Page 1

ABSTRACT. Background and aims: The influ-

ence of sociobiological variables and aging on

the variability of the Trail Making Tests (TMT), the

Symbol Digit Substituting Test (SDT), and the

Line Trait Test (LTT) in the general healthy pop-

ulations are not well known. Even less is known

about the reliability at re-testing. This study aimed

at determining the reference range of these tests,

taking into account sociobiological variables and

age, and the re-testing effect. Methods: We stud-

ied 300 healthy subjects from 20 to 80 years of

age. The sample was derived by the pooling of two

samples stratified by age and sex: a randomized

sample of 161 subjects collected from the city reg-

isters of Padova, and a convenience sample of 139

subjects collected in 20 towns (mainly rural) of

Northern Italy. After normalization, data were

assayed for the influence of age, education, job,

and gender. Results: Age was found to be a sig-

nificant independent predictor for all the tests, ed-

ucation for all but the LTT, job only for the TMT-

B and a geometrical version of the same test

(TMT-G) which was proved to be highly correlated

with the TMT-B (r=0.80, p<0.01). J ob and the in-

teraction age × education level influenced the

difference TMT-B minus TMT-A. From the pre-

dicting equations, the normative data and the

formulas to obtain Z scores for each test were de-

rived. Reliability was lowest for L TT errors

(CV=67%), highest for the SDT (13%), whereas

the TMT obtained intermediate values (22-33%,

depending on the test). Conclusions: This study

provides the most reliable normative data range

for the TMT, SDT and LTT to date because it con-

siders important demographic variables such as

age, education and job.

(Aging Clin Exp Res 14: 117-131, 2002)

©2002, Editrice Kurtis

INTRODUCTION

The Trail Making Test (TMT), comprised of two

tasks (TMT-A and TMT-B), was developed by Reitan

(1) on the basis of the Taylor number series in order

to detect organic brain damage (1, 2). Zeegen (3)

applied the TMT in evaluating patients who un-

derwent port-caval shunt, and Conn (4) used the

TMT-A (renamed Number Connection Test, NCT)

as a parameter to quantify hepatic encephalopathy

(5). Indeed, the TMT has a wide applicability; it

has been used to test early stages of cognitive de-

terioration (6), dementia (7), cognitive dysfunction in

HIV positive patients (8), and in head trauma (9).

Nonetheless, demographic factors influence its vari-

ability, and their weight in assessing reference

ranges is disputed. Parsons et al. (10) found many

false positives in normal controls applying Reitan’s

criteria of normality. Age and education were found

to influence the TMT in some studies (10), in others

intelligence seemed to be the only significant pre-

dictor (11). More recently, Weissenborn et al. (12),

Giovagnoli et al. (13) and Amodio et al. (14) sug-

gested a parametric approach based on multivariate

regression to define the reference ranges of the

TMT. In the study of Weissenborn et al. (12) age,

education, and job appeared significant predictors of

117Aging Clin Exp Res, Vol. 14, No. 2

Aging Clinical and Experimental Research

Variability of Trail Making Test, Symbol Digit Test and

Line Trait Test in normal people. A normative study

taking into account age-dependent decline and

sociobiological variables

Piero Amodio1, Helmut Wenin1, Franco Del Piccolo1, Daniela Mapelli1,2, Sara Montagnese1, Andrea

Pellegrini1, Carmine Musto1, Angelo Gatta1, and Carlo Umiltà2

1Department of Clinical and Experimental Medicine, 2Department of General Psychology, University of

Padova, Padova, Italy

Key words: Line Trait Test, healthy people, psychometric performance, reference values, Symbol Digit Test, Trail Making Test.

Correspondence: P. Amodio, M.D., Clinica Medica 5, Via Giustiniani 2, 35128 Padova, Italy. E-mail: piero.amodio@unipd.it

Received August 2, 2001; accepted in revised form December 20, 2001.

Page 2

TMT variability in the normal population, whereas

Giovagnoli et al. (13) considered only age and ed-

ucation.

The Symbol Digit Test (SDT) (15), and similar

symbol-substitution tasks like the Digit Symbol Test

(16), have also been used to assess the extent of or-

ganic brain damage, and to detect and quantify

mild hepatic encephalopathy for many years (17-

19). A performance decline on the SDT is a well-

documented correlate of aging (20). Other recog-

nized variability factors are education (21) and,

possibly, gender (22).

More recently, the Line Trait Test (LTT) was in-

troduced by Hamster (23), mainly to study hepatic

encephalopathy, and to discriminate alcoholic from

liver-related encephalopathy (24). Only age was

considered as a variable influencing LTT perfor-

mance in the normalization studies conducted in

Germany (25, 26).

As a whole, despite the popularity of these tests,

the factors affecting their variability in the general

healthy population (in particular, the Italian popu-

lation) are not well known, and therefore even less

is known about the weight that such factors might

have in the assessment of reference values.

The aim of the present study was to determine

the major demographic factors predicting the vari-

ability of the TMT, SDT, and LTT in normal sub-

jects. We also assessed the applicability of a geo-

metric variant of the TMT-B in which the alphabet

sequence is substituted by a geometrical one; this

variation may overcome problems arising from the

use of the TMT-B alphabetic sequence in modern

multiethnic societies in which people with poor

knowledge of the Roman alphabet is common (18,

27).

