Data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey were used to calculate weighted norms for the written version of the Symbol Digits Modalities Test (SDMT) by gender, 5-year age groups and four levels of educational attainment. The sample comprised 14,456 Australians (47% male; age range 15–100), of whom 25% reported a tertiary qualification, 30% reported a technical qualification (diploma or trade certificate), 16% reported completing Year 12 (final year of high school), and 29% reported their highest level of educational attainment to be Year 11 or below. Participants were excluded if they reported physical or neurological conditions that limited performance. Age, gender, and education were all significantly associated with SDMT performance, as was poor health, and cultural background. The reported norms are of greater scope and precision than previously available and have utility in a range of clinical and research settings. Indeed, normative data for the SDMT that are representative of a national population have not previously been published.

## Introduction

The Symbol Digit Modalities Test (SDMT) is a screening instrument commonly used in clinical and research settings to assess neurological dysfunction (Smith, 2007). Like other substitution tasks, performance on the SDMT is underpinned by attention, perceptual speed, motor speed, and visual scanning. Although the SDMT is unable to differentiate between specific disorders, it is sensitive to a variety of neurological conditions and therefore has application in a range of clinical populations. For example, impaired performance has been associated with traumatic brain injury, concussion in athletes, multiple sclerosis, Huntington's disease, Parkinson's disease, and stroke (Strauss, Sherman, & Spreen, 2006). The SDMT is also sensitive to change in neurocognitive status, making it useful for evaluating interventions and tracking disease progression over time. In addition to its clinical utility, the SDMT features in many studies of age-related cognitive decline; as a measure of perceptual processing speed, it reflects a core construct in theories of cognitive ageing (Salthouse, 1996, 2000). The written format of the SDMT is promoted as being relatively free from cultural bias and purported to be an ideal screen for people who are not fluent in the testing language (Smith, 2007; Western Psychological Services [WPS], 2014) or have speech disorders (Strauss et al., 2006). Further, it has been shown that ethnicity is not predictive of performance in a healthy sample of college students (O'Bryant, Humphreys, Bauer, McCaffrey, & Hilsabeck, 2007). Nevertheless, cultural and racial differences in SDMT (or modified SDMT) performance have been reported in other studies (Agranovich, Panter, Puente, & Touradji, 2011; Gonzalez et al., 2007; Kennepohl, Shore, Nabors, & Hanks, 2004; Uchiyama et al., 1994).

A number of studies have published normative data for the SDMT in nonclinical samples (for a review, see Sheridan et al., 2006). However, these studies have typically been characterized by small cell sizes, convenience samples and restricted population coverage, limiting their precision and generalizability. For example, healthy volunteers have been used to provide SDMT norms for 127 adults aged 15–40 (Yeudall, Fromm, Reddon, & Stefanyk, 1986), and 354 adults aged 50–90 (Pena-Casanova et al., 2009), while Sheridan and colleagues (2006) published SDMT norms derived from a community-based sample comprising just 238 adults (aged between 21 and 49). These modest sample sizes have necessitated norms only being reported for wide age bands (up to 20 years) and broad socio-demographic categories, such as binary categories of educational attainment. This is problematic because time-dependent substitution tasks, such as the SDMT, have been shown to undergo rapid nonlinear age declines after mid-life (Jorm, Anstey, Christensen, & Rodgers, 2004) and are highly associated with education (Lezak, 2004). Indeed, this may explain why Sheridan and colleagues (2006) did not find gender, age, or education to be predictive of SDMT performance in their younger sample.

Ideally, normative data for neuropsychological tests should be current, representative of the general population, and based on a sample of sufficient size to enable reporting by all pertinent socio-demographic subgroups (Kiely et al., 2011; Strauss et al., 2006). To the authors knowledge, there are currently no nationally representative norms for the SDMT derived from large population-based epidemiological surveys. Normative data for a modified version of the SDMT have been reported for African Americans, Caribbean Black Americans, and non-Latino whites in a representative sample of 4545 respondents from the National Survey of American Life (Gonzalez et al., 2007), but this study was also limited to reporting norms for broad age bands and two levels of education. The aim of this study is to present current normative data for the SDMT with written responses across a broad age range 15–100, measured from a large nationally representative sample of the Australian population, stratified by gender, 5-year age groups, and four levels of education.

## Methods

### Survey Design

Data were collected in 2012 as part of the 12th wave of the Household, Income and Labour Dynamics in Australia (HILDA) Survey (Watson & Wooden, 2012), a longitudinal household panel survey with a multi-stage sampling design that has conducted interviews annually since 2001. Data are provided by each household member aged 15 and older via both personal interview and self-completion questionnaire. At baseline, there were 7682 sampled households (response rate 66%) yielding interviews with 13,969 individual participants. In wave 11 (2011), the original sample was augmented with a top-up of an additional 2153 households (69% response rate) to improve the population representativeness of the sample.

In wave 12 (2012), 16,091 individual participants completed face-to-face interviews and were invited to participate in the SDMT. A further 1384 participants completed interviews by telephone and therefore did not participate in the SDMT, while one participant, despite completing the interview face-to-face, was mistakenly not invited to participate in the SDMT.

### Participants

Of the 16,091 survey participants invited to undertake the SDMT, complete data was provided by 15,165 persons (47.2% male; 2.7% Aboriginal and Torres Strait Islander). After applying all exclusions (as described below in Exclusion and Inclusion Criteria), there were 14,456 participants remaining in the sample used to generate SDMT norms.

