �3.14*Education 0.82 0.09 1.79Year submitted �0.01 �0.01 �0.18Age � Education �0.15 �0.10 �0.27Age � Year Submitted 0.01 �0.73 �1.47Age � Age Groups (within groups) 0.40 1.20 1.70

Note. Models were least squares regressions weighted by n. Model 1 usedthree predictors, and Model 2 used six predictors. Data for year submittedwere the years indicated in the date of submission for the manuscripts.* p � .05.

Figure 1. Digit symbol scores as a function of age. Triangles indicateyounger adults, and circles indicate older adults. DSST � Digit SymbolSubstitution Test.

Figure 2. Digit symbol scores as a function of number of years ofeducation. Triangles indicate younger adults, and circles indicate olderadults. The solid line indicates the regression line for younger adults, andthe broken line indicates the regression line for older adults. DSST � DigitSymbol Substitution Test.

Figure 3. Digit symbol scores by year submitted. Triangles indicateyounger adults, and circles indicate older adults. The solid line indicatesthe regression line for younger adults, and the broken line indicates theregression line for older adults. DSST � Digit Symbol Substitution Test.

213BRIEF REPORTS

the combination of coding and substitution processes that compriseDSST performance is slower for older adults than for youngeradults. Furthermore, the age–DSST relation, derived here from alarge and wide-ranging set of descriptive data, was independent ofyears of education and was invariant across years of measurement(estimated by year of submission). One implication of the robust-ness of the age–DSST relationship is to suggest that the DSST beused routinely as a general marker in age-comparative studies.

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Received January 8, 2003Revision received March 31, 2003

Accepted April 7, 2003 �

Figure 4. Frequency distribution of education scores for samples ofyounger adults (unfilled bars) and older adults (hatched bars).

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