Test of Attentional Performance

Abbreviation: TAP

Since the beginnings of the TAP, the evaluation of the results in the form of tables and graphics has been integrated into the computer program. In this process, the results are adjusted for the effects of age, gender and/or education on test performance empirically observed in the samples. The calculations are based on regression analyses that were carried out for both trend effects and dispersion effects. The calculations performed can be reproduced with the help of the information in the norm manual. They are fairly complex and specific to each test, each administration condition and each parameter. The degree of complexity depends on whether the influence of age, gender and/or education was significant in the normative sample. The raw scores adjusted in this way are linearized by an percentile-to-normal transformation and are available as T scores or percentile ranks.

TDB2Online, by contrast, generally standardizes an examinee's performance against the values of young adults in order to obtain a performance parameter that is comparable across tests (“performance score”). As an aid for interpreting a test performance, parameters for the performance to be expected at the examinee's age are entered into the test profile and an age-normed score is calculated. Systematic performance differences between women and men are rather rare in cognitive functions and not very large. In the TAP tests that can be evaluated in TDB2Online they play a role only in Alertness, where men are on average about 15 milliseconds faster than women, a difference that can matter in sports but is irrelevant for clinical questions. All other factors, which include education, training, occupational activity, and also hobbies and interests, are not independent of cognitive functions. There is a mutual influence here. With the methods of regression analysis, interdependencies can be handled statistically only insufficiently. We therefore prefer a clinical weighting here.

To generate purely age-dependent norms, we drew on the manual norm determination documented in the manual. For the mean age of each age group (for the group of 40–44-year-olds, for example, 42 years) we calculated the corrected value for every possible raw score using the formulas for the trend and dispersion correction, read off the T score from the norm table, and transformed it into the deviation IQ score with a mean of 100 and a standard deviation of 15 used in TDB2. This score thus incorporates the manifold parameterizations (depending on the test and parameter) from the regression calculations in the sense of trend and dispersion corrections. Gender and education, which occasionally entered the regression calculations as two-level characteristics (0 for less than 12 years of schooling and for men, 1 for 12 or more years of schooling and for women), were each included in the calculation with 0.5 in order simply to average over both factors.

For all TAP tests, the performance scores were aligned to the age group of the 20–24-year-olds.

For the Alertness test, only the two global raw scores for mean reaction time are evaluated in TDB2Online, the median without signal and the median with signal. In the series without a signal (the first and the fourth series), the median reaction times in the average of the normative sample (T score 50) are about 230 milliseconds; in the series with a signal (series two and three) they are about 220 milliseconds. The fastest possible reaction times are around 160 milliseconds; for the slowest there is only the limit, imposed by the test paradigm, of a stimulus presentation time of at most 2000 milliseconds, whereby reactions outside an individual limit of M plus 2.35 * SD already count as outliers and are not included in the calculation of Md and SD. Mean response times beyond 600 milliseconds are very rare even in older persons.

Figure 1 shows the transformation curves from raw scores to age-related standard scores on the IQ scale for the median without signal in the Alertness test for 13 age groups from 19 to 79 years. One can see that the middle age groups hardly differ and the curves from 25 to 60 all lie very close together.

Figure 1: Linearization transformation of the median without signal in the Alertness test from raw scores to age-dependent IQ standard scores

The transformation is - as is to be expected for reaction time measures - nonlinear, because the initial distribution of the reaction time raw scores is skewed. This is easier to see in Figure 2, which shows the distribution density back-calculated from the normalization transformation for four selected age groups. One sees the expected negatively skewed distribution of the raw scores and the very similar distributions of the two middle age groups.

Figure 2: Raw score distribution of the median without signal in the Alertness test in four age groups

Figure 3 shows, in a composite graphic, the relationship between raw scores and performance scores as well as the influence of age on performance in the parameter median without signal in the Alertness test. In this and all following age norm diagrams, the vertical bars mark the performance scores from 40 to 145. The raw scores are entered in their correct positions on the black horizontal line. The lines drawn alternately in red and blue contain the norm limits for all age groups in 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 examinee's age group, is drawn (in a different form) in the TDB2Online profile sheet to help with the individual interpretation of the test results. Because the performance scores were calculated from the results of the 20–24-year-old young adults, the 5 markers of the 20–24 age group lie exactly at the performance scores 70, 85, 100, 115 and 130.

