Letter-Number Span
Background
The Letter-Number Span was first described in 1997 by Gold et al. in a journal article under the name “Letter-Number (LN) Span”2). It consists of 24 items. For each item, a span of 2 to 7 letters and numbers is read aloud, with four series per span length in ascending difficulty. The task consists of mentally reordering the presented numbers and letters (for a span of four, e.g., 7-W-4-B) and reciting first the numbers in ascending order and then the letters in alphabetical order (for the example: 4-7-B-W). The test may be discontinued if not a single correct sequence is recalled at a given span length. A maximum of 24 correct responses is possible.
The test requires the manipulation of content in working memory. In 2008, the LN Span was included as a working memory test in the MATRICS Consensus Cognitive Battery3), a test battery intended in particular to capture cognitive deficits in schizophrenic disorders. Holmen et al. (2009)4) described the test as the University of Maryland Letter-Number Span, referring to the work of Gold et al. (1997).
At the same time as the publication of Gold et al. (1997), the test also found its way into the WAIS-III5) under the name “Letter-Number Sequencing” (designation in the German WIE6): Buchstaben-Zahlen-Folgen), albeit in a modified form: only three series are presented per span, but the span length goes up to eight elements. Raw scores thus range from 0 to 21. There are five practice items with span lengths of two to three.
The task was also retained in the WAIS-IV7), but in modified form. Here, six items are presented at span length 2 and even nine at span length 3, instead of only three each, and the instructions are also more detailed. This allows lower-performing individuals, who can make little of the abstract instructions, to learn the task from the example. For span lengths 4 to 8, there are three items each, as in the WAIS-III. Raw scores in the WAIS-IV task thus range from 0 to 30.
Test material
The Letter-Number Span is more a procedural instruction than a standardized test. Unlike the Letter-Number Sequencing subtests of the WAIS-III and WAIS-IV, there is no standardized test material here. However, the material for the LN Span can easily be produced oneself. At the Department of Psychiatry of the LMU, we work with two parallel test forms that were constructed ad hoc.
Copyright
The LN Span is not based on copyrighted material. Everything needed for administration can be produced oneself.
Administration
After the test instructions, a practice phase follows in which four sequences (one with two characters, one with three, and two with four characters) are presented. The main test begins only when one can be sure that the instructions have been understood.
In the main test, four character sequences each of spans 2 to 7 are presented. The test is to be discontinued if all four responses at a span length were wrong. Most examinees complete the test in 5 minutes; there is no time limit.
Test raw scores
There is only one raw score, the sum of the correctly answered items. With four presentations each in the six spans from 2 to 7, raw scores range from 0 to 24.
Norms
The LN Span in the form discussed here was administered as part of the norming of the MATRICS test battery (Kern et al., 2008)8), together with many other neuropsychological tests used to measure cognitive performance in patients with schizophrenia. Representativeness was aimed for in collecting the norms. In the appendix of the cited work, relatively coarse norms are printed for the age groups 20-39, 40-49 and 50-59, each based on 100 examinees. We use the values of the age group 20-39 to compute performance scores.
However, we introduced one change: The standard deviations of the three age groups are 3.6, 2.9 and 3.3. The difference between the first two age groups is highly implausible; it is in all likelihood a chance fluctuation. For these two groups, we used as standard deviation the mean of 3.6 and 2.9, that is, 3.25.
A comparison of the LN Span norms with those of the corresponding subtests from the WAIS-III or WAIS is not possible because of the different design of the tests.
Distributional properties of the raw scores
No distribution analyses are available from the MATRICS norming, only means and standard deviations per age group. There is therefore no alternative to a linear standardization.
Figure 1 shows the transformation of the scores of each individual age group into IQ standard scores. It can be seen that only the oldest examinees (50–59) differ appreciably from the 20–39-year-olds. There is practically no difference from the 40–49-year-olds.
Figure 1: Linear transformation of the LN Span raw scores into IQ standard scores according to the MATRICS norms
The measurement range is somewhat limited at the upper end. The maximum raw score of 24 yields an IQ standard score of only 136 in 20–39-year-olds. Higher performance scores cannot be attained with this test. At the lower end, the capacity for differentiation is much better. For a test intended primarily to quantify performance deficits, this is not unreasonable.
The assumption of a normal distribution is justified at least in the central ranges of the distribution, as can be approximately read from the reconstructed distribution data of the (very similar) subtest Letter-Number Sequencing in the WAIS-IV.
Overview of performance norms and age norms
Figure 2 shows the performance norms for the Letter-Number Sequencing.
Figure 2: Raw and performance scores for the LN Sequencing
Discussion
The Letter-Number Span was incorporated into TDB2 on the occasion of a scientific study in patients with schizophrenia. With its very narrow age range of norming, it is only moderately suited to individual assessment. In addition, there are very similar tests, the Letter-Number Sequencing subtest in the WAIS-III and WAIS-IV, which are better standardized.