METHODS

Participants

Two samples were considered:

1. A randomized sample collected from the elec-

toral register of the city of Padova by random num-

bers was stratified according to sex and age in order

to have participants for each of the following age

classes: 18-30 years, 31-40 years, 41-50 years, 51-

60 years, 61-70 years, and 71-80 years. For each

age group, 60 subjects (30 males and 30 females)

were selected; the first 30 subjects (balanced by

gender) constituted the interviewed group, while

the second 30 subjects served as a reserve for sub-

stituting non-cooperative or excluded subjects.

2. A convenience sample from 20 towns and ru-

ral villages of North Italy was collected among the

acquaintances of the students of the University of

Padova and referred to our team.

The subjects of both groups underwent a struc-

tured interview reporting demographic data (birth

date, sex, education, job, marital status) and medi-

cal history. J ob was classified as “blue collar” and

“white collar”. “Blue collar” workers consisted of

craftsmen, farmers, housewives, nurses and hospi-

tal technical staff. Their daily work was predomi-

nantly manual. “White collar” workers consisted

of clerks, students, technical assistants, tradesman,

secretaries and university graduates. Additionally, as

regards the Italian education system, 4 groups were

defined according to years of formal education: at

least 5 years (grade of education: 1); at least 8

years (grade of education: 2); at least 13 years

(grade of education: 3); and qualification for a uni-

versity degree (17 years, grade of education: 4).

However, all subjects were required to have a fair

knowledge of the numerical and Italian alphabetical

sequence.

Exclusion criteria were: subjects not found at

home after five attempts; refusal to participate in the

study; less than 5 years of education (elementary

school in Italy); alcohol consumption >70 g/day for

males or 40 g/day for females; severe hypertension

(duration greater than 5 years and requiring two or

more drugs); history of coronary heart disease or

cerebrovascular disease, insulin-treated diabetes,

severe renal, liver or pulmonary disease; psychiatric

history or consumption of psychotropic drugs; his-

tory of any kind of cerebral disease. Following their

informed consent, each participating subject un-

derwent the 5 paper and pencil psychometric tests

in random sequence.

Psychometric tests

The five tests were: 1) the TMT-A, 2) the TMT-

B, 3) a geometric version of the TMT-B, that we

named TMT-G, 4) the SDT, and 5) the LTT.

1) The TMT-A (1, 2) consisted of 25 circles with

a diameter of 2 cm (thickness 0.2 mm) numbered

from 1 to 25, written with the font Arial 24 (height

5 mm, thickness 0.7 mm) (Fig. 1). An initial demon-

stration was performed to familiarize the subjects

with the test, then a variation of equal difficulty

was used. The subject’s task was to connect the cir-

cles in sequential order as rapidly as possible.

2) The TMT-B (1, 2) consisted of 25 circles with

a diameter of 2 cm containing numbers from 1 to

13 and 12 letters from A to N, all written using the

font Arial 24 (Fig. 1). The letters “M” and “N”

substituted for the letters “J ” and “K” of the original

form because the Italian alphabet does not con-

TMTs, SDT, LTT in normal subjects

Aging Clin Exp Res, Vol. 14, No. 2 118

Page 3

tain these letters. The task was to connect the circles

in sequential order alternating between numbers

and letters as rapidly as possible.

3) The TMT-G consisted of 8 circles (diameter

1.75 cm, thickness 0.2 mm), 8 squares (side 1.85

cm), and 8 crosses (height 1.95 cm), each con-

taining a number from 1 to 8 written in font Arial

24. The figures and numbers were placed on an A4

sheet using random numbers (Fig. 1). The task was

to connect the circle, the square, and the cross

containing the number 1, then the circle, the square

and the cross containing the number 2, and so on

P. Amodio, H. Wenin, F. Del Piccolo, et al.

119 Aging Clin Exp Res, Vol. 14, No. 2

TMT-A

TMT-BTMT-G

4

8

1

start

end

8

5

2

6

7

4

1

2

4

2

7

6

6

7

8

M

2

3

5

1

3

5

3

end

13

12

1

7

6

N

F

A

G

H

C

3

4

9

8

start

5

B

D

i

10

25

10

23

11

8

E

L

24

22

11

21

20

16

15

18

19

3

13

2

17

14

5

7

1

end

start

9

6

4

12

SYMBOL DIGIT TESTLINE TRAIT TEST

1

2

3

4

5

6

7

8

9

L

U

0

V

X

=

T

–

U

TT

TT

TT

U

U

U

U

U

V V

L X –

–

U L

L

–

–

U

L

–

0

T

T

U

V

L

X

U

–

L

0

T

U

V

X

–

–

U

L

L

U

L

–

0

V T

T

T

U

U

V

L

X

– U

L

–

U

L

0

0

UU

U

V

X

X

V

=

T

T

T

U

U

V

X

L

–

U L

0

0

U

U

U

V

X

V

=

= L

0 –

0

=

=–

0 X

=

V

X U

=

X

X

=

0

V

=

V

=

U

0

X

X 0

V

=

U

=

Figure 1 - The tests used in the study. On the top: the TMT-A, the TMT-B, and the TMT-G; on the bottom: the SDT and the LTT.