The sample profile is presented in Table 1. Participants were aged between 15 and 100. Age was categorized into 5-year age groups for ages 15 through 80, and top coded at 85+. A variable reflecting highest educational attainment was coded into four levels in line with Australian standards for classifying education variables (tertiary degree, postsecondary certificate or diploma, completed high school, and Year 11 or less). Tertiary degrees include bachelor and postgraduate level qualifications. Postsecondary (but nontertiary) certificates and diplomas reflect trade, vocational and technical qualifications that are below tertiary level but higher than high school completion. Completing high school is equivalent to 12 years of education. Due to small cell sizes and reduced variability, education was collapsed into a binary variable (completed high school versus Year 11 or less) for the youngest age group (15–19) and the older age groups (75–79, 80–84, and 85+). Two binary variables reflecting cultural background were coded. The first variable was an indicator of non-English-speaking background, which identified participants who were born outside Australia and reported that English was not their first language spoken. The second variable indicated whether participants identified themselves as being of Aboriginal and Torres Strait Islander background. As part of the personal interview, participants were shown a 17-item showcard and asked to report if they experienced any of the listed long-term health conditions, impairments, or disabilities for a period of 6 months or more.

Table 1.

Cohort profile in 2012 (N = 14,456)

Highest education (%)

Cultural background (%)

Health conditionsa (%)

n Tertiary Postsecondary Completed high school ≤Year 11 NESB ATSI 2+
Males
15–19 641 0.2 3.8 26.8 69.3 3.1 1.3 92.2 6.7 1.1
20–24 688 9.5 26.4 43.2 21.0 5.1 0.6 91.4 6.3 2.3
25–29 660 25.8 34.5 24.6 15.2 10.0 0.8 89.6 6.7 3.8
30–34 546 34.1 39.1 13.9 12.8 11.2 0.6 89.5 7.5 2.9
35–39 573 33.3 41.5 14.3 10.8 11.3 0.4 86.9 8.2 4.9
40–44 585 30.8 43.7 9.6 15.9 8.9 0.0 86.3 10.1 3.6
45–49 589 27.6 42.7 7.1 22.6 10.4 0.0 80.4 9.7 9.9
50–54 581 25.6 46.8 8.1 19.5 9.5 0.2 77.2 13.1 9.7
55–59 490 31.3 39.9 8.6 20.3 11.7 0.2 71.0 15.1 13.9
60–64 415 24.4 41.1 9.2 25.4 10.1 0.0 59.9 16.4 23.7
65–69 363 24.0 39.5 8.0 28.5 11.9 0.0 57.2 19.3 23.5
70–74 273 17.7 42.1 9.2 31.0 14.7 0.0 51.5 22.4 26.1
75–79 201 20.6 39.7 4.0 35.7 12.1 0.0 46.5 21.0 32.5
80–84 122 11.5 41.0 0.8 46.7 13.9 0.0 41.8 27.9 30.3
85+ 71 14.1 38.0 12.7 35.2 11.3 0.0 38.0 29.6 32.4
TOTAL 6,798 23.0 36.0 16.0 25.1 9.5 0.4 78.6 11.5 9.9
Females
15–19 684 0.3 5.6 32.4 61.8 3.2 1.2 91.7 6.6 1.8
20–24 762 16.8 24.8 42.8 15.6 5.8 1.1 86.6 9.6 3.8
25–29 702 36.0 31.5 19.7 12.8 10.3 0.3 88.5 8.0 3.6
30–34 596 44.4 30.3 14.7 10.6 15.7 0.2 83.5 9.9 6.6
35–39 645 40.6 30.5 13.5 15.4 12.9 0.2 84.3 9.5 6.2
40–44 696 34.8 29.3 13.9 22.0 11.1 0.1 82.5 9.5 8.1
45–49 654 30.2 30.3 13.0 26.5 12.9 0.0 78.1 12.9 9.0
50–54 648 30.6 31.1 10.1 28.3 13.5 0.2 74.8 10.8 14.4
55–59 575 26.8 29.0 10.3 33.9 11.3 0.0 63.7 16.7 19.7
60–64 489 23.2 25.6 7.6 43.7 15.2 0.0 58.2 18.2 23.6
65–69 425 18.8 21.6 8.3 51.3 10.4 0.0 59.5 17.1 23.5
70–74 311 12.9 20.3 6.4 60.5 11.9 0.0 47.9 21.5 30.6
75–79 193 11.9 16.6 4.7 66.8 9.8 0.0 45.1 19.2 35.8
80–84 165 12.3 14.1 8.6 65.0 9.2 0.0 37.4 25.8 36.8
85+ 113 3.6 7.1 10.7 78.6 8.0 0.0 32.7 26.6 40.7
TOTAL 7,658 25.9 25.3 16.9 31.9 10.8 0.3 75.2 12.4 12.4
Highest education (%)

Cultural background (%)

Health conditionsa (%)

