Trail Making Tests A and B

Abbreviations: TMT, TMT-A, TMT-B

The Trail Making Tests, usually referred to in the singular as the Trail Making Test (TMT), have borne this name since their inclusion in the Army Individual Test Battery ¹⁾ in 1944. However, they had already been in use before 1944 under other names, including the Pathway Test. The two tests are usually administered as a pair, although they by no means measure the same thing. In Part A, the numbers from 1 to 25 scattered across a letter size page must be connected with a pencil in the correct order as quickly as possible. Part A thus primarily captures visuomotor speed. In Part B, the task is extended by a working memory component in that numbers and letters must be connected alternately in their natural order (from 1 to A, to 2, to B, and so on up to the number 13). Figure 1 shows a sample page for Part A, which is used to explain the test task.

Figure 1: Sample page for the TMT A

Although the test was initially used as a subtest of a general intelligence battery, its sensitivity to performance deficits resulting from brain damage soon became known. The test is discussed in all the major English-language textbooks of neuropsychological assessment ^{2) 3) 4)}. Further background information can be found in these sources. The test version in common use today goes back to Ralph Reitan ⁵⁾.

Since the 1950s, the Trail Making Test has been part of the Halstead-Reitan test battery (HRNTB, see for example Reitan & Wolfson, 1993⁶⁾), which for many decades was frequently used as the standard neuropsychological test battery, above all in the USA. The test material could be purchased from Reitan's Neuropsychology Laboratory. The sales catalog on the laboratory's website showed in 2009 that a set consisting of 100 templates for the TMT-A, 100 templates for the TMT-B, and a manual cost 50 US dollars. Although the website appeared to have been orphaned for some time in 2012, it is now (August 2021) accessible again and the price of the set is still the same. In the meantime, the test material for all tests of the HRNTB has also been made available by another manufacturer, the “Neuropsychology Center (NPC)”, a company in Texas run by former employees of the Reitan laboratory.

The TMT templates have been circulating from laboratory to laboratory for decades and are copied or redrawn again and again, certainly even before their inclusion in the Halstead-Reitan test battery. The Testzentralen (test distributors) in Göttingen and Bern currently (as of August 2021) do not offer a corresponding test. The Memory Clinic in Basel offers professionals the CERAD material and, in connection with it, the TMT templates (Parts A and B) for purchase. In the past, the Basel templates differed considerably from those used in the Halstead-Reitan battery: The numbers and letters were displayed in a relatively small serif font instead of a large sans-serif font and were therefore harder to read, which has a particular effect on older examinees. In the meantime, the templates available there can be used without problems. The norming studies listed below used - as far as is known - a page layout corresponding to that of the Halstead-Reitan battery. A considerably different arrangement of the numbers, or of the numbers and letters, could lead to different norms.

Reitan's laboratory does not claim any explicit copyright on the templates. It presumably would not go very far anyway, because the templates already existed before their inclusion in the HRNTB and anyone could, and still can, easily redraw them.

For reasons of test security, it is necessary that the material be accessible only to professionals. It is also important that the templates are in fact always used in the same form.

Internationally, administration according to Reitan's instructions has become established, in which the examiner closely supervises the examinee. Errors that occur are pointed out immediately and the examinee is asked to correct them. This makes separate recording of errors unnecessary. If any occur, they increase the administration time and thereby enter into the test result.

In individual neuropsychological laboratories, it has mostly become customary to set an upper limit on the administration time. Part A is often discontinued after 90 seconds, at the latest after three minutes, and Part B after five minutes. The ability to differentiate between different times is no longer given in this range, as the norm tables also show.

When administered according to Reitan, there is only a single raw score per subtest of the TMT, namely the seconds the patient needs to complete it. Errors are not noted individually but corrected in the course of the test and thereby increase the administration time. There are thus two raw scores, the administration time for Part A and that for Part B.

Young healthy adults need on average about 23 seconds for the TMT A. One can hardly take less than 14 seconds to connect 25 numbers, even if one is extremely fast. For the faster half of people, the times thus vary within a very narrow range. For the slower half, by contrast, the scope for variation is much greater; in principle it is unlimited. In fact, completion times of two minutes do occur among older examinees. For the TMT-B the situation is in principle exactly the same; the administration times are just generally longer. These boundary conditions result in a positively skewed distribution of the raw scores, as is the case for most speed-dependent tests in which the administration time serves as the raw score.

Empirical data on this are available in the collection of norms by Heaton et al. (2004)⁷⁾. It compiles the results of 634 white and 578 black Americans aged between 20 and 85 years on a series of tests, including the TMT. The authors converted the raw scores into scaled scores (mean 10, standard deviation 3) by means of a percentile rank transformation (across all persons in the sample) and presented the result as a table of values (raw score to scaled score). From this, the original distributions of the data at the level of time could be back-calculated (after making the coarse scaled score scale continuous and smoothing it). Figure 2 shows the raw score distribution back-calculated in this way across the total sample of 1212 persons for Part A, Figure 3 for Part B.