Page 4

up to number 8 as rapidly as possible. In this way,

the subject has to pay attention both to the se-

quence of the geometric figures and to that of the

numbers. The subject was aided because the correct

sequence of geometric figures was reported on the

top of the form.

In the TMT-A, TMT-B and TMT-G (TMTs), when

the subject makes an error, he/she is required to

correct it and continue in the proper sequence.

Errors therefore add to the overall time required to

complete the task.

Moreover, the differences between TMT-B minus

TMT-A (TMTB-A) and the difference between TMT-

G minus TMT-A (TMTG-A) were examined, since

they depend on shifting ability, reflecting attention

capacity (28).

4) The SDT (15, 29) consisted of 5 rows each

containing 25 cases for a total of 125 cases (squares

of 14 × 7 mm); each case contained one of nine

symbols in the top half of the square and was emp-

ty in the bottom half. On the top of the form,

there was the key to the test: 9 cases containing the

nine symbols on the upper half and the corre-

sponding digits on the bottom half (Fig. 1). The

character used was Arial 20. The task was to fill as

many as possible of the empty half-squares with the

digit corresponding to each symbol in 90 seconds.

The operator filled in the first three cases, the sub-

sequent seven served as a practice. Time was mea-

sured from the tenth case onward.

5) The LTT (25) consisted of a 4 mm-wide con-

torted track drawn by two parallel lines (thickness

0.4 mm) (Fig. 1). The task was to draw quickly a line

inside the track and avoid touching the borders of

the track itself. Both the errors and the time to

complete the track were considered. The errors

were the number of times that the drawn line

touched or crossed the limits of the track, and were

counted by a transparent template that allowed a dif-

ferent weight of the errors depending on their am-

plitude. A variant was introduced with respect to the

original LTT evaluation: a variable, time × errors,

was used based on the observation that the time and

errors in performing the test were linked to each

other, i.e., the faster the performance, the greater

the number of errors [LTT errors =135 – 25 × Ln

(LTT time); r=0.32, p<0.001].

Test reliability

To assess the reliability of the tests, 24 subjects in

the convenience sample were re-tested a day after

the first trial.

Statistics

The raw data for each test were checked by the

Kolmogorov-Smirnov test for normality using Lil-

liefors probabilities. Since the data of no test fitted

the Gaussian distribution, after visual inspection

different transform functions were applied to nor-

malize the data for each test (see note on bottom of

Table 2).

Test results of the random and the convenience

samples were compared by ANCOVA adjusting for

age and education.

The education levels effective in explaining the

variability of each test were assessed by ANCO-

TMTs, SDT, LTT in normal subjects

Aging Clin Exp Res, Vol. 14, No. 2 120

Table 1 - Demographic characteristics of the subjects enrolled in the study.

Age (years)No. of subjectsRandom sample

(N=161)

Convenience sample

(N=139)

Males

(%)

Education level *

(%)

2

Males

(%)

Education level

(%)

2134134

18-30 30500126622530265816

31-40 47523214531440404020

41-50 5537415225947836479

51-60 6348197264850 25392214

61-70 544824102838555017330

71-80 515924183523464615318

Totals30048111438374918313912

* Education levels: 1= 5 years, 2= 8 years, 3= 13 years, 4= ≥17 years.

Page 5

VA, adjusting for age and job (blue vs white collars),

and post-hoc assessment by the Scheffé test.

The role of age, education levels, job and gender

to explain the variability of each test was assessed by

multiple regression. Moreover, a variable indicating

the group of origin (convenience or randomized) was

used to verify that the pooling of the two samples

was correct.

The reference ranges of the tests were calculated

from the predictive equations, adjusting the standard

errors by functions that allow a better fit to the

empirical findings.

Reliability was measured by the coefficient of re-

peatability according to Bland and Altman (30), i.e., by

the standard deviations of the repeated measuring, and

by a coefficient of variability given by the ratio of

the coefficient of repeatability to the mean value of the

test. This technique provides clear information, since

a repeated measure has 95% probability of falling in

the interval twice the coefficient of repeatability with

respect to the first measure (30). In addition, Pearson’s

coefficient of correlation between repeated measures

was calculated.

The package “Statistica 5.5” (StatSoft Inc., Tulsa,

Oklahoma, USA) was used for the statistical analysis.

RESULTS

Sample

Of the 360 subjects randomized from the elec-

toral register of the city of Padua, 161 were enrolled

in the study. One hundred ninety-nine subjects

were excluded: 1 for education less than 5 years, 37

for severe diseases or psychotropic drug consump-

tion, 4 for high alcohol consumption, 42 because

they had changed their residence, 100 denied their

consent, and 6 because their age group had been al-

ready completed.

The convenience sample comprised 139 sub-

jects fulfilling the same criteria adopted for the ran-

domized sample. To collect 139 subjects, 144 sub-

jects were considered: 5 were excluded because

an accurate interview disclosed alcohol abuse or

diseases considered in the exclusion list.

The demographic characteristics of the subjects

enrolled in the study are reported in Table 1.