n Tertiary Postsecondary Completed high school ≤Year 11 NESB ATSI 2+
Males
15–19 641 0.2 3.8 26.8 69.3 3.1 1.3 92.2 6.7 1.1
20–24 688 9.5 26.4 43.2 21.0 5.1 0.6 91.4 6.3 2.3
25–29 660 25.8 34.5 24.6 15.2 10.0 0.8 89.6 6.7 3.8
30–34 546 34.1 39.1 13.9 12.8 11.2 0.6 89.5 7.5 2.9
35–39 573 33.3 41.5 14.3 10.8 11.3 0.4 86.9 8.2 4.9
40–44 585 30.8 43.7 9.6 15.9 8.9 0.0 86.3 10.1 3.6
45–49 589 27.6 42.7 7.1 22.6 10.4 0.0 80.4 9.7 9.9
50–54 581 25.6 46.8 8.1 19.5 9.5 0.2 77.2 13.1 9.7
55–59 490 31.3 39.9 8.6 20.3 11.7 0.2 71.0 15.1 13.9
60–64 415 24.4 41.1 9.2 25.4 10.1 0.0 59.9 16.4 23.7
65–69 363 24.0 39.5 8.0 28.5 11.9 0.0 57.2 19.3 23.5
70–74 273 17.7 42.1 9.2 31.0 14.7 0.0 51.5 22.4 26.1
75–79 201 20.6 39.7 4.0 35.7 12.1 0.0 46.5 21.0 32.5
80–84 122 11.5 41.0 0.8 46.7 13.9 0.0 41.8 27.9 30.3
85+ 71 14.1 38.0 12.7 35.2 11.3 0.0 38.0 29.6 32.4
TOTAL 6,798 23.0 36.0 16.0 25.1 9.5 0.4 78.6 11.5 9.9
Females
15–19 684 0.3 5.6 32.4 61.8 3.2 1.2 91.7 6.6 1.8
20–24 762 16.8 24.8 42.8 15.6 5.8 1.1 86.6 9.6 3.8
25–29 702 36.0 31.5 19.7 12.8 10.3 0.3 88.5 8.0 3.6
30–34 596 44.4 30.3 14.7 10.6 15.7 0.2 83.5 9.9 6.6
35–39 645 40.6 30.5 13.5 15.4 12.9 0.2 84.3 9.5 6.2
40–44 696 34.8 29.3 13.9 22.0 11.1 0.1 82.5 9.5 8.1
45–49 654 30.2 30.3 13.0 26.5 12.9 0.0 78.1 12.9 9.0
50–54 648 30.6 31.1 10.1 28.3 13.5 0.2 74.8 10.8 14.4
55–59 575 26.8 29.0 10.3 33.9 11.3 0.0 63.7 16.7 19.7
60–64 489 23.2 25.6 7.6 43.7 15.2 0.0 58.2 18.2 23.6
65–69 425 18.8 21.6 8.3 51.3 10.4 0.0 59.5 17.1 23.5
70–74 311 12.9 20.3 6.4 60.5 11.9 0.0 47.9 21.5 30.6
75–79 193 11.9 16.6 4.7 66.8 9.8 0.0 45.1 19.2 35.8
80–84 165 12.3 14.1 8.6 65.0 9.2 0.0 37.4 25.8 36.8
85+ 113 3.6 7.1 10.7 78.6 8.0 0.0 32.7 26.6 40.7
TOTAL 7,658 25.9 25.3 16.9 31.9 10.8 0.3 75.2 12.4 12.4

Notes: NESB = non-English-speaking background (participants who were born outside Australia and reported a language other than English as their first language spoken); ATSI = Aboriginal and Torres Strait Islander.

aNumber of reported health conditions (0 = no health conditions, 1 = one health condition, 2+ = two or more conditions).

### Exclusion and Inclusion Criteria

Participants were immediately excluded if they were not asked (principally because they were interviewed by telephone), refused, were unable to complete the SDMT, or received outside assistance to complete the test. Of those with missing SDMT data (n = 926, 5.8%), 175 respondents were unable to understand the instructions, 630 respondents refused testing, and 121 respondents started but did not complete the test. A further 49 respondents were reported by interviewers as receiving outside assistance and excluded. A priori, a set of physical and neurological conditions were identified as factors that may limit performance on the SDMT. These self-reported health conditions, impairments, and disabilities were evaluated as potential confounders and, therefore, potential exclusion criteria. These conditions included: sight problems not corrected by glasses/lenses; blackouts, fits, or loss of consciousness; difficulty learning or understanding things; long-term effects as a result of a head injury, stroke, or other brain damage; limited use of arms or fingers; difficulty gripping things; and any disfigurement or deformity. Those physical and neurological conditions that independently predicted lower SDMT scores after controlling for the effect of socio-demographic factors (as described in Statistical Methods) were used as exclusion criteria.

Previous substitution task norms studies reporting population-based data have excluded cases with clinically diagnosed common psychiatric disorders (e.g., Gonzalez et al., 2007; Wang et al., 2011). However, given that the SDMT is designed to assess neurological disorders (cerebral dysfunction) and as there were no standardized clinical DSM or ICD diagnoses, a more inclusionary approach was adopted. This approach retains participants who report health conditions that are common in the general community (particularly among older populations) and not directly implicated in SDMT performance. Health conditions, impairments, and disabilities that were not considered as exclusions included: speech problems; a nervous or emotional condition which requires treatment; any mental illness which requires help or supervision; hearing difficulties; limited use of feet or legs; any condition that restricts physical activity or physical work (e.g., back problems and migraines); a long-term condition or ailment which is still restrictive even though it is being treated or medication being taken for it; shortness of breath or difficulty breathing; chronic or recurring pain; and any other long-term condition.

### Symbol Digit Modalities Test

The SDMT (Smith, 2007) was administered in English by trained interviewers to participants individually. Participants were required to use a coded key to match nine abstract symbols paired with numerical digits. Participants were given 10 practice items before commencing the test. The final score is the correct number of substitutions in 90 s, and scores range between 0 and 110. Only the written response format of the SDMT was administered.

### Statistical Methods

Multivariate linear regression (Equation (1)) was used to test for independent predictors of SDMT scores. The results of the regression analysis were used to assess the optimal age and education subgroups for norms generation, identify exclusions, and investigate if non-exclusionary health conditions were associated with lower SDMT scores. Interaction terms between gender, educational attainment, and age were also tested.

(1)
$SDMT=β0+β1iagegroup+β2gender+β3ieducationalattainment+β4non-English-speakingbackground+β5AboriginalandTorresStraitIslander+β6ihealthcondition+ε$
where β1i is a vector of coefficients for 14 dummy-coded age groups, β2 is the coefficient for gender, β3i is a vector of coefficients for 3 dummy-coded education levels, β4 is the coefficient for non-English-speaking background, β5 is the coefficient for Aboriginal and Torres Strait Islander status, and βik is a vector of coefficients for the 17 health conditions (see Table 2 for model estimates).
Table 2.