Figure 2: Frequency distribution of the raw scores of the TMT-A in the total sample (N=1212) of Heaton et al. (2004)

Figure 3: Frequency distribution of the raw scores of the TMT-B in the total sample (N=1212) of Heaton et al. (2004)

As expected, the raw score distribution is strongly positively skewed in both parts of the test and is therefore not readily interpretable without a non-linear transformation. Two examples are meant to illustrate this:

• A direct consequence of skewed distributions is the unpleasant property that equal differences at different points of the scale mean different things. An increase in completion time on the TMT-A from 15 to 20 seconds is substantively associated with a much greater loss of performance than an increase from 45 to 50 seconds. The time scale, however, does not reflect this.

• Skewed distributions have a further unpleasant property. In arbitrary subgroups differing in performance, for example in age cohorts, the standard deviations are not equal but correlate positively with the means. This, too, can be demonstrated well using the data of Heaton et al. (2004). In Figure 4, the raw score distributions on the TMT-A, back-calculated from the percentile tables, are contrasted for white women and men with 12 years of education in two age groups, the 20 to 34 age group in blue and the 60-64-year-olds in red. It can be seen at a glance that the distribution is much broader in the older examinees than in the younger ones, corresponding to the higher mean. For the most part, however, this broadening is not due to greater variability of the attribute itself, but to the properties of the time scale, which depicts the psychological attribute in a distorted way.

Figure 4: Back-calculated frequency distributions of the TMT-A raw scores for two age groups (data from Heaton et al., 2004)

For the TMT there was the rare opportunity that empirical data could be drawn on for the linearization, albeit only in summarized form and with certain compromises. In the large study mentioned above by Heaton et al. (2004)⁸⁾, a transformation of the percentiles of the time raw scores into normally distributed standard scores had been carried out. Unfortunately, this had been done only across the total sample, which is not ideal, because in this heterogeneous sample, besides the scale influences of interest here, further effects are reflected that influence the shape of the distribution. These are in particular effects of age, especially for such an age-sensitive test as the TMT. But still, after making the scaled score scale continuous and smoothing it, a finely graded table of values could be created from the data, which could serve as the basis for the linearization of the performance scores.

To calculate the performance scores, however, the data of a young healthy sample are needed. These are not presented separately in the manual by Heaton et al. (2004). The authors had chosen the approach of using polynomial regression to calculate the influences of age, sex, and years of education on the raw scores. The results are tabulated in the form of T scores corrected for age, sex, and education. The education duration of the total sample of Heaton et al. (2004) deviated markedly upward from the American average. For the calculation of the performance scores, therefore, only the subsample with 12 years of education was used (N=114). At that time, this corresponded to the mean education duration of the American population. Because of the relatively coarse classification, a broader grouping of ranges would not have been possible. This would have meant accepting a large deviation from the average, which was judged to be more serious. As presented below, the performance of the subsample chosen here corresponded relatively well to the performance of the meta-analytically pooled samples.

In the Army Individual Test Battery, the time raw scores were at that time transformed into scaled scores between 1 and 10 (and thus presumably at least approximately linearized). With the application as neuropsychological tests, cutoff scores for distinguishing between “normal” and “pathological” initially became established, which, however, were quickly and rightly criticized. The test scores in both parts of the TMT (Part B even more than Part A) depend strongly on intelligence, in particular visuomotor speed, and on age, which is why uniform cutoff scores cannot be advisable.

Today, the neuropsychological textbooks ^{9) 10)} offer different normative data, partly as percentile ranks, partly as means and standard deviations of particular reference groups. The recommended norms differ considerably from one another. In the collection of norms by Mitrushina et al. (2005) ¹¹⁾, a recommendation is dispensed with altogether. The authors cite many different norm sources and recommend choosing the one that most closely corresponds to the population to which an examinee to be assessed belongs. Such a practice would lead to a fusion of measurement and interpretation that is difficult to separate.

A reliable and uniform summary of the different norm sources does not exist to date.

For the creation of the TDB2Online performance norms, recourse was systematically taken to as many accessible studies as possible that contained TMT data of healthy examinees. Since the TMT is a largely language-free test (although tied to the Latin alphabet), no restriction was imposed on the national and/or linguistic origin of the normative data. The condition for the inclusion of a study was that means and standard deviations of the time raw scores of a sample of healthy examinees were reported for several differentiated age ranges. It was possible to locate 22 individual studies in 18 publications that provided normative data of around 4,000 examinees in the age range between 15 and 94 years. By means of a meta-analytic summary, these norms were integrated and thereby made independent of the peculiarities of the individual study.