Figure 3: Performance scores for the median without signal in the Alertness test with raw scores and age norm limits (see text)

On the raw score scale one can trace the nonlinear transformation of raw scores into performance scores: in the high performance range, 10 milliseconds amount to 10 standard score points; in the low range, 100 milliseconds correspond to 10 standard score points. The linearization succeeded in all age ranges, even though the somewhat peculiar S-shaped course of the age values is conspicuous, especially in the high performance range. This is probably an artifact of the regression corrections, which for Alertness without signal have coefficients for all three age effects (linear, quadratic and cubic).

In the middle two series, two and three, a warning tone is played before each cross to which one must respond. It increases phasic alertness and leads to somewhat faster responding. Figure 4 shows the transformation curves from raw scores to age-related standard scores on the IQ scale for the median with signal. Here the younger age groups in particular lie close together. If one compares the transformation curves of the two medians with and without signal, then despite the general similarity of the course one must nevertheless note large differences, especially in the lower performance range. Here age has a large influence on trials without a signal, but a much smaller one on those with a signal. In the upper performance range, by contrast, the influence of age is similar with and without a signal. I hesitate to try to explain the differences in any way, because it is not clear what role the regression-analytic correction, which proceeds differently from parameter to parameter, might play.

Figure 4: Linearization transformation of the median with signal in the Alertness test from raw scores to age-dependent IQ standard scores

One sees this just as clearly in the density curves: Figure 5 shows the distribution density back-calculated from the normalization transformation for four selected age groups, of which the two younger ones are practically congruent.

Figure 5: Raw score distribution of the median with signal in the Alertness test in four age groups

The usual summary of the age norms for the median with signal in the Alertness test is shown in Figure 6.

Figure 6: Performance scores for the median with signal in the Alertness test with raw scores and age norm limits (see text)

The linearization succeeded well in all age groups. Conspicuous is a reduction in variance with advancing age, which is implausible. In the upper performance range the expected slowing with increasing age occurs, whereas in the lower performance range there are practically no age-related effects. This is not very plausible and is perhaps also an effect of the regression correction.

The Working memory test is evaluated in TDB2Online for difficulty level 3. In this version, single-digit numbers are presented. One must respond as quickly as possible when the current number is the same as the one before the last (laboratory jargon: 2-back). In TDB2Online two parameters are evaluated: the median as a measure of response speed and the number of omissions as a measure of performance quality. Figure 7 shows the transformation graphs for converting the median reaction times into standard scores (100;15) for all age groups from 19 to 79.

Figure 7: Linearization transformation of the median raw scores in the Working memory test into age-dependent IQ standard scores

It is odd that there are practically no age differences among persons with good performance and, conversely, very large ones at low performance. In the slow performance range all curves end with a strong curvature. Pure percentile-to-normal transformations occasionally have such artifacts at the ends when the samples are not very large. Here, however, the transformation curves are quite peculiar. For the medians of Alertness without signal in Figure 1, the transformation curves end without any additional curvature. Here the sample is somewhat larger, but that cannot explain this difference.

In the exemplary density distributions for four selected age groups in Figure 8, the abrupt end of the distributions can likewise be seen.

Figure 8: Raw score distribution of the median in the Working memory test in four age groups

If one summarizes the results of the transformations, the performance scores and age norm limits result as shown in Figure 9.

Figure 9: Performance scores for the median in the Working memory test with raw scores and age norm limits (see text)

On the performance score scale, the difference in mean performance between the youngest and the oldest group amounts to about one standard deviation.

In the Working memory test, 15 critical stimuli are presented to which one must respond by pressing a key. One can make both errors (a key press outside a critical stimulus) and omissions (no key press at the critical stimulus). The number of omissions is the more important quality index because it directly reflects how successfully the task is solved. Figure 10 shows the linearization transformation for all age groups, Figure 11 the resulting density distribution.