Results from linear regression predicting Symbol Digits Modalities Test (SDMT) scores (N = 15,101)

Variable B SE (95% CI)
Intercept 59.59*** 0.36 (58.89, 60.29)
Age group (reference: 15–19)
20–24 −1.36*** 0.39 (−2.12, −0.61)
25–29 −1.52*** 0.40 (−2.30, −0.74)
30–34 −2.24*** 0.42 (−3.06, −1.42)
35–39 −3.76*** 0.41 (−4.57, −2.95)
40–44 −4.55*** 0.41 (−5.35, −3.76)
45–49 −6.60*** 0.41 (−7.40, −5.80)
50–54 −7.83*** 0.41 (−8.63, −7.03)
55–59 −9.40*** 0.42 (−10.23, −8.58)
60–64 −11.77*** 0.44 (−12.64, −10.91)
65–69 −14.92*** 0.45 (−15.81, −14.03)
70–74 −18.62*** 0.50 (−19.59, −17.64)
75–79 −22.05*** 0.57 (−23.16, −20.94)
80–84 −25.24*** 0.63 (−26.48, −24.01)
85+ −29.45*** 0.76 (−30.94, −27.97)
Gender (reference: male)
Female 3.09*** 0.17 (2.76, 3.41)
Education (reference: tertiary)
Postsecondary, nontertiary −4.20*** 0.23 (−4.65, −3.76)
Completed high school −2.68*** 0.28 (−3.22, −2.14)
Year 11 or below −7.16*** 0.24 (−7.64, −6.68)
Cultural background
Non-English-speaking background −2.84*** 0.27 (−3.38, −2.30)
Aboriginal and Torres Strait Islander −3.96*** 0.51 (−4.96, −2.97)
Health conditions
Sight problems −1.71** 0.57 (−2.82, −0.59)
Speech problems −5.50*** 1.47 (−8.39, −2.61)
Blackouts and loss of consciousness −3.22** 1.01 (−5.19, −1.24)
Learning difficulties −6.55*** 0.84 (−8.18, −4.91)
Stroke or brain injury −3.22*** 0.88 (−4.95, −1.49)
Nervous or emotional condition −2.07*** 0.47 (−2.99, −1.15)
Mental illness −2.99*** 0.72 (−4.40, −1.57)
Hearing difficulties −0.06 0.43 (−0.91, 0.79)
Limited use of arms or fingers 0.15 0.62 (−1.07, 1.37)
Difficulty gripping things −0.30 0.64 (−1.55, 0.95)
Limited use of feet or legs −1.42** 0.44 (−2.29, −0.55)
Any condition that restricts physical activity −0.51 0.35 (−1.20, 0.18)
Any disfigurement −1.44 1.24 (−3.86, 0.99)
Shortness of breath −1.20* 0.50 (−2.18, −0.23)
Chronic pain −0.29 0.40 (−1.07, 0.48)
Requires treatment or medication −1.60*** 0.35 (−2.28, −0.91)
Other unspecified long-term conditions −1.02*** 0.30 (−1.60, −0.44)
Variable B SE (95% CI)
Intercept 59.59*** 0.36 (58.89, 60.29)
Age group (reference: 15–19)
20–24 −1.36*** 0.39 (−2.12, −0.61)
25–29 −1.52*** 0.40 (−2.30, −0.74)
30–34 −2.24*** 0.42 (−3.06, −1.42)
35–39 −3.76*** 0.41 (−4.57, −2.95)
40–44 −4.55*** 0.41 (−5.35, −3.76)
45–49 −6.60*** 0.41 (−7.40, −5.80)
50–54 −7.83*** 0.41 (−8.63, −7.03)
55–59 −9.40*** 0.42 (−10.23, −8.58)
60–64 −11.77*** 0.44 (−12.64, −10.91)
65–69 −14.92*** 0.45 (−15.81, −14.03)
70–74 −18.62*** 0.50 (−19.59, −17.64)
75–79 −22.05*** 0.57 (−23.16, −20.94)
80–84 −25.24*** 0.63 (−26.48, −24.01)
85+ −29.45*** 0.76 (−30.94, −27.97)
Gender (reference: male)
Female 3.09*** 0.17 (2.76, 3.41)
Education (reference: tertiary)
Postsecondary, nontertiary −4.20*** 0.23 (−4.65, −3.76)
Completed high school −2.68*** 0.28 (−3.22, −2.14)
Year 11 or below −7.16*** 0.24 (−7.64, −6.68)
Cultural background
Non-English-speaking background −2.84*** 0.27 (−3.38, −2.30)
Aboriginal and Torres Strait Islander −3.96*** 0.51 (−4.96, −2.97)
Health conditions
Sight problems −1.71** 0.57 (−2.82, −0.59)
Speech problems −5.50*** 1.47 (−8.39, −2.61)
Blackouts and loss of consciousness −3.22** 1.01 (−5.19, −1.24)
Learning difficulties −6.55*** 0.84 (−8.18, −4.91)
Stroke or brain injury −3.22*** 0.88 (−4.95, −1.49)
Nervous or emotional condition −2.07*** 0.47 (−2.99, −1.15)
Mental illness −2.99*** 0.72 (−4.40, −1.57)
Hearing difficulties −0.06 0.43 (−0.91, 0.79)
Limited use of arms or fingers 0.15 0.62 (−1.07, 1.37)
Difficulty gripping things −0.30 0.64 (−1.55, 0.95)
Limited use of feet or legs −1.42** 0.44 (−2.29, −0.55)
Any condition that restricts physical activity −0.51 0.35 (−1.20, 0.18)
Any disfigurement −1.44 1.24 (−3.86, 0.99)
Shortness of breath −1.20* 0.50 (−2.18, −0.23)
Chronic pain −0.29 0.40 (−1.07, 0.48)
Requires treatment or medication −1.60*** 0.35 (−2.28, −0.91)
Other unspecified long-term conditions −1.02*** 0.30 (−1.60, −0.44)

Notes:Includes participants later excluded from norms data due to sight problems not corrected by lenses, blackouts, fits and loss of consciousness, learning difficulties, and brain injury or stroke.