Variability of psychometric tests and the ref-

erence values

The raw data did not show statistically significant

differences between the randomized and the con-

venience samples, except for the time of perfor-

mance of the LTT which was statistically, albeit

negligibly, higher in the random sample than in

the convenience sample (84±29 vs 74±29 sec,

p<0.001) where people seemed to give higher val-

ue to accuracy (27±28 vs 31±21 errors, p=0.23).

When the time of performance was weighted for ac-

curacy, there was no difference in the two samples

(230±81 vs 223±75 sec × errors, p=0.43). There-

fore the data of the randomized and convenient

samples were pooled together.

P. Amodio, H. Wenin, F. Del Piccolo, et al.

121 Aging Clin Exp Res, Vol. 14, No. 2

Table 2 - Comparison of normalized psychometric tests according to education levels.

5 years 8 years 13 years

≥17 yearsp∞

TMT-A0.26±0.02$,#,§

0.29±0.03*0.29±0.03*0.30±0.03*0.002

TMT-B0.21±0.02$,#,§

0.23±0.02*,#,§

0.24±0.02*,$

0.25±0.02*,$

0.003

TMT-G0.20±0.02$,#,§

0.23±0.02*0.24±0.02*0.24±0.02*0.001

TMTB-A

TMTG-A

SDT

4.24±0.66$,#,§

3.72±0.53*,#,§

3.41±0.54*,$

3.37±0.62*,$

0.034

4.51±0.56$,#,§

3.82±0.59*3.65±0.54*3.65±0.64*0.001

4.87±0.06$,#,§

4.75±0.10*,#,§

4.69±0.10*,$

4.69±0.10*,$

0.001

LTT-t4.45±0.36#

4.27±0.304.27±0.344.37±0.320.33

LTT-er3.52±0.80#,§

3.23±0.703.05±0.802.97±0.870.16

LTT-wt5.69±0.31$,#,§

5.41±0.29*5.34±0.355.42±0.310.58

∞ p-values adjusted for age and job (ANCOVA). p<0.05 with respect to education of 5 years *, 8 years $, 13 years #, ≥17 years § (Scheffé test for

multiple comparison was performed when ANCOVA was significant). t: time; er: errors; wt: weighted time; e: number of Euler, i.e., 2.71828.

Note: Transform functions applied for normalizing the distributions of crude psychometric test results: TMT-A: 1/Ln (TMT-A). TMT-B: 1/Ln (TMT-B). TMT-G:

1/Ln (TMT-G). TMT-B minus TMT-A: Ln (TMTB-A). TMT-G minus TMT-A: Ln (TMTG-A). SDT: Ln (160-SDT). LTT-t: Ln (LTTt). LTT-er: Ln (e + LTT-er).

LTT-wt: Ln LTT-wt

Page 6

The distribution of the data for each test showed

non-normality, therefore each test was normalized

according to an appropriate transform function

(see note on bottom of Table 2).

When adjusted for age and job, education level

was found to influence the TMTs, TMTB-A, TMTG-A

and SDT, but not the LTT (Table 2). The perfor-

mances of the TMT-A, TMT-G, and TMTG-A were

significantly lower in the subjects who had only 5

years of education (elementary school), whereas

those of the TMT-B, TMTB-Aand SDT were lower in

the subjects who had 5 years of education, inter-

mediate in the subjects who had 8 years of educa-

tion, and higher in the subjects who had 13 years of

education (high school) or more (University degree)

(Table 2).

Variables to indicate sampling (convenience or

randomized sampling), education levels, job, age,

and gender, and their interactions were used as

predictors in multiple regression models to assess

the combined influence that they may have in ex-

plaining the variability of psychometric tests. Of

the predictors considered, only age was found to ex-

plain significantly the variability of all the tests. In ad-

dition, education influenced the TMTs (p<0.01)

and SDT (p<0.001), while job influenced only the

TMT-B (p<0.001) and TMT-G (p<0.01). Gender

never entered as an independent predictor of any

test. An interaction between age and education in

the TMTB-Awas found (p<0.001).

In order to define the cut-off values, we calcu-

lated the regression equations and the standard

deviations (SD) for each test according to the pre-

dictors found to be significant, using differing equa-

tions for the various education levels. However, the

use of the mean +2 SD of the expected values to

define the upper limit of normality exaggerates

the widening effect for the upper end of the mod-

el (i.e., in older people) due to the exponential

models used to transform the raw data. There-

fore, to fit the empirical data and define the limits

of normal values in healthy people, we applied

equations progressively reducing the exponential in-

crease of the SD due to age progression (Tables 3

and 4, and Appendix). Visual inspection was ap-

plied to verify these concepts (Appendix). Applying

this principle, the adjusted value of a psychometric

test can be expressed as the standardized residual

from the actual value and the value expected by

age, and possibly other confounders (education

and job), according to the equations shown in the

Appendix.

TMTs, SDT, LTT in normal subjects

Aging Clin Exp Res, Vol. 14, No. 2 122

Table 3 - The limits of the reference range for the TMTs, LTT, and SDT.

AgeTMT-A (sec) TMT-B (sec) TMT-G (sec) SDT (items/90 sec)LTT-t (sec) LTT-er LTT-wt

years 5 y.*

≥8 y. 5 y.8-13 y. ≥13 y.

≥13 y.