Figure 10: Linearization transformation of the omission raw scores in the Working memory test into age-dependent IQ standard scores

Figure 11: Raw score distribution of the omissions in the Working memory test in four age groups

Both figures show that the age dependence of performance is relatively high: whereas the young omit on average only about one critical stimulus, this happens with two or three stimuli in the older persons. Most distributions are censored at the raw score 0, most strongly in the younger age groups, many of whom respond correctly to all critical stimuli. As a consequence, a raw score of 0 omissions leads to a performance score of only about 114. Higher performances cannot be measured in this paradigm.

Figure 12 summarizes performance scores and age norm scores. Even though the Working memory test at the difficulty level 3 used here makes certain demands on working memory and is not understood as quickly by some persons, many - above all younger - persons nevertheless achieve error-free performance without any omission. The restriction of the test scores at the upper performance edge (at an IQ standard score of 114) can also be seen very well in this figure. The age-related loss in performance amounts to about one standard deviation from the younger to the oldest group, and it has its effect particularly in the middle performance range. This could already be seen before in the shape of the transformation curves in Figure 10, which show large differences between the age groups in the upper range.

Figure 12: Performance scores for the omissions in the Working memory test with raw scores and age norm limits (see text)

The Flexibility test is recorded in TDB2Online in the variant “verbal/letters and numbers alternating”. In this version two stimuli appear, a letter and a number, to the right and left of the center of the screen. Sometimes the letter is on the left and the number on the right, sometimes it is the other way round. There are two keys for the response, one for the left and one for the right hand. The “flexibility” enters the task through the fact that the target stimulus changes constantly: one must respond alternately to the letter or the number. In this task the median reaction times are markedly higher than in simpler tests. Figure 13 shows the linearization transformations of the reaction times into age-dependent IQ standard scores, Figure 14 the associated density functions and Figure 15 the overview of performance scores and age norm scores. From Figure 13 with the linearization transformations one first gets the impression that increasing age has a reliable and uniform influence on reaction speed. Figure 14 reinforces this impression. In Figure 15, however, one sees that the transformation into performance scores, which we carry out on the age group of the 20-24-year-olds, was not well suited to linearize the scale for all age groups. At the level of performance scores, the younger have much higher variances than the older. At least one reason for this is likely to lie in the unusual nature of the transformation curves in Figure 13. At the lower end the curves do not run out, as would be expected and as is the case, for example, in the Alertness test (see Figure 1). Instead they have an additional inflection point and change the direction of curvature. This makes no sense and probably again has its origin in the regression equation used.

For the age-normed scores that TDB2 outputs, this is immaterial. It affects only the display in the profile, whose linearization did not succeed.

Figure 13: Linearization transformation of the median raw scores in the Flexibility test into age-dependent IQ standard scores

Figure 14: Raw score distribution of the median in the Flexibility test in four age groups

Figure 15: Performance scores for the median in the Flexibility test with raw scores and age norm limits (see text)

Neither age nor gender or education level has an influence on the errors in the Flexibility test (verbal, letters and numbers alternating). For us this simplifies the work: there is only a single curve.

Figure 16: Linearization transformation of the error raw scores in the Flexibility test into age-dependent IQ standard scores

Figure 17: Raw score distribution of the errors in the Flexibility test in four age groups

Figure 18: Performance scores for the errors in the Flexibility test with raw scores and age norm limits (see text)

The density distribution is censored at the upper performance edge at 0 errors; fewer than 0 errors is not possible, and the highest achievable IQ standard score is 120.

One is somewhat surprised that age should have no influence on the errors in this test. In action tests, especially in those with a time limit and/or working memory load, poorer performance is seen in older persons than in younger ones. In the normative sample there was evidently no (significant) correlation with age. We recalculated this in a clinical sample from the psychiatric hospital: in 1014 persons who performed the Flexibility test in the variant discussed here, there was a correlation of 0.12 between age in years and the number of errors. That is not zero, but still quite small. A possible explanation is that committing errors in this test is probably not a very reliable performance measure and can have many causes.

The TDB2Online evaluation of this test applies to administration form 1, in which two synchronously running tasks have to be managed, one visual and one auditory. On the screen, between 6 and 8 small crosses appear at 16 points arranged in a square. Whenever these form a small square of adjacent crosses anywhere, a key must be pressed as quickly as possible. At the same time, synchronously with the patterns on the screen, a high or a low tone sounds, mostly alternating. If the high or the low tone occurs twice in a row, one must likewise respond with the same key as quickly as possible. For this test, three measured values are evaluated in TDB2Online: the median reaction time to the tones, the median reaction time to the squares and the total number of omissions for patterns or tones.

