A three-dimensional haptic matrix test of nonverbal reasoning.

Abstract: Three-dimensional haptic matrices were pilot-tested as a nonvisual measure of cognitive ability. The results indicated that they correlated with convergent measures, with emphasis on spatial processing and that the participants who described items "visually" completed them more quickly and accurately and tended to have become visually impaired more recently than the other participants.

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Norm-referenced tests of cognitive abilities often provide information that is useful in developing curricula, behavioral management strategies, and the like for students with special needs, including those with visual impairments (that is, those who are blind or have low vision). Although direct observation of the behavior of students and the evaluation of specific academic skills through testing provides crucial contextual clues to current function or dysfunction, cognitive-neuropsychological testing may provide estimates of broad, less contextual, abilities that underlie a variety of observable behaviors. Testing may both confirm direct observations and explain why behaviors do or do not manifest, often allowing teachers, psychologists, and other professionals to address the "root" of an academic or adjustment problem.

Most standardized measures of nonverbal ability are administered and interpreted visually. That is, vision is required for participants to interact with the test materials during the administration of such measures (Wechsler, 1997), and when the results are interpreted, functional vision is assumed; measures of "sensory-motor integration" are, more specifically, measures of the integration of movement and vision (McGrew & Flanagan, 1998). Although tests have been developed to assess various nonverbal cognitive abilities of persons who are visually impaired (Newland, 1971; Reid, 2002), many of them are not made available to assessment professionals (Taylor & Ward, 1990), were never renormed to remain current (see, for example, Shurrager, 1961), or are not as widely used with persons who are visually impaired as are more familiar instruments that were developed for use with sighted people, such as the Wechsler scales (see Bauman & Kropf, 1979; J. Miller & Skillman, 2003).

Background

TESTS OF NONVERBAL ABILITIES

The disuse of specialized instruments is distressing, given the wealth of evidence suggesting that the application of standard verbal tests to persons who are visually impaired is inappropriate. Although the administration of standard verbal tests is not intuitively contraindicated, research has shown an item bias in the Wechsler verbal subscales (Tillman, 1967). Other research has found differences in specific abilities as a function of visual status and history--for example, a greater auditory memory span among people who are blind than among those who are sighted (Vander Kolk, 1977a, 1977b) and among children who are congenitally blind versus those who are adventitiously blind (Hull & Mason, 1995). Because blindness reduces the opportunity for incidental learning, it may skew the performance on verbal tests, which often sample heavily from "crystallized knowledge" (such as vocabulary, the mastery of facts or trivia, and knowledge of social norms). It is likely that test takers with visual impairments display a unique array of verbal-cognitive competencies that are distinct from those of the sighted norming sample (L. R. Miller, 1977).

Nonverbal portions of popular test batteries are more obviously suspect. Although most standardized nonverbal tests are inarguably inaccessible to persons without useful vision, severe decrements in performance have also been observed with even modest reductions in visual acuity (Groenveld & Jan, 1992). The absence of nonverbal tests (the use of only verbal tests) reduces the breadth and interpretability of assessment data, lowering the reliability of composite scores (like factor scores and intelligence quotient) or precluding their estimation. New norms for existing tests or new instruments are needed if assessment data are to be considered valid, representative, and interpretable--at least to the extent that these criteria are met for sighted persons.

CONVERGENT-DIVERGENT EVIDENCE OF VALIDITY

A valid measure should correlate highly with known measures of the same (convergent) construct and less highly with measures of irrelevant (divergent) constructs (Campbell & Fiske, 1967)--that is, a valid test should measure only what it claims to measure. Convergent validity would be established if a new nonverbal test correlated highly with existing nonverbal tests. Divergent validity would be supported if the new nonverbal measure did not correlate as highly with existing measures of verbal ability, a related, but distinct, construct--that is, correlations with a distinct type of intelligence would be expected to be lower, but not zero, given the known intercorrelation of all scores on cognitive tests. Furthermore, because one would not want to measure developmental influences per se, correlations with visual-developmental factors (such as age of onset of visual impairment and visual acuity) should be correlated least of all. In other words, the point is to demonstrate that irrelevant variables do not correlate with the measure. The study presented here attempted to establish the convergent-divergent validity of a proposed instrument, with respect to visual-developmental factors and verbal and nonverbal abilities.