White

collar

5 y

≥8 y.

Blue

collar

≥8 y

White

collar

5 y.8-13 y.

≥13 y.

Blue

collar

20463910093105821361008834404411561261

254942111101113881481099632374212067279

3053441221091229416311910430354012473298

35574713611913310118013011428323812881319

40625115113014410919914312425293613388342

45675516914215611722015813623273313897365

507259189155170126244174149212431143105391

557863211169184135271191163192129148114418

608367236184199145299210178171927153123447

658872263199213154329230194151625159132479

709276291214227163356249208131423165141512

759579318227239171379265221111221170150548

8095813432382481763942762309919177157586

*y.= years of education.

Page 7

Relationship across psychometric tests

A general view of the relationships among these

psychometric tests is given in Table 5. The TMT-B

and TMT-G were found to be closely linked (r=0.8,

p<0.0001), confirming that it was reasonable to as-

sume that they reflect, at least in part, analogous

cognitive functions. Examination of the LTT dis-

closed that neither LTT performing time (LTTt) or

LTT errors (LTT-er) alone appeared to be linked

with the other psychometric variables, whereas the

LTT time weighted (LTT-wt) by the errors appeared

more consistent with the other psychometric tests.

P. Amodio, H. Wenin, F. Del Piccolo, et al.

123Aging Clin Exp Res, Vol. 14, No. 2

Table 4 - The limits of the reference range for the TMTB-Aand the TMTG-A.

AgeTMTG-A(sec)

5 y.*

TMTB-A(sec)

8-13 y. White collaryears

≥8 y.5 y.8-13 y. Blue collar

≥13 y. Blue collar

≥13 y.White collar

20104 72 706355 74 55

25 115 787969 58 7958

30 126869077 618461

35139 931028567 88 65

40152102 11594749368

45167111129104829771

501821211451159010275

551991311631259910778

6021714118213610711181

6523615120314711511585

7025716122615612312088

7527916925016412912491

8030217727716913312894

*y.= years of education.

Table 5 - Matrix of correlations (Parson’s r) across the TMTs, LTT and SDT.

TMT-ATMT-BTMT-GTMTB-A

TMTG-A

SDTLTT-tLTT-er

TMT-B0.74

p=0.000

TMT-G0.71

p=0.000

0.80

p=0.000

TMTB-A

0.45

p=0.000

0.85

p=0.000

0.65

p=0.000

TMTG-A

0.49

p=0.000

0.66

p=0.000

0.85

p=0.000

0.68

p=0.000

SDT-0.68

p=0.000

-0.75

p=0.000

-0.75

p=0.000

-0.67

p=0.000

-0.67

p=0.000

LTT-t0.38

p=0.000

0.37

p=0.000

0.31

p=0.000

0.32

p=0.000

0.25

p=0.000

-0.33

p=0.000

LTT-er0.21

p=0.002

0.21

p=0.001

0.26

p=0.000

0.17

p=0.003

0.22

p=0.000

-0.35

p=0.000

-0.42

p=0.000

LTT-wt0.53

p=0.000

0.54

p=0.000

0.51

p=0.000

0.46

p=0.000

0.44

p=0.000

-0.62

p=0.000

0.60

p=0.000

0.43

p=0.000

t: time; er: errors; wt: performing time weighted by the errors.

Page 8

Test reliability

Reliability of the tests was evaluated by the co-

efficients of correlation, the coefficient of repeata-

bility (CR) and the coefficient of variability (CV). Re-

liability was higher for the SDT and LTT-wt; medi-

um for TMT-A, TMT-G, and LTT-t; lower for the

TMT-B, TMTB-A, TMTG-A, and LTT-er (Table 6).

DISCUSSION

The agreement between the psychometric tests in

the randomized sample collected in the city and

the convenience sample collected in villages suggests

the consistency and validity of the samples. Cer-

tainly, a much more accurate sampling technique

would use the randomization for the entire sample,

but it is worth noting that exact sampling tech-

niques have not been applied in any of the previous

studies on the TMTs, the LTT, or the SDT. All

were performed on convenience samples, and some

even with paid volunteers, a technique that may eas-

ily cause selection bias. Therefore, even if not un-

questionable, our data may represent an improve-

ment in sampling collection and provide a better

representation of the general healthy population

across a wider age range than that considered in the

majority of the previous studies.

In disagreement with Boll and Reitan (11), we

confirmed the studies (12-14, 21, 31-34) showing

the influence of age on the TMTs. The importance

of aging in psychometric performance was also

confirmed for the SDT and LTT, in agreement

with previous observations (8, 15, 25, 26, 35).

Moreover, the direct correlations of age with TMT-

B minus TMT-A, and TMT-G minus TMT-A showed

that aging more relevantly impairs the tasks needing

a higher attention and/or working memory capac-

ity. This finding agrees with the observation of

Cabeza et al. (36), suggesting that aging selectively

decreases the metabolic activity of pre-frontal areas

subserving these cognitive functions.

Of the other variability factors, education was

confirmed to be an important confounder of the

TMTs and SDT, in agreement with previous studies

(12, 13, 21, 37). In addition, we observed that

people with 8 or 13 years of education (in relation

to the test considered) not only performed the tests

definitely better than people with a lower education

level, but also reached a plateau of performance.