Figure 19 shows the linearization transformations of the auditory reaction times into age-dependent standard scores (100;15), Figure 20 the associated density functions and Figure 21 the overview of performance scores and age norm scores.

Figure 19: Linearization transformation of the medians of the auditory trials in the Divided attention test from raw scores into age-dependent IQ standard scores

Figure 20: Raw score distribution of the medians of the auditory trials in the Divided attention test in four age groups

Figure 21: Performance scores for the median of the auditory trials in the Divided attention test with raw scores and age norm limits (see text)

The median auditory reaction times lie between 520 and 540 milliseconds for all age groups, thus quite close together. Figure 21 makes clear that the difference from the youngest to the oldest group amounts in performance scores to only one third of a standard deviation, 5 points. We will see in the next section that this is quite different for the visual reaction times.

The median reaction times to the squares (see Figures 22 to 24) are, firstly, markedly longer than the auditory ones, which is well known. Secondly, however, there is also a massive age dependence here. Whereas the young respond on average after 700 milliseconds, the old need 900 milliseconds. The corresponding difference in the performance scores (see Figure 24) adds up to about one and a half standard deviations. Similar to the reaction times in Flexibility (see Figure 15), for the reaction times to the squares, too, the linearization on the performance score scale did not succeed so well.

Figure 22: Linearization transformation of the medians of the visual trials in the Divided attention test from raw scores into age-dependent IQ standard scores

Figure 23: Raw score distribution of the medians of the visual trials in the Divided attention test in four age groups

Figure 24: Performance scores for the median of the visual trials in the Divided attention test with raw scores and age norm limits (see text)

There are 17 target stimuli for the squares and 16 for the tones, thus opportunity for 33 omissions. Mostly, however, the persons in the normative sample work quite carefully and omit only 0 to 2 target stimuli in the median. This leads to strong censoring of the distribution at the end of the scale. Zero omissions, the best possible test score, leads to a performance score of only 114; better performances are not possible. The mean decline in performance from the youngest to the oldest group is somewhat more than half a standard deviation.

Figure 25: Linearization transformation of the omission raw scores in the Divided attention test into age-dependent IQ standard scores

Figure 26: Raw score distribution of the omissions in the Divided attention test in four age groups

Figure 27: Performance scores for the omissions in the Divided attention test with raw scores and age norm limits (see text)

The Go/NoGo test is evaluated in TDB2Online in the administration form “1 of 2”. On the screen, an upright (+) and a tilted (x) cross are shown in irregular order. One is to respond as quickly as possible only to the tilted cross. Here, in addition to the median reaction time to the target stimulus, the number of errors is especially relevant, because it can indicate disturbances of impulse control.

Figure 28 shows the linearization transformations from milliseconds into standard scores (100;15) for all age groups. The median reaction times vary across the age range from about 370 to 450 milliseconds, a difference that, transformed into the performance score scale (see Figure 30), amounts to about one standard deviation. Somewhat peculiar are the convergence of the transformation curves at the long end and the erratic course of the curves, probably also a result of the regression correction.

Figure 28: Linearization transformation of the raw scores of the medians in the Go/NoGo test into age-dependent IQ standard scores

Figure 29: Raw score distribution of the medians in the Go/NoGo test in four age groups

Figure 30: Performance scores for the median in the Go/NoGo test with raw scores and age norm limits (see text)

For the errors in the Go/NoGo test, no influence of age was recognizable in the normative sample; therefore there is also only one curve for all age groups in Figures 31 to 33. In the task there are 20 non-critical stimuli to which errors are possible. In the normative group only one error was made on average; the distribution is cut off at zero. Zero errors lead only to a standard score (100;15) of 108.

Figure 31: Linearization transformation of the error raw scores in the Go/NoGo test into age-dependent IQ standard scores

Figure 32: Raw score distribution of the errors in the Go/NoGo test in four age groups

Figure 33: Performance scores for the errors in the Go/NoGo test with raw scores and age norm limits (see text)