Method

PARTICIPANTS

Twenty-one adults (11 women and 10 men) with various levels of visual impairment were recruited from the University of South Dakota student body, from the student population of the Sioux Falls Lion' s Rehabilitation Center, and from throughout South Dakota through the South Dakota Services for the Blind and Visually Impaired. The participants ranged in age from 18.7 to 79.1 years with a mean age of 39.9 years (SD = 17.7 years). The age of onset of visual impairment ranged from birth to 73.0 years (mean = 21.6 years; SD = 19.9 years). The mean length of time that the participants were visually impaired was 17.4 years (SD = 19.8 years) and varied between 0.8 and 69.9 years. The mean number of years of education was 13.6 years (SD = 1.9 years), and only one participant did not have a high school diploma or a general equivalency diploma. Of the 21 participants, 20 were white, and 1 was Native American. Four participants were totally blind (no light perception), 2 could report the presence and direction of a light source at best, and 4 more were legally blind with the best correction (logMAR [greater than or equal to] 1.0). The remainder were visually impaired to some degree with the best correction but were not legally blind.

APPARATUS

We defined haptics as "active touch" involving tactile sensitivity, motor planning, and higher-order spatial ability. For example, pressing a braille character onto a motionless fingertip does not represent haptic perception because the perceiver does not move; however, braille reading, in which the reader moves his or her hand, arm, and fingers, does.

Three-dimensional haptic matrices (3-DHM) were constructed as an analog to visual matrix tests, such as Ravens Progressive Matrices. Instruments of this type require the examinee to find a pattern within the elements of a matrix and to select the appropriate missing element from a set of alternatives. Tasks range from pattern matching to mental analysis and the subsequent comparison of various dimensions along which characteristics of the element vary. Matrix tasks have been described as good indicators of executive functioning, abstract reasoning, and induction (Carpenter, Just, & Shell, 1990; McGrew & Flanagan, 1998) with a high g-loading (or correlation with general intelligence) (Snow, Kyllonen, & Marshalek, 1984), which is no doubt why matrix tasks are included in many popular test batteries (see, for example, Wechsler, 1997). We hoped that these qualities would translate to the 3-DHM.

The 3-DHM materials consisted of two boards, each with several .25-inch diameter, 4-inch-long dowels inserted perpendicular to the boards' surfaces--one with four dowels in a 2 x 2 arrangement, and one with nine dowels in a 3 x 3 arrangement, allowing beads to be stacked in various vertical and horizontal configurations (see Figure 1). The beads varied in shape and size: 0.6-inch, 1-inch, and 1.25-inch cubes and 0.8-inch and 1.5-inch spheres. All the beads were drilled through with quarter-inch holes. A five-compartment tray was used to hold the beads that the participants used to construct their solutions.

The test consisted of 6 2 x 2 practice matrices and 19 3 x 3 test matrices. Each matrix consisted of beads that were stacked in various horizontal and, in some cases, vertical configurations on all but the lower-right post. To solve each puzzle, a participant haptically identified the progressive pattern and determined the combination of beads to be stacked on the unoccupied post, thereby completing the pattern. For example, to solve matrix 15 (see Figure 1), the participants noted that the round bead moves down one place in each progression across posts from left to right and stacked the next logical combination of round and square beads on the empty post to complete the pattern.

[FIGURE 1 OMITTED]

As a measure of convergent validity, the five performance subtests of the Cognitive Test for the Blind (CTB; Dial et al., 1990) were administered. The verbal subtests of the third edition of the Wechsler Adult Intelligence Scales (WAIS-III; Wechsler, 1997) were also administered. Uncorrected and best-corrected visual acuity were measured in units of the minimum angle of resolution, or logMAR (Ferris, Kassoff, Bresnick, & Baily, 1982), which allowed for the linear interpolation of distance acuity up to a Snellen acuity of 20/800. When visual acuity was less than 20/800, numbers were assigned to qualitative descriptions of perception (such as light perception and motion perception; see Newell, 1996) and were translated to numbers on the logMAR scale.

PROCEDURE

The participants were first interviewed to obtain visual developmental and demographic information, such as age at the time of testing, age at onset of visual impairment, length of time of visual impairment, and uncorrected and best-corrected visual acuity. WAIS-III verbal scales and CTB performance scales were administered to all the participants in the manner and order that were specified by the tests' administration manuals.

