Structural models of cognitive and perceptualmotor abilities

Pergamon PII:

STRUCTURAL

Person. indicid. D(f/: Vol. 24, No. 5. pp. 603614. 1998 Published by Elsevier Science Ltd Printed in Great Britain 0191-8869/98 $19.00+0.00 S019144869(97)00021~X

MODELS OF COGNITIVE MOTOR ABILITIES

AND PERCEPTUAL-

William C. Tirre*’ and Karen K. Raoufl ’ U.S.A.F. Branch,

Armstrong Laboratory, Aircrew Training Research Division, Aircrew Performance Research 7909 Lindbergh Dr, Brooks Air Force Base, Texas 782355352 and ‘Control Data Systems Inc. (Received 30 June 1997)

Summary-A collection of 25 computer-administered tests was given to a sample of 172 adults to examine the overlap between the cognitive and perceptual-motor abilities domains. The focus was on multilimb coordination ability as a criterion variable, as this ability has a long history of validity in predicting pilot training performance. Structural equation modeling was used to test two related models of human abilities. The first one being a causal model and the second being a nested hierarchical model. The results suggest that multilimb coordination ability is not simply another manifestation of general cognitive ability, but instead the result of several abilities such as dynamic visual processing, visuo-spatial processing and working memory. A second narrower perceptual-motor factor, target tracking, was found to be related to processing speed but no other cognitive factor. Published by Elsevier Science Ltd

Since the early 1980’s, industrial and military psychologists have been interested in applying advances in computer technology and cognitive psychology to identify abilities that cannot be measured with paper-and-pencil tests, but which are critical to the performance of job tasks. The advantage of computer-based ability measurement is most clear in the case of perceptual-motor abilities which are used in piloting aircraft and operating various other vehicles including naval landing craft and construction equipment. Perceptual-motor abilities include coordinated movements of two or more limbs, precisely controlled movements in response to dynamic stimuli, arm movement rate and arm and hand movement steadiness, to name a few identified factors (Fleishman, 1964). Carroll (1993) reviewed and reanalyzed the available correlational data on perceptual-motor abilities and concluded that 11 perceptual-motor abilities were identifiable through factor analysis. Given the observation of positive manifold in the intercorrelations of abilities, it is likely that considerable overlap exists between the perceptual-motor and cognitive ability domains, yet the extent and nature of this overlap is not well understood. Except for a series of studies starting with Fleishman and Hempel (1954) (see review by Fleishman, 1972), there has been little effort to understand perceptual-motor abilities in terms of cognitive abilities or operations. Fitts (1964) contended that “sharp distinctions between verbal and motor processes, or between cognitive and motor processes served no useful purpose”. A stronger position was taken by Ree & Carretta (1994) who presented a “not much more than g” argument. Ree & Carretta argued that the incremental predictive validity of perceptual-motor abilities as measured by the Basic Attributes Test (a pilot selection battery) would be small because of substantial overlap with cognitive abilities measured by tests such as the Armed Services Vocational Aptitude Battery (ASVAB). Our previous research on this issue suggested little overlap. For example, Tirre and Raouf (1994) found that the three perceptual-motor factors identified by their battery

*To whom all correspondence should be addressed: William Tirre, c/o Armstrong Laboratory, AL/HRAA, 7909 Lindbergh Dr, Brooks Air Force Base, Texas 782355352. Tel.: (210) 536-2027 (Voice); Fax: (210) 536-6429; E-mail: [email protected] Author Note: William C. Tirre, Armstrong Laboratory, Human Resources Directorate, Aircrew Training Research Division. Brooks Air Force Base, Texas. This research was supported in part by the Air Force Office of Scientific Research Grant 61102F, Work Unit 2313T147, Task 2313/BA Learning Abilities Measurement Program (LAMP) and by the Armstrong Laboratory, Work Unit 1123A2-02. Portions of this research were presented at the American Psychological Association, August 1996 in Toronto, Canada. 603