Non-English-speaking background: participants who were born outside Australia and reported a language other than English as their first language spoken. ATSI = Aboriginal and Torres Strait Islander; SE = standard error; 95% CI = 95% confidence interval.

*p < .05, **p < .01, ***p < .001

The population to which the SDMT norms reported in this paper relate are people aged 15 and over living in private dwellings, excluding very remote parts of Australia. Population survey weights provided with the HILDA Survey dataset adjust for selection probabilities and attrition bias to enhance the comparability of the data to the Australian population. As the SDMT was one part of the overall interview, further adjustments to these weights were made to account for noncompletion of the SDMT, adjusting for those who did not commence the SDMT or did not complete it unassisted. This additional step models the response propensity for the SDMT given the overall interview was completed and uses a range of individual characteristics such as the participant's language speaking ability, education level, mobility, geographic area, hours of work, and household structure. The nonresponse adjusted individual weight was multiplied by the inverse of the SMDT response propensity, giving higher weight to the participants who completed the SDMT and had similar characteristics to those who did not complete the SDMT.

SDMT norms were calculated as weighted means, SD, and quintiles stratified by gender, age group, and education level.

## Results

Compared with participants who completed the SDMT, those with missing SDMT data were more likely to be: older (odds ratio [OR] = 1.02, p < .001), male (OR = 1.16, p = .032); have lower levels of education (ORYear 12 = 1.57, p = .001; ORYear 11 = 2.67, p < .001); come from a non-English-speaking background (OR = 3.29, p < .001); be an Aboriginal or Torres Strait Islander (OR = 1.71, p = .005); or report a long-term health condition (OR = 1.78, p < .001).

Overall, the mean SDMT was 49.16 (SD = 13.14; range 0–110) with slightly negative skew (−0.33). The distributional shape was relatively stable across all subgroups. The results from linear regression analysis are presented in Table 2. Scores on the SDMT were relatively stable up to age 35, after which they declined with increasing age. Age differences were more pronounced after the age 55. When age was modelled as a continuous variable, there were significant quadratic and cubic age trends (results not reported). On average, scores were lower among respondents from non-English-speaking backgrounds (who were born outside Australia) compared with native English speakers, and Aboriginal and Torres Strait Islanders compared with non-indigenous Australians, but were higher for females compared with males. Of the health conditions considered as exclusion criteria, self-reported sight problems not corrected by lenses, blackouts, fits and loss of consciousness, learning difficulties, and brain injury or stroke all predicted lower SDMT scores. A total of 864 participants who reported these conditions were excluded from further analyses, these participants were more likely to be older (OR = 1.03, p < .001), nontertiary qualified (OR = 2.35, p < .001), and of Aboriginal or Torres Strait Islander origin (OR = 1.87, p = .003). Lower scores on the SDMT were also independently associated with speech problems (B = −5.50, p < .001), self-reported mental illness (B = −2.99, p < .001), nervous or emotional conditions (B = −2.07, p < .001), breathing difficulties (B = −1.20, p = .015), limited use of legs or feet (B = −1.42, p = .001), restrictive conditions requiring medication (B = −1.59, p < .001), and other unspecified health conditions (B = −1.02, p = .001), but these were not considered a priori reasons for exclusion from the published norms. Six hundred and seven respondents reported nervous or emotional conditions or mental illness and were retained for the reporting of norms.

There was evidence of a two-way interaction between gender and education: the gradient in SDMT scores across levels of educational attainment (i.e., those reporting lower levels of educational attainment having poorer SDMT scores) was stronger for males than for females (Supplementary material online, Table S1). To further investigate this, analysis of the sample stratified by 15-year age groups indicated that the interaction between gender and education was only evident in the mid-age and older age cohorts. Thus, there was no gender difference in the association between educational attainment and SDMT scores among respondents <30 years of age (Supplementary material online, Table S2).

After all exclusions, norms from the 14,456 participants were calculated. The remaining three tables present the normative data for the SDMT, by key characteristics. Tables 3 and 4 show the cell counts, weighted means, and SDs stratified by age group and level of education for males and females, respectively. Cell sizes ranged from 20 (females aged 70–74 who had completed Year 12 only) to 442 (males aged 15–19 who had completed Year 11 or less), the average cell size was 138.68 cases. Table 5 shows the cut points for the (weighted) means, SDs, 20th, 40th, 60th, and 80th percentiles for males and females by age group. The quintiles and means are relatively stable for younger age groups but start to decline between ages 35 and 39. For all subgroups, the upper bound of the lowest quintile was slightly less than 1 SD below the mean (between 3.3 and 0.2 units).

Table 3.

Cell frequencies, weighted SDMT means and SD for males by 5-year age group and level of education