For the TMT norms calculated here, there were two large reference works. One is a collection of normative data for a series of standard neuropsychological procedures, published as a monograph under the title Handbook of Normative Data for Neuropsychological Assessment (Mitrushina et al., 1999 ¹²⁾ ). For the TMT, this handbook discusses a total of 24 studies with normative data. Fourteen of them, namely those designated as studies 1 ¹³⁾, 2 ¹⁴⁾, 4 ¹⁵⁾, 5 ¹⁶⁾, 7 ¹⁷⁾, 8 ¹⁸⁾, 9 ¹⁹⁾, 10 ²⁰⁾, 11 ²¹⁾, 12 ²²⁾, 15 ²³⁾, 18 ²⁴⁾, 20 ²⁵⁾, and 21 ²⁶⁾, met our inclusion criteria. For studies 8, 11, and 18, only the first test administration was included in each case. In studies 5 and 10, the groups with different educational qualifications were each included individually. Reasons for exclusion of the other studies were: an age range that was too wide and undifferentiated in studies 6, 19, 23, and 24; the selective administration of Part B without Part A in studies 16 and 22; the inclusion of ill persons in the samples of studies 3 and 17; and a selection of conspicuously high-performing examinees in study 14 (all references to these in Mitrushina et al., 1999).

A special case is study 13 ²⁷⁾. This study was not included because it is the predecessor study to the already mentioned normative handbook by Heaton et al. (2004) ²⁸⁾, which includes the older data. This handbook is the second important reference work for the present norms, in particular because the linearization of the TMT raw scores was possible with the aid of the data collected there. The handbook contains detailed, statistically processed data of a sample of 1212 healthy US citizens who had completed almost all procedures belonging to the Halstead-Reitan battery and further intelligence tests. A subsample of this study, namely the white US Americans with 12 years of education, was included as a further sample in the norms meta-analysis presented here.

Three further samples that are not listed in Mitrushina et al. (1999) were included in the meta-analysis:

• In a smaller norming study ²⁹⁾, 101 healthy examinees aged between 18 and 85 years were tested with the TMT and other neuropsychological procedures. Despite the relatively small sample size, this study was distinguished by the fact that the age, education, and sex of the examinees largely corresponded to the population census.
• The Memory Clinic Basel (http://www.memoryclinic.ch) presented in 2005, in addition to the normative data of the CERAD battery, norms for the Trail Making Tests on its website as well, which were obtained in a multicenter study of 604 healthy examinees aged between 50 and 88 years. The normative data are available as a download for professionals (after login). They are available for the three age ranges 50-69, 70-79, and 80-92 (and additionally - not used here - broken down by sex and education). The allocation of these normative data to the finer age classification in five-year intervals used here was estimated on the basis of the likewise reported statistics of the age distribution (mean, standard deviation). (This is somewhat more accurate than an equal distribution of the cases across all age groups involved.)
• Another relatively extensive publication of norms was published by Tombaugh ³⁰⁾. From several experimental studies with healthy examinees, normative data for the Trail Making Tests of 911 persons in the age range between 18 and 89 years were compiled, broken down by age group and educational level. For the present meta-analysis, the youngest group (18-24 years) was not included, since it consisted exclusively of students. In the remaining age range, the older cohorts between 55 and 84 in particular were comparatively well represented. In total, data from 752 persons were included.

In total, 3976 persons were included in the norming of Part A and 3972 persons in that of Part B. Table 1 gives some details of the studies. It can be seen that the total sample has a relatively high level of education, especially considering the age of the studies.

Table 1: Overview of the meta-analytically pooled norming studies

In summarizing the normative data, sample sizes, means and standard deviations in five-year classes between 15 and 85 years were first compiled. If a source had a coarser age division (which was often the case), the cases were distributed evenly across the five-year classes involved and the same mean and the same standard deviation were assumed for all of them. All means and standard deviations in the sources referred to raw scores in seconds; more detailed statistics were hardly ever given. Percentile distributions were available only for the data of Heaton et al. (2004), which could therefore be the only ones transformed directly into performance scores.

Because of the strong positive skew of the distribution, both the mean and the standard deviation contain a relatively strong systematic bias toward higher values, which could not have been corrected by merely transforming the sample parameters: had the raw scores been percentile-to-normal-transformed before computing the statistics, both means and standard deviations would be lower. The influence of these transformation processes was corrected with the help of a simulation: the transformation table from raw scores to performance scores, based on the data of Heaton et al. (2004), was used to undo the influence of the scale on the averaging. This is an approximation procedure that, by varying the first two moments of the performance score scale, searches for the distribution that, given the transformation table, produces the mean and the standard deviation of the source distribution. The procedure was implemented with the Solver function of Microsoft Excel. In practice, very good variance-stabilizing properties were found.