The participants were then blindfolded (unless they were totally blind) and completed the 3-DHM. They were oriented first to the 2 x 2 matrix board and then to the wooden tray containing a number of each of the five types of beads. Six practice trials followed in which the participants completed increasingly complex 2 x 2 matrix puzzles and received feedback on their solutions. In all cases, the instructions were understood by the time of the administration of the sixth 2 x 2 matrix.

The participants were then oriented to the 3 x 3 matrix board and solved the 19 3 x 3 matrices in sequence (a preliminary ordering of items was established with a pilot study of 10 participants). The time required for a participant to construct a solution was measured with a stopwatch, beginning with the first tactile contact with the board and ending when the participant reported that he or she had finished. The participants were not given feedback on their solution of the matrixes.

Results

The standard scores of the sample on the CTB performance and WAIS-III verbal subscales were compared with the appropriate norms (see Figure 2). On the WAIS-III verbal subscale, the participants' scores were generally superior to the mean of the scores of the norming sample. The data on the CTB subtest reflected better-than-average haptic spatial memory (spatial pattern recognition) and constructional (spatial analysis) performance by the group, with slightly lowerthan-average incidental memory for tactile displays (haptic category memory) and recognition of texture (haptic memory recall). Mean elevations greater than one standard deviation above the norming sample mean (standard scores > 13) were observed for WAIS-III letter-number sequencing and spatial analysis on the CTB.

Two methods of scoring were applied to 3-DHM responses: (1) correct or incorrect (simple scores) and (2) the time required to construct a solution following the first tactile contact with the board (latency). The range of simple scores was small (SD = 1.86, with a possible range of 0 to 19). To avoid range-attenuation problems (Nunally & Bernstein, 1994), the two scoring systems were integrated. Adjusted scores were calculated by applying a latency-mediated coefficient to the simple scores:

Adjusted 3-DHM = 3-DH[M.sub.Simple] [2 - (3-DH[M.sub.Latency / [Mean.sub.Latency] + S[D.sub.Latency)]

[FIGURE 2 OMITTED]

The adjusted score for any item was greater than 1 if latency was less than 1 SD above the mean latency for that item. Latencies greater than the mean plus 1 SD were scored less than 1, with the score decreasing as a function of increasing latency. As with the simple scores, incorrect responses were scored 0. Thus, adjusted scores allowed for an incorporation of the efficiency of exploration and solution, as reflected in response latency, into the simple score estimate of accuracy, while increasing the range of score variation from an SD of 1.96 to an SD of 3.58. This combination of simple and latency scores also served to increase the similarity between the 3-DHM and the other two instruments, both of which use criteria of speed and accuracy in their scoring systems.

The construct validity of the 3-DHM was assessed using a simplified convergent-divergent correlation matrix (see Table 1) comparing the 3-DHM adjusted scores, WAIS-III verbal IQ (V-IQ), CTB performance index scores (CTB-P), visual acuity, and age of onset of visual impairment. To satisfy assumptions of the correlation procedure, skew was reduced by taking the square root of the scores for age of onset of visual impairment ([AO.sup.1/2]). The logarithm of time since the onset of visual impairment (LogTI), also transformed to reduce skew, was not included in the matrix, because of the high correlation with [AO.sup.1/2] (r = -.71, p > .01).

The correlation between 3-DHM and V-IQ was less than the correlation between 3-DHM and CTB-P, indicating the nonverbal content of the 3-DHM. The correlation between CTB-P and V-IQ (r = .429) was comparable to a reported correlation between CTB-P and WAIS-R V-IQ (r = .50; Dial et al., 1990) and somewhat larger than the correlation between V-IQ and 3-DHM. The correlations between each of the cognitive measures and visual-developmental variables (divergent) were small, whereas the correlations between 3-DHM and visual acuity and age of onset of visual impairment were smaller than the mean of correlations between the other two instruments and the two visual-developmental variables.

The CTB-P subscale scores were correlated with the 3-DHM adjusted item and total scores to assess the content of the proposed instrument better. The 3-DHM scores correlated most highly with spatial analysis (r = .508, p > .05) and spatial pattern recognition (r = .528, p > .05), described by Dial et al. (1990) as constituting a "spatial" factor. The first eight 3-DHM items were significantly correlated (p > .05) most frequently with either or both of the CTB spatial factor subtests (r = .458 to .617).