Age group Tertiary

Postsecondary, nontertiary

Completed high schoola

Year 11 or below

n Mean (SDn Mean (SDn Mean (SDn Mean (SD
15–19       196 57.28 (13.35) 444 52.76 (12.05)
20–24 65 59.54 (9.38) 182 51.87 (12.10) 296 56.86 (9.52) 145 46.13 (11.80)
25–29 170 55.76 (7.74) 227 53.59 (11.91) 162 53.18 (9.72) 100 49.37 (11.55)
30–34 186 56.17 (9.62) 214 51.49 (9.82) 76 56.16 (9.49) 70 49.93 (10.82)
35–39 191 56.07 (8.04) 238 50.93 (9.71) 82 50.67 (9.85) 62 45.62 (11.97)
40–44 180 55.63 (9.86) 255 49.37 (9.67) 57 51.31 (10.25) 93 44.08 (10.76)
45–49 162 52.79 (8.69) 251 46.14 (9.83) 42 50.57 (7.22) 134 45.19 (10.28)
50–54 148 48.91 (9.92) 271 45.89 (8.81) 47 46.27 (8.77) 115 41.68 (10.56)
55–59 153 47.60 (9.28) 195 46.15 (10.48) 42 43.53 (11.45) 99 39.80 (9.66)
60–64 101 47.60 (7.90) 170 42.59 (9.25) 38 40.35 (9.54) 106 39.14 (10.60)
65–69 87 45.13 (8.57) 143 39.00 (10.20) 29 40.19 (10.50) 104 35.15 (10.74)
70–74 49 41.13 (9.26) 114 34.60 (10.43) 25 37.85 (10.60) 84 31.10 (10.51)
75–79       129 31.70 (10.69) 71 26.21 (10.02)
80–84       65 30.85 (11.23) 57 23.07 (9.59)
85+       46 26.54 (8.52) 25 25.86 (8.78)
Age group Tertiary

Postsecondary, nontertiary

Completed high schoola

Year 11 or below

n Mean (SDn Mean (SDn Mean (SDn Mean (SD
15–19       196 57.28 (13.35) 444 52.76 (12.05)
20–24 65 59.54 (9.38) 182 51.87 (12.10) 296 56.86 (9.52) 145 46.13 (11.80)
25–29 170 55.76 (7.74) 227 53.59 (11.91) 162 53.18 (9.72) 100 49.37 (11.55)
30–34 186 56.17 (9.62) 214 51.49 (9.82) 76 56.16 (9.49) 70 49.93 (10.82)
35–39 191 56.07 (8.04) 238 50.93 (9.71) 82 50.67 (9.85) 62 45.62 (11.97)
40–44 180 55.63 (9.86) 255 49.37 (9.67) 57 51.31 (10.25) 93 44.08 (10.76)
45–49 162 52.79 (8.69) 251 46.14 (9.83) 42 50.57 (7.22) 134 45.19 (10.28)
50–54 148 48.91 (9.92) 271 45.89 (8.81) 47 46.27 (8.77) 115 41.68 (10.56)
55–59 153 47.60 (9.28) 195 46.15 (10.48) 42 43.53 (11.45) 99 39.80 (9.66)
60–64 101 47.60 (7.90) 170 42.59 (9.25) 38 40.35 (9.54) 106 39.14 (10.60)
65–69 87 45.13 (8.57) 143 39.00 (10.20) 29 40.19 (10.50) 104 35.15 (10.74)
70–74 49 41.13 (9.26) 114 34.60 (10.43) 25 37.85 (10.60) 84 31.10 (10.51)
75–79       129 31.70 (10.69) 71 26.21 (10.02)
80–84       65 30.85 (11.23) 57 23.07 (9.59)
85+       46 26.54 (8.52) 25 25.86 (8.78)

Notes:aDue to small cell sizes, tertiary and postsecondary education levels were collapsed to “completed high school” for age groups 15–19, 75–79, 80–84, and 85+.

Data exclude people reporting sight problems not corrected by lenses, blackouts, fits and loss of consciousness, learning difficulties, and brain injury or stroke.

Table 4.

Cell frequencies, weighted SDMT means and SD for females by 5-year age group and level of education

Age group Tertiary

Postsecondary, nontertiary

Completed high schoola

Year 11 or below

n Mean (SDn Mean (SDn Mean (SDn Mean (SD
15–19       262 59.48 (11.27) 422 55.45 (10.56)
20–24 128 61.34 (9.71) 189 57.96 (11.45) 326 59.04 (10.01) 119 52.57 (10.54)
25–29 253 58.47 (9.18) 221 55.47 (10.84) 138 56.85 (9.98) 90 53.97 (10.68)
30–34 264 57.73 (9.63) 182 57.51 (11.04) 87 55.75 (11.30) 63 49.57 (10.83)
35–39 261 56.87 (9.14) 196 54.60 (11.03) 87 54.32 (10.44) 99 50.20 (11.04)
40–44 242 57.06 (9.03) 204 53.28 (10.44) 97 52.26 (9.86) 153 50.69 (10.36)
45–49 198 53.60 (10.81) 198 50.67 (10.14) 85 51.13 (11.10) 173 45.90 (11.63)
50–54 198 51.93 (7.74) 201 50.83 (9.08) 65 50.92 (13.00) 184 47.49 (11.78)
55–59 154 51.19 (9.66) 167 48.70 (9.53) 59 46.22 (10.09) 195 45.60 (10.58)
60–64 113 48.23 (10.89) 126 43.49 (9.62) 37 45.85 (12.39) 213 42.58 (12.25)
65–69 79 43.53 (10.98) 91 42.92 (10.01) 35 42.26 (8.14) 219 38.97 (10.59)
70–74 40 40.56 (8.22) 63 38.00 (10.18) 20 39.80 (11.36) 188 35.07 (11.59)
75–79       64 37.97 (9.65) 129 32.00 (10.89)
80–84       57 32.34 (11.53) 108 28.31 (10.09)
85+       24 27.37 (6.62) 88 22.62 (8.84)
Age group Tertiary