This finding means that the years of education did

not have a linear effect on psychometric perfor-

mance. Moreover, that no interaction was found be-

tween education level and age (as reinforced by

the parallelism of the curves of psychometric decline

as a function of age in subjects with different edu-

cation levels) in all tests (but in the difference TMT-

B minus TMT-A) is in line with current knowledge

that education generally does not influence the rate

of age-related cognitive decline (38-40). Howev-

er, an important exception was given by the dif-

ference TMT-B minus TMT-A which evidenced a

lower age-related rate of cognitive decline in high-

educated subjects. This finding might be explained

by a training effect on alphabet sequence in high-ed-

ucated subjects. In any case, if confirmed, this find-

ing would represent an important exception to the

theory that age-related cognitive decline is a mere

biological process that cannot be influenced by so-

ciobiographical variables (39).

The role of job as an explanatory factor of TMTs,

SDT, or LTT variability has not been considered

previously, except for the study of Weissenborn et

TMTs, SDT, LTT in normal subjects

Aging Clin Exp Res, Vol. 14, No. 2 124

Table 6 - The coefficients of correlation, repeatability, and variations between repeated measures of the TMTs, SDT and LTT.

TestCoefficient of correlation Coefficient of repeatabilityCoefficient of variation

TMT-A r=0.87 p<0.0018 sec24%

TMT-Br=0.86 p<0.00122 sec33%

TMT-Gr=0.89 p<0.00116 sec22%

TMTB-A

TMTG-A

SDT

r=0.82 p<0.00118 sec54%

r=0.74 p<0.00117 sec40%

r=0.93 p<0.0017 items13%

LTT-err=0.67 p<0.00118 errors67%

LTT-tr=0.65 p=0.00119 sec24%

LTT-wtr=0.86 p<0.00140 sec18%

Page 9

al. (12). We found that job has a role as perfor-

mance predictor for the TMT-B and TMT-G, which

are the two similar and highly correlated tests with

higher sustained attention loads. It is conceivable

that the kind of job may have a training effect on

sustained attention and/or working memory. Nev-

ertheless, job, compared to age and education, ap-

peared only as a minor, possibly negligible, predictor

of the TMT-B and TMT-G, as found by Weis-

senborn et al. (12). The lack of any influence of gen-

der in the performance of the TMTs, SDT, and

LTT was in line with the majority of the studies (20,

35, 41), except for a few references suggesting

better performance of the SDT (21, 22) and TMTs

(33) in women. However, findings based on these

last studies are questionable, because they were

derived from convenience samples (some on paid

volunteers). In addition, the technique used to adjust

for confounders that may account for gender dif-

ference was not always adequate.

Due to the transforms used to normalize the

tests, the effect of the predictors on the tests was ex-

ponential. Based on visual inspection, this mod-

elling was quite satisfactory for the curve that fitted

the mean values of the age-related psychometric de-

cay. However, in this model the extremes of a ref-

erence range defined by the mean +2 SD increased

exaggeratedly with aging, so that they appeared to

be clearly overestimated in older people. On closer

inspection, this overestimation is also present in the

study of Weissenborn et al. (12) who used an ex-

ponential model. For this reason, a better fit may be

given by the introduction of an age-dependent re-

ducing coefficient that decreases the spread of the

upper limits of the reference ranges in old peo-

ple. Nevertheless, such an approach to the problem

of describing the variability of a parameter in a

population is rather atypical, because it gives in-

formation derived from a definite function, as in

parametric models, as well as the empirical obser-

vation of data dispersion, as in non-parametric ap-

proaches. In this way, the expression of the re-

sults by Z-values, though adjusted for age, is still pos-

sible. Indeed, the expression of results as Z-values

(SD) from those expected for age, education, and

possibly job may simplify their interpretation and

comparison, avoiding the need to subdivide results

into subgroups (14). In such a way, the rather crude

distinction between tests performed within or with-

out a reference range is overcome, because the

use of a Z-score immediately provides information

on the spread from the expected values in the ref-

erence population.

A strict comparison of the normative data of

the present study with those of previous studies

on the TMTs, SDT and LTT is not possible, because

details concerning the forms of psychometric tests

and sample collection are generally lacking, as well

as proper handling of confounders. Moreover, the

range of age that we considered is wider than that

of previous research. However, a rough comparison

showed that our normative data fell in line with

those reported in previous studies, at least in the age

groups where the comparison was possible. More in

detail, our data showed a slightly quicker perfor-

mance of the TMTs compared to the data of Gio-

vagnoli et al. (13). LTT performance was slower but

more accurate than the findings of Ennen (26), but

faster and less accurate compared with the findings

of Hamster et al. (23). Moreover, data on the LTT-

wt have never been reported before, notwithstand-

ing the fact that its link with the other psychomet-

ric tests suggests that it provides more relevant

psychometric information than the time or the er-

rors in performing the LLT by themselves.

As regards the reliability of the tests, to our

knowledge no study adequately considered this

point. Even the study of Giovagnoli et al. (13),

which considers the repeatability of the TMT, only

applied a statistical tool (i.e., the correlation) that

merely indicated the non-random relationship be-

tween the first and second psychometric session.