Discussion

CONVERGENT-DIVERGENT VALIDITY

The profile of convergent and divergent correlation coefficients is consistent with 3-DHM adjusted scores as valid indicators of nonverbal, rather than verbal, cognitive ability, because correlations were high with the CTB-P scores and moderate with the WAIS-III verbal scores. The CTB-P was, in fact, more similar to verbal scores than the 3-DHM. Furthermore, because correlations with visual-developmental variables were the smallest for the 3-DHM, it is possible that the 3-DHM are less sensitive to differences in age of onset of and degree of visual impairment than either the CTB or WAIS-III.

The high correlations between the 3-DHM scores and CTB spatial factor subscales, however, seem to indicate that the 3-DHM measure, in large part, haptic spatial ability, rather than general nonverbal ability. The pattern of correlations suggests less reliance on the discrimination of textures and memory for textures and spatial displays, as measured by the CTB haptic category memory, and haptic memory recall subtests. The finding of significant correlations between the first eight 3-DHM items and the CTB spatial factor subtests was surprising, given that these earlier items were simpler than the later items, as measured by error rate. The two CTB subtests require the examinee to assemble a pattern of rough and smooth textured tiles into a pattern memorized from a model (spatial pattern recognition) and to assemble geometric shapes from simpler components with progressively fewer cues to the placement of the constituent parts (spatial analysis), both of which were reported as challenging by many participants. It is possible that performance on the first eight 3-DHM items was more dependent on the speed of perceiving patterns (and manual motor speed more generally) within the matrix than was true for subsequent items, especially the last three items, which showed a markedly higher error rate (> 60%) than was evidenced for the first eight items (< 20%). These data suggest that the efficiency of haptic-spatial processing is an important component of what the 3-DHM measure. A post-hoc analysis was conducted to explore this issue.

Qualitative analysis of solution strategies

Any haptic test of higher-order ability, like the 3-DHM, must account for basic haptic-visual differences in perception and spatial processing, especially if performance varies as a function of visualdevelopmental variables (see the review by Thinus-Blanc & Gaunet, 1997). Therefore, we sought to clarify the relationship between 3-DHM performance and the visual-developmental variables in our sample.

PROCEDURE

A grounded theory approach (Strauss & Corbin, 1990) was used, with five psychology graduate students at the University of South Dakota constituting the analytic team. After completing each 3 X 3 matrix, the participants were asked to explain their reasoning ("tell me why you chose that block [or those blocks]"). Videotapes and transcripts of the participants' explanations were scrutinized, and descriptive categories were developed iteratively, with a regular review of the source materials. A scoring system was developed to capture the array of types of solutions that the participants described or demonstrated. Given that the first eight 3-DHM items were most highly correlated with the CTB spatial factor subtests, only these items were analyzed.

[FIGURE 3 OMITTED]

RESULTS

The final scoring system, illustrated in Figure 3, used a sentence structure to relate the characteristic of the beads described (shape, size, or shape and size--the "what" code) to its spatial distribution across part or all of the matrix board (the "where" code). "Where" codes were divided broadly into gestalt or analytic codes. Gestalt codes were those in which the "what" were related using a clearly visual description (for example, "these small ones form an 'X,'" or "the round ones are in an arrow"). Analytic "where" responses were devoid of pictorial references and used either a regular, systematic (such as using columns or rows) or a less systematic (like matching a row to a column or matching the contents of three posts) breakdown of spatial elements to describe a pattern. Other descriptors were used to code the manner in which a characteristic varied across a spatial element ("how"), whether such variation occurred between or within a set of identified spatial elements ("chunking"), whether an identified pattern was restricted to one level of the board's posts ("dimension"), and whether all the beads were used in the description of the pattern ("completeness"). All the participants' responses were coded using these guidelines (see examples in Figure 4).