Postsecondary, nontertiary

Completed high schoola

Year 11 or below

n Mean (SDn Mean (SDn Mean (SDn Mean (SD
15–19       262 59.48 (11.27) 422 55.45 (10.56)
20–24 128 61.34 (9.71) 189 57.96 (11.45) 326 59.04 (10.01) 119 52.57 (10.54)
25–29 253 58.47 (9.18) 221 55.47 (10.84) 138 56.85 (9.98) 90 53.97 (10.68)
30–34 264 57.73 (9.63) 182 57.51 (11.04) 87 55.75 (11.30) 63 49.57 (10.83)
35–39 261 56.87 (9.14) 196 54.60 (11.03) 87 54.32 (10.44) 99 50.20 (11.04)
40–44 242 57.06 (9.03) 204 53.28 (10.44) 97 52.26 (9.86) 153 50.69 (10.36)
45–49 198 53.60 (10.81) 198 50.67 (10.14) 85 51.13 (11.10) 173 45.90 (11.63)
50–54 198 51.93 (7.74) 201 50.83 (9.08) 65 50.92 (13.00) 184 47.49 (11.78)
55–59 154 51.19 (9.66) 167 48.70 (9.53) 59 46.22 (10.09) 195 45.60 (10.58)
60–64 113 48.23 (10.89) 126 43.49 (9.62) 37 45.85 (12.39) 213 42.58 (12.25)
65–69 79 43.53 (10.98) 91 42.92 (10.01) 35 42.26 (8.14) 219 38.97 (10.59)
70–74 40 40.56 (8.22) 63 38.00 (10.18) 20 39.80 (11.36) 188 35.07 (11.59)
75–79       64 37.97 (9.65) 129 32.00 (10.89)
80–84       57 32.34 (11.53) 108 28.31 (10.09)
85+       24 27.37 (6.62) 88 22.62 (8.84)

Notes:aDue to small cell sizes, tertiary and postsecondary education levels were collapsed to “completed high school” for age groups 15–19, 75–79, 80–84, and 85+.

Data exclude people reporting sight problems not corrected by lenses, blackouts, fits and loss of consciousness, learning difficulties, and brain injury or stroke.

Table 5.

Weighted SDMT means, SDs, and percentiles for males and females by age group

Age group Males

Females

Mean (SD20th percentile 40th percentile 60th percentile 80th percentile Mean (SD20th percentile 40th percentile 60th percentile 80th percentile
15–19 54.09 (12.31) 45 50 56 63 56.91 (11.25) 49 54 58 65
20–24 53.98 (11.27) 46 51 57 63 58.21 (10.97) 50 56 61 67
25–29 53.74 (9.79) 46 50 56 62 56.87 (10.36) 49 54 60 65
30–34 53.87 (10.00) 46 50 57 63 56.63 (10.91) 48 55 59 66
35–39 52.29 (9.66) 44 50 55 60 54.66 (10.79) 47 52 58 63
40–44 50.71 (10.44) 43 48 53 60 53.80 (10.45) 46 52 57 62
45–49 48.23 (9.76) 40 46 51 57 50.16 (11.61) 41 48 53 60
50–54 45.92 (9.56) 38 44 49 53 50.20 (10.41) 43 49 53 59
55–59 44.92 (10.30) 36 43 49 53 47.91 (10.59) 39 47 50 57
60–64 42.58 (9.68) 34 41 46 51 44.22 (11.97) 35 43 48 53
65–69 39.14 (10.58) 31 37 42 49 40.95 (10.76) 33 40 45 49
70–74 34.79 (10.65) 26 32 38 44 36.65 (11.40) 28 35 40 46
75–79 29.76 (10.54) 20 28 32 39 33.97 (11.13) 24 31 36 44
80–84 27.08 (10.87) 18 23 29 38 29.53 (10.92) 19 28 32 39
85+ 26.29 (8.42) 19 23 29 34 23.55 (8.77) 15 18 25 32
Age group Males

Females

Mean (SD20th percentile 40th percentile 60th percentile 80th percentile Mean (SD20th percentile 40th percentile 60th percentile 80th percentile
15–19 54.09 (12.31) 45 50 56 63 56.91 (11.25) 49 54 58 65
20–24 53.98 (11.27) 46 51 57 63 58.21 (10.97) 50 56 61 67
25–29 53.74 (9.79) 46 50 56 62 56.87 (10.36) 49 54 60 65
30–34 53.87 (10.00) 46 50 57 63 56.63 (10.91) 48 55 59 66
35–39 52.29 (9.66) 44 50 55 60 54.66 (10.79) 47 52 58 63
40–44 50.71 (10.44) 43 48 53 60 53.80 (10.45) 46 52 57 62
45–49 48.23 (9.76) 40 46 51 57 50.16 (11.61) 41 48 53 60
50–54 45.92 (9.56) 38 44 49 53 50.20 (10.41) 43 49 53 59
55–59 44.92 (10.30) 36 43 49 53 47.91 (10.59) 39 47 50 57
60–64 42.58 (9.68) 34 41 46 51 44.22 (11.97) 35 43 48 53
65–69 39.14 (10.58) 31 37 42 49 40.95 (10.76) 33 40 45 49
70–74 34.79 (10.65) 26 32 38 44 36.65 (11.40) 28 35 40 46
75–79 29.76 (10.54) 20 28 32 39 33.97 (11.13) 24 31 36 44
80–84 27.08 (10.87) 18 23 29 38 29.53 (10.92) 19 28 32 39
85+ 26.29 (8.42) 19 23 29 34 23.55 (8.77) 15 18 25 32

Notes: Data exclude people reporting sight problems not corrected by lenses, blackouts, fits and loss of consciousness, learning difficulties, and brain injury or stroke.

## Discussion

The SDMT is a widely used neuropsychological instrument which assesses divided attention, perceptual processing speed, visual scanning, and memory (Strauss et al., 2006). The utility of the test and interpretation of individual test scores can be enhanced by the availability of robust comparison data, particularly if differentiated by important population characteristics to interpret individual scores. The aim of this study was to report nationally representative normative data for the SDMT in a large sample, separately by gender, with a broad age range, narrow age groups, and four levels of educational attainment. Our results indicate that the SDMT is significantly associated with age, gender, education, cultural background, and health. There was a strong nonlinear effect of age, and the linear regression estimates did not support the reporting of norms for age bands >5 years. The enhanced performance among females may be explained by their superior verbal encoding of the abstract symbols (Lezak, 2004; Van der Elst, Dekker, Hurks, & Jolles, 2012). For those aged 30 years and older, the association between educational attainment and SDMT scores was stronger for males than for females, but this was not the case for the youngest age groups. This is likely to reflect the greater access to higher education for women from younger cohorts. Interestingly, self-reported limitations with fingers or hands, difficulty gripping objects and other physical impairments did not predict performance on the SDMT, despite requiring written responses. One explanation for this finding is that performance on the SDMT is primarily underpinned by central cognitive processes rather than peripheral fine-motor function.