Our study confirmed that the tests were well cor-

related on re-testing; in addition, the use of the

coefficient of repeatability provided a reliable mea-

sure of variability that allowed assessment of the sig-

nificance of a difference between repeated measures

(30). In this way, it was evidenced that small varia-

tions in repeated measures of single subjects should

be interpreted cautiously, because intra-subject vari-

ability is not negligible.

In conclusion, our study provides the most reliable

normative data range to date for the TMTs, SDT

and LTT, which takes into account important de-

mographic variables such as age, education and

job.

APPENDIX

Calculation of the adjusted Z-score considering the main

confounders for each psychometric test.

For each test the Z-scores adjusted for the main confounders

were calculated by the difference between the performance expected

on the basis of the predictive regression and the observed perfor-

mance, divided by the standard errors of the predictive regressions.

Different regressions were applied for each education level. The

standard errors were adjusted by functions reducing the age-de-

pendent exponential increase of the errors, when needed. The

goodness of the adjusting functions was assessed by visual inspec-

tion (Appendix Figures 1-7).

P. Amodio, H. Wenin, F. Del Piccolo, et al.

125Aging Clin Exp Res, Vol. 14, No. 2

Page 10

TMTs, SDT, LTT in normal subjects

Aging Clin Exp Res, Vol. 14, No. 2 126

sec

30 4050 607080 90

Age (years)

140

120

100

80

60

40

20

EDUCATION: 5 years

observed values

regression

adjusted upper

limit

+ 2 SD

sec

10 203040

Age (years)

50 6070 8090

120

100

80

60

40

20

EDUCATION ≥ 8 years

observed values

regression

adjusted upper

limit

+ 2 SD

Figure 1 - Relationships between TMT-A, age, and education. The circles show the observed values, the continuous line shows the mean

square fitting, the line with shorter dashes represents the expected upper limit, without adjustment, the line with longer dashes represents

the adjusted upper limit.

sec

450

400

350

300

250

200

150

100

50

EDUCATION = 5 years, independent of job

1525 35 4555657585

Age (years)

sec

260

220

180

140

100

60

20

EDUCATION >13 years; job: blue collars

1525354555657585

Age (years)

EDUCATION =8 years, independent of job

EDUCATION >13 years; job: blue collars

sec

240

200

160

120

80

40

1525354555657585

Age (years)

adjusted upper

limit

observed values

regression

+ 2 SD

adjusted upper

limit

observed values

regression

+ 2 SD

adjusted upper

limit

observed values

regression

+ 2 SD

adjusted upper

limit

observed values

regression

+ 2 SD

sec

320

280

240

200

160

120

80

40

152535455565 7585

Age (years)

Figure 2 - Relationships between TMT-B, age, education, and job. The circles show the observed values, the continuous line shows the

mean square fitting, the line with shorter dashes represents the expected upper limit, without adjustment, the line with longer dashes

represents the adjusted upper limit.

Page 11

P. Amodio, H. Wenin, F. Del Piccolo, et al.

127Aging Clin Exp Res, Vol. 14, No. 2

15 25 35 45

Age (years)

556575 85

200

160

120

80

40

0

EDUCATION ≥ 13 years; job: white collar

observed values

adjusted upper

limit

+ 2 SD

regression

1025 40

Age (years)

55 7085

240

200

160

120

80

40

0

EDUCATION 8 years; job: blue collar

3040 50 60 7080 90

Age (years)

450

350

250

150

50

-50

EDUCATION 5 years

1020 304050 607080 90

EDUCATION ≥13 years; job: blue collar

observed values

regression

EDUCATION 8 years; job: white collar

observed values

adjusted upper

limit

+ 2 SD

regression

observed values

adjusted upper

limit

+ 2 SD

regression

observed values

adjusted upper

limit

+ 2 SD

regression

adjusted upper

limit

+ 2 SD

Age (years)

140

120

100

80

60

40

20

0

-20

1020304050607080

Age (years)

160

140

120

100

80

60

40

20

0

Figure 3 - Relationships between the difference TMT-B minus TMT-A, age, education, and job. The circles show the observed values, the

continuous line shows the mean square fitting, the line with shorter dashes represents the expected upper limit, without adjustment, the

line with longer dashes represents the adjusted upper limit.

Page 12

TMT-A

Education = 5 years

Z=[(0.3212-0.00098 × age)-1/Log(TMT-A)]/(0.02-age5/120 ×

805);

Education ≥8 years

Z=[(0.3356-0.000914 × age)-1/Log(TMT-A)]/(0.0223-

age7/200 × 807)

TMT-B

Education = 5 years

Z=[(0.267-0.0009 × age)-1/Log (TMT-B)]/(0.016-age5/3 ×

806)

Education ≥8 years

Z=[(0.268-0.00077 × age)-1/Log (TMT-B)]/(0.016-age5/3 ×

806)

Education ≥13 years

Z=[(0.265-0.0007 × age+0.012 × job)-1/Log (TMT-B)]/(0.018-

age5/3 × 806)

TMT-G

Education = 5 years

Z=[(0.25-0.000745 × age)-1/Log (TMT-G)]/(0.0157-age6/3 ×

807)