[FIGURE 4 OMITTED]

More than any other, "where" codes seemed to capture spatial perceptions of the matrix patterns. These codes were divided into three categories, on the basis of the extent to which they reflected an analysis of the stimulus. A low level of analysis consisted of gestalt codes and most closely reflected the "simultaneous" processing of matrix elements. An intermediate level of analysis included codes that divided the matrix into systematic elements, such as "size increases across rows." A high level of analysis consisted of codes indicating a less systematic parsing and comparison of spatial elements, generally ignoring some significant portion of the matrix, for instance, matching beads on three different posts or matching beads within three groups of posts that did not relate in a regular manner, such as columns or rows.

Four analyses of variance (ANOVAs) were used to detect any significant differences between the means of visual-developmental variables (A[O.sup.1/2]), LogTI, and visual acuity) using level of analysis (high, intermediate, and low) as the factor. Tests yielded significant (p = .015) effects of level of spatial analysis on LogTI (F = 4.28 [2, 215]) and significant (p = .001) effects of level of analysis on adjusted 3-DHM scores (F = 6.73 [2, 215]). No significant effects were observed for either LogTI or visual acuity. An inspection of the mean plots for the two ANOVAs (see Figure 5) revealed that the lion's share of effect came from the differences between the low-analysis (gestalt) responses and the intermediate-and high-analysis responses. It should be noted that the small sample resulted in low statistical power for the tests; it is possible that "real" effects may not have been detected.

[FIGURE 5 OMITTED]

DISCUSSION

Owing in large part to the speed of visual saccades, vision has often been described as a more "simultaneous" spatial sense, and touch has been described as more "sequential" (see Thinus-Blanc & Gaunet, 1997). The qualitative analysis points to simultaneous versus sequential representational ability as an important factor in performance on tests. We observed that 3-DHM performance was greater when at least the solutions of some items included visual descriptions, and items in which such visual descriptions were observed tended to be completed by persons whose visual impairment was more recent. The implication is that a simultaneous "visual" perception of the matrices in the absence of vision yielded greater efficiency and accuracy in solutions and was more likely among participants who had become visually impaired more recently. The relationship between visual (gestalt) descriptions and 3-DHM performance is stronger and perhaps more interesting, assuming that a spontaneous verbal report of imagery is reliably related to the actual use of imagery in the tasks. The importance of the use of imagery in predicting the performance of tasks when the use of imagery is not generally related to visual-developmental variables is perplexing unless the 3-DHM are more sensitive to the presence of specific types of mental representations than to visual-developmental variables that are reputed to influence them. Regardless, the data suggest the importance of visual-developmental variables, such as the length of time that one has been visually impaired, to the performance of haptic analogs of nonverbal visual assessments and call for greater attention to these variables in the development of tests. Because time since the visual impairment and visual acuity were confounded in this study, in the future, the development of tests should account for the effects of each separately and in combination.

General discussion

Because of the small sample, the analyses should be considered preliminary. It is impossible to represent the diverse range of demographic variables that are pertinent to performance on cognitive tests--let alone the necessary range of participants' ages, socioeconomic status, regions, ethnicities, and the like--with 21 cases. The interpretation of statistical tests is also made difficult, since results that were nonsignificant with a small sample may have been significant with a larger sample. Furthermore, measuring "intelligence" through haptics presents its own potential challenges. The qualitative analysis of 3-DHM suggests that "visual experience" relates to performance on tests; there can be little doubt, in general, that one's spatial ability is both influenced by one's history of visual impairment and an important contributor to one's performance on haptic measures of ability, such as the 3-DHM. To avoid confusion, we suggest that the current instrument assesses haptic-spatial reasoning ability; broader analytic or reasoning skills are, most likely, only part of what the test measures. Therefore, the future development of the 3-DHM (and similar tests) must account for an individual's manual-motor skills (such as speed and coordination, use of one or both hands, and age-related declines in motor and processing speed) and the visual-developmental factors that affect spatial processing. At least, solvers' use of more or less "simultaneous" gestalt representations should be accounted for.

These points granted, data from even the small current sample raise the possibility that 3-DHM may be a promising means for assessing nonverbal cognitive (among other) abilities in the absence of vision. Although the constellation of convergent and divergent correlations was consistent with 3-DHM as a valid measure of nonverbal cognitive ability, convergent validity of the instrument was less than optimal and may be due to the apparently restricted scope of the current, versus the criterion (CTB), measure. The exploratory qualitative analysis points tentatively to simultaneous spatial-representational ability as an important factor in performance on tests, although a more rigorous reanalysis is called for. Also, greater attention was paid in the current version of the test to the spatial layout of the matrices. It was obvious, through observations of the participants' solutions, that all the matrices could be perceived and solved in either a simultaneous or sequential manner. Future versions of the 3-DHM may include systematic variations in the number and complexity of descriptive dimensions relating matrix elements, presumably offering a better measure of executive functioning in a haptic-spatial context (Carpenter et al., 1990). If successful, such a measure will allow for testing both spatial and general cognitive ability using the same materials. At present, the 3-DHM is best considered

a "promising" test, rather than a "validated" one.