Although participants with self-reported mental illness, nervous conditions, or other health conditions requiring treatment or medication were not excluded, these participants generally performed worse compared with those without such long-term health conditions. Our findings suggest that the presence of a common psychiatric disorder may result in an average performance deficit of three symbol digit pairings. Depending on a person's gender, age, and level of education, this corresponds to between one quarter to one third of a SD below mean performance levels.

The SDMT is purported to be appropriate for people with speech disorders, relatively free from cultural bias, and suitable for people for whom the testing language is not their native language (Smith, 2007; WPS, 2014). Nevertheless, the three relevant measures included in the present analyses were all independently associated with significantly poorer performance. The presence of a speech problem was one of the strongest predictors of lower SDMT scores, and was associated with a loss in performance of approximately half a SD. It is possible that speech problems are markers of other unobserved disadvantage. Indigenous Australians and those with non-English-speaking backgrounds tended to perform more poorly than non-indigenous Australians and native English speakers. This finding is consistent with previous studies that have examined the effects of culture, ethnicity, and race on the SDMT (Agranovich et al., 2011; Kennepohl et al., 2004) and could be due to the language of the test administration, or familiarity and prior experience with neuropsychological testing. Alternatively, these cultural factors may be markers of social disadvantage and poor-quality education.

Cultural, cohort, and personal attitudes and values could also underlie differences in neuropsychological test performance. For example, cross-national differences have been demonstrated between American and Russian or European populations on the SDMT and similar speeded tasks, which may reflect American attitudes that value faster performance over precision (Agranovich et al., 2011; Roivainen, 2010). Similarly, it is conceivable that cross-sectional age differences in SDMT could, in part, be attributed to older adults' tendency to place greater value on accuracy, whereas younger cohorts value faster performance. However, this explanation is countered by the numerous longitudinal studies that have consistently demonstrated intraindividual change in substitution task performance over time (e.g., Bielak, Anstey, Christensen, & Windsor, 2012; MacDonald, Hultsch, Strauss, & Dixon, 2003; Sacktor et al., 2010; Sliwinski & Buschke, 1999). Clearly, a range of noncognitive factors must be taken into account when analyzing and interpreting SDMT scores, including an individual's health status, acculturation and cultural values, attitudes towards neuropsychological testing, and the context of the test administration.

Though our results are generally consistent with previous studies, the age group means in the HILDA Survey data are slightly higher than those reported by Centofanti (1975, cited in Sheridan et al., 2006) and Pena-Casanova and colleagues (2009), but lower than those reported by Jorm and colleagues (2004) and Yeudall and colleagues (1986). These differences likely reflect both differences in the sampled populations, and methodological differences in generating age norms. The differences with Centofanti's original study could be attributed to a birth cohort (the Flynn) effect. In contrast, Yeudall and colleagues (1986) analyzed data from a volunteer sample which may be subject to stronger selection bias than our sample, whereas Jorm and colleagues (2004) analyzed representative data from three narrow age cohorts (20–24, 40–45, and 60–64) in Canberra, Australia, a region with higher levels of education attainment compared with the general Australian population.

### Limitations

The presented norms need to be interpreted within the context of the study's limitations. Data on health conditions were obtained by self-report, and only conditions that were considered by participants to be long term (>6 months) were recorded. It is, therefore, possible that our sample includes participants with neurological conditions that are not perceived to be long-term health conditions. Although the presented analyses adjusted for non-English-speaking background and Indigenous status, norms for specific cultural groups within Australia have not been reported. The HILDA survey lacks information on other potentially important cultural and racial factors. It is therefore unclear how these results apply to people from other cultural backgrounds. There remains a need for culturally, nationally, and language-specific norms (Gonzalez et al., 2007; Pena-Casanova et al., 2009; Strauss et al., 2006; Wang et al., 2011). Only data for the written version of the SDMT are presented. There is a lack of published normative data for the verbal response modality, which should be expected to yield higher scores (Sheridan et al., 2006). Though the HILDA Survey provided a large overall sample size, there remained small cell counts (n < 30) among some older subgroups. In some contexts, it may be necessary to generate norms from more specific subpopulations (e.g., people with speech disorders).

Despite these limitations, the normative data presented here are representative of the Australian population and directly relevant to Australian research. In addition, compared with other norms published for the SDMT, the scope and scale of the norms reported in this paper provide a valuable benchmark for international research with a general population and should be useful in a broad range of both clinical and research settings. The use of weights specific to participants completing the SDMT facilitated inference about the population based on the sample as it adjusts for nonrandom nonresponse, attrition, and for mode selection effects. Finally, the large size of the HILDA Survey sample enabled the measurement of gender, age, and education-specific norms with a greater degree of precision, and generalizability than was previously possible.

## Funding

KK is supported by an Alzheimer's Australia Dementia Research Foundation (AADRF) Fellowship (#DGP13F00005). PB is supported by Australian Research Council (ARC) Future Fellowship (#FT130101444). This paper uses unit record data from the Household, Income and Labour Dynamics in Australia Survey, a project initiated and funded by the Australian Government Department of Social Services (DSS) and managed by the Melbourne Institute of Applied Economic and Social Research. The findings and views reported in this paper, however, are those of the authors and should not be attributed to either DSS or the Melbourne Institute. The data are available for research purposes under license. Details of how to obtain the data can be found at http://melbourneinstitute.com/hilda/.

None declared.

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