Education ≥8 years

Z=[(0.266-0.000792 × age+0.00598 × job)-1/Log (TMT-

G)]/(0.0165-age6/3 × 807)

TMTs, SDT, LTT in normal subjects

Aging Clin Exp Res, Vol. 14, No. 2 128

3040 50

Age (years)

6070 80 90

400

350

300

250

200

150

100

50

0

EDUCATION = 5 years

observed values

regression

adjusted upper

limit

+ 2 SD

10203040

Age (years)

5060708090

260

220

180

140

100

60

20

-20

EDUCATION ≥8 years

observed values

regression

adjusted upper

limit

+ 2 SD

Figure 4 - Relationships between the difference TMT-G minus

TMT-A, age, education. The circles show the observed values, the

continuous line shows the mean square fitting, the line with

shorter dashes represents the expected upper limit, without ad-

justment, the line with longer dashes represents the adjusted

upper limit.

Age (years)

sec

25354555657585

600

500

400

300

200

100

0

EDUCATION level = 5 years

observed values

regression

adjusted upper

limit

+ 2 SD

Age (years)

sec

102540557085

300

200

100

0

EDUCATION ≥ 8 years; job: white collar

observed values

regression

adjusted upper

limit

+ 2 SD

Age (years)

sec

1525354555657585

400

300

200

100

0

EDUCATION ≥8 years, blue collar

observed values

regression

adjusted upper

limit

+ 2 SD

Figure 5 - Relationships between TMT-G, age, education, and job.

The circles show the observed values, the continuous line shows

the mean square fitting, the line with shorter dashes repre-

sents the expected upper limit, without adjustment, the line with

longer dashes represents the adjusted upper limit.

Page 13

Difference TMT-B minus TMT-A

Education 5 years

Z=[Log (TMT-B – TMT-A)-(2.5+0.028 × age)]/(0.6022-

age2/2002)

Education 8 years

Z=[Log (TMT-B – TMT-A)-(2.81+0.021 × age -0.24 × job)]/

(0.453-age5/1205)

where: job = 0 for blue collars

job = 1 for white collars

Education ≥13 years

Z=[Log (TMT-B – TMT-A)-(3.03+0.014 × age -0.31 × job)]/

(0.5102-age2/2002)

where: job = 0 for blue collars

job = 1 for white collars

Difference TMT-G minus TMT-A

Education 5 years

Z=[Log (TMT-G – TMT-A)-(3.2+0.021 × age)]/(0.518-

age2/2502)

Education ≥8 years

Z=[Log (TMT-G – TMT-A)-(2.876+0.018 × age)]/(0.517-

age5/1305)

SDT

Education = 5 years

Z=[Log(-(SDT-160))-(4.667+0.0032 × age)]/(0.054-age4/905),

Education 8-13 years

Z=[Log (-(SDT-160))-(4.545+0.0044 × age)]/(0.078-age3.1/804),

P. Amodio, H. Wenin, F. Del Piccolo, et al.

129Aging Clin Exp Res, Vol. 14, No. 2

Age (years)

items/90 sec

30 4050607080

50

40

30

20

10

EDUCATION = 5 years

Age (years)

items/90 sec

20304050607080

70

60

50

40

30

20

10

EDUCATION = 8 years

Age (years)

items/90 sec

20304050607080

80

70

60

50

40

30

20

10

EDUCATION ≥ 13 years

observed values

regression

adjusted lower

limit

- 2 SD

observed values

regression

adjusted lower

limit

- 2 SD

observed values

regression

adjusted lower

limit

- 2 SD

Figure 6 - Relationships between SDT, age, and education. The cir-

cles show the observed values, the continuous line shows the mean

square fitting, the line with shorter dashes represents the expected

lower limit, without adjustment, the line with longer dashes rep-

resents the adjusted lower limit.

sec

203040

Age (years)

50607080

160

120

80

40

0

LTT errors

observed values

adjusted upper

limit

regression

+ 2 SD

Age (years)

sec

1525354555657585

550

450

350

250

150

50

LTT time weighted by the errors: t x In (e+errors)

observed values

regression

upper limit

(+2SD)

Age (years)

sec

1525354555657585

220

180

140

100

60

20

LTT time

observed values

regression

upper values

(+2SD)

Figure 7 - Relationships between LTT and age. The circles show

the observed values, the continuous line shows the mean square

fitting, the line with shorter dashes represents the expected upper

limit, without adjustment, the line with longer dashes repre-

sents the adjusted upper limit.

Page 14

Education ≥13 years

Z=[Log(-(SDT-160))-(4.523+0.00374 × age)]/(0.077-age3/804)

LTT-time

Z=[Log (LTT)-(3.98+0.0071 × age)]/0.313

LTT-errors

Z=[Log(e+LTT-er)-(2.248+0.0188 × age)]/(0.762-age4/10 ×

804)

LTT-time weighted by the errors

Z={Log[Log(e+LTT-er) × LTT-t]-(4.776+0.0135 × age)}/0.258

ACKNOWLEDGEMENTS

We thank Anthony Schork, Professor Emeritus at the University

of Michigan (USA) and Adjunct Statistician at the University of Pado-

va (Italy) for reviewing the manuscript. This work was supported in

part by the Italian Liver Foundation.

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