The participants reported that interaction with 3-DHM test materials was generally more enjoyable and less frustrating than interaction with the comparison measures. That the 3-DHM scores were generally unrelated to the CTB subtests that emphasized fine tactile discriminations suggests that large, simple 3-DHM materials were less demanding of fine tactile acuity. The 3-DHM materials are comparatively self-contained and therefore amenable to presentation in a variety of real-world contexts (such as bedside). Last, the "open architecture" of the matrix board and bead combination provides flexibility in the development and presentation of a variety of haptic tasks, allowing more opportunities for practitioners to conduct applied research. The basic 3-DHM test materials hold the potential for a future instrument that is intrinsically interesting to examinees, more accessible to persons with reduced tactile sensitivity, more easily administered to a variety of examinees in different contexts, and readily adaptable to a variety of haptic-cognitive tasks.

References

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Miller, J., & Skillman, G. (2003). Assessor satisfaction with measures of cognitive ability as applied to persons with visual impairments. Journal of Visual Impairment & Blindness, 97, 769-773.

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Reid, J. (2002). Testing nonverbal intelligence of working-age visually impaired adults: Evaluation of the Adapted Kohs Block Design Test. Journal of Visual Impairment & Blindness, 96, 585-595.

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Thinus-Blanc, C., & Gaunet, F. (1997). Representation of space in blind persons: Vision as a spatial sense? Psychological Bulletin, 121, 20-42.

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This research was funded by PHS Predoctoral Research Fellowship F31 EY06958. The authors thank the staff of the South Dakota Services for the Blind and Visually Impaired, the staff and clients of the Lion's Rehabilitation Center in Sioux Falls, and all others in South Dakota and Nebraska who offered invaluable assistance in the conduct of the research.

Joseph C. Miller, Ph.D., Department of Psychology, University of North Dakota, Box 8380, Grand Forks, ND 58203; e-mail: <joseph.miller@und. nodak.edu>. Gemma D. Skillman, Ph.D., associate professor, Department of Psychology, University of South Dakota, 414 East Clark Street, Vermillion, SD 57069; e-mail: <gskillma@usd. edu>. Joanne M. Benedetto, M.A., interface design specialist, State Farm Insurance, 3 State Farm Plaza South, L2-198, Bloomington, IL 61791; e-mail: <[e-mail]>. Ann M. Holtz, M.Ed., graduate student, Department of Psychology, University of South Dakota; e-mail: <[e-mail]>. Carrie L. Nassif, Ph.D., assistant professor and staff psychologist, Kelly Center, Department of Psychology, Fort Hays University, 600 Park Street, Hays, KS 67601; e-mail: <[e-mail]>. Anh D. Weber, Ph.D., clinical psychologist, Kaiser Permanente Autism Spectrum Disorder Center, 175 Bernal Road, San Jose, CA 95119; e-mail: <[e-mail]>.

Table 1
Correlation matrix for convergent-divergent validation of 3-DHM
time-adjusted scores with WAIS-III V-IIQ and CTB P-IIQ as convergent
measures and best-corrected visual acuity and age of onset of visual
impairment (transformed) as divergent measures.

         3-DHM   V-IQ    CTB-P    VA      [AO.sup.1/2]

3-DHM    --      .319    .609 *   -.055   -.055
V-1Q             --      .429      .152   -.173
CTB-P                    --       -.037   -.295
VA                                --      -.175
                                          --

Note: 3-DHM = three dimensional haptic matrices adjusted scores,
V-IQ = WAIS-III Verbal IQ, CTB-P = performance index (P-IQ) of
the Cognitive Test for the Blind, VA = best-corrected visual acuity,
and [AO.sup.1/2] = square root of the age at onset of the visual
impairment.

* p < .01.