Figure 5: Age courses of the TMT-A raw scores of all norm sources and of the meta-analytic summary.

Figure 5 shows the age courses of the original values of all norm sources for the TMT-A. The first 22 studies given in the legend of this figure supplied the data for the meta-analysis. The performance score transformation comes from the study of Heaton et al. (2004), drawn in orange. The bold curve and the two outer curves show the percentile ranks 50, 16 and 84 of the meta-analytic aggregation. (These values were computed at the measurement level of the performance scores. They have been transformed back to completion times here so that they can be compared with the original data of the studies.) One can see quite clearly that the range of the mean completion times in the individual studies is considerable. In some age groups, the means of the individual studies touch or exceed the percentile ranks 16 and 84 from the meta-analysis, that is, those limits which, in a normal distribution, correspond to the one-sigma limits (or 15 IQ points). One can also see that the relatively recent and extensive normative data of Tombaugh (2004) lie well in the middle of the norms. For the norms of Heaton et al. (2004) this can still be said with the qualification that the times turn out systematically better, above all in the higher age range. Incidentally, this does not hold in this way for the TMT-B, as the next figure shows.

Figure 6: Age courses of the TMT-B raw scores of all norm sources and of the meta-analytic summary.

Figure 6 shows the same data for the TMT-B. What was said about the heterogeneity of the samples applies to the TMT-B just as to the TMT-A. It is noteworthy that the means of the study by Heaton et al. (2004) now lie almost exactly at the mean of all studies. Their examinees were evidently fitter in visuomotor speed than in working memory. In general, the studies keep their relative rank in the two test parts. If the means of a study tend to lie in the upper performance range in Part A, this remains so in Part B.

The following figures show the results of the entire norming in a graphical overview, namely in Figure 7 for the TMT-A and in Figure 8 for the TMT-B. On these figures, the vertical lines mark the performance scores from 40 to 145; the raw scores in seconds are plotted on the black horizontal line. The alternately red and blue lines contain the norm limits for all age groups in the overview. The five markers on each line stand for the percentile ranks 2.5, 16, 50, 84 and 97.5. One such line, namely the one corresponding to the age group of the examinee, is drawn (in a different form) in the TDB2Online profile sheet to help with the individual interpretation of the test results.

Figure 7: Performance scores of the TMT-A with raw scores and age norm limits (see text)

Figure 8: Performance scores of the TMT-B with raw scores and age norm limits (see text)

The effects of the linearization transformation can be seen in the figures. To see this, one has to look more closely at the black scale with the raw scores, for example for the TMT-A in Figure 7. On the right side of the diagram, at the short times, about 4 seconds make up 15 IQ standard score points; at the long times, almost 20 seconds stand for the same standard score difference. Only the standard scores reflect the psychological meaning of the difference correctly; the times distort it.

The variance-stabilizing effect of the linearity transformation can also be seen clearly. As expected for a normal distribution, the five markers are approximately equally spaced in all age groups.

Across the age groups, the variance stabilization is not as good. From about age 65 on, the older age groups have broader distributions than the younger ones. It can be assumed that at least a certain part of this broadening of variance is actually “real” - not least due to different gradients of cognitive decline in different persons, which lead to the broadening of variance in old age. However, the linearization transformation is also not particularly robust in this range, because it is based on the measurements of the young adults, whose distribution covers the range of the very old examinees only inadequately. For tests that measure functions highly susceptible to decline, one has to live with this flaw.

Since 1996, a modified version of the Trail Making Tests has existed in the form of the Color Trails Test (CTT)⁴⁹⁾. It was constructed with the aim of creating a version of the TMT usable worldwide. In particular, the Latin letters in the TMT B were to be replaced by a more universal concept. Part 1 of the CTT essentially corresponds to Part A of the TMT: The numbers from 1 to 25 are to be connected with one another as quickly and correctly as possible, even though in the CTT1 they are printed in different colors. In Part 2 of the CTT, the numbers from 1 to 21 appear twice on the sheet of paper, once with a yellow and once with a pink background. The task consists of starting at the yellow 1 and drawing a line to the pink 2, yellow 3, pink 4, and so on. The numbers that do not match in each case must therefore be ignored. However, this version differs considerably from the TMT B, because instead of the 13 letters in the correct order, only two colors in alternating order have to be heeded here. The demands on working memory are correspondingly lower. In a study on a small sample ⁵⁰⁾, a very high correlation was found between the CTT1 and the TMT A (r=.91) and a considerably lower one between the CTT2 and the TMT B (r=.72).