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William C. Tirre and Karen K. Raouf

correlated 0.00-0.11 with general cognitive ability as measured in the ASVAB. The range of estimated correlation reported by Tirre and Raouf (1994) is probably low and in this research, we investigated the relationship between cognitive and perceptual-motor abilities with a broader sampling of tests in both domains. We also attempted to understand the nature of the domain overlap by conducting a cognitive components analysis of a class of complex perceptual-motor tasks. We began this research with the assumption that the ability that enables one to perform complex perceptual-motor tasks such as operating a light aircraft would have multiple determinants or components. We selected a complex perceptual-motor ability known as multilimb coordination for study because its relationship to piloting aircraft is well-established (Griffin & Koonce, 1996). We hypothesized four underlying components for the multilimb coordination ability: general cognitive ability/working memory, cognitive speed, dynamic visual processing and spatial ability. We devised a path or causal model and a structural model of the relationships among these abilities corresponding to the “g is primary” (Spearman, 1923) framework. Our “g is primary” model is actually better described as a “g/working memory is primary” model as we basically equate psychometric g with working memory capacity (Kyllonen & Christal, 1990; Tirre & Pena, 1993; Kyllonen, 1995). Our specific hypotheses, described below, were expressed in terms of structural equation models (Bentler, 1993). The “g/working memory is primary” model can be described as follows: (1) Working memory (WM) has a limited capacity, either a fixed workspace or finite pool of attentional resources, that must be shared between current operations and temporary storage of intermediate results and freshly encoded data. It is the central bottleneck in information processing and its capacity varies considerably across individuals. Like Baddeley (1986), we hypothesized that individuals have a characteristic general working memory capacity; and like Kyllonen & Christal (1990) we used a variety of complex cognitive tasks in addition to tasks explicitly designed to measure working memory to indicate this factor. Our specific hypothesis was that working memory capacity constrained the effectiveness and speed of other operations including basic cognitive processes (e.g. encoding, retrieval, comparison etc.) and set limits on real-time activities such as event monitoring and multitasking such as the coordination of eyes, hands and feet. This hypothesis translates to direct effects of WM on processing speed, dynamic visual processing, and multilimb coordination. (2) Processing speed, although functionally limited by working memory resources, has direct effects on both dynamic visual processing and multilimb coordination. (3) Dynamic visual processing involves interpretation of moving or briefly exposed visual stimuli. Similar factors have been researched by Gibson (1947), Roff (1952), Scialfa, Garvey, Gish, Deering, Leibowitz and Goebel(l988) and Law, Pellegrino and Hunt (1993). Success on dynamic visual tasks requires focused attention on visual stimuli whose features, size, or location change rapidly and so we hypothesized that WM would have a direct effect on this factor. There is also a processing speed requirement in that the observer must quickly orient to changes in the visual stimulus in order to make judgments about it. Thus, we hypothesized a direct path from processing speed to dynamic visual processing. Dynamic visual processing has a direct effect on multilimb coordination because the latter ability requires examinees to visually track moving targets. (4) Independent of the other abilities considered in this group, a perceptual ability that enables the interpretation of graphically displayed spatial information will play a role in guiding perceptualmotor tracking. Cattell (1971) wrote of “provincials” which were specialized abilities for visuospatial and auditory processing. A similar theoretical notion was advanced by Fodor (1983) who wrote of modularized “faculties” that were not dependent on a common cognitive resources pool (e.g. working memory). To depict the role of visuo-spatial processing ability in the model, we have a direct causal link from this ability, which is a truly exogenous or independent ability, to multilimb coordination ability. The hypothesis set for the “g/working memory is primary” model is depicted as a path diagram (Fig. 1). Note that the variables used to predict other factors in the path analysis were always mutually orthogonal. This was accomplished by using the disturbance term corresponding to a factor that itself was a dependent variable in a structural equation. The disturbance terms may be regarded as residual variables, i.e. the part of the factor that is not correlated with its predictors.

Cognitive and perceptual-motor abilities

Fig.

1. The “g/WM is primary”

path or causal model. D denotes disturbance (E) reflecting uniqueness are not shown.

605

term. Error

variance

terms

An alternative model that is similar in logic to the path model in Fig. 1 is the so-called nested model (Gustaffson & Balke, 1993) which evolved from the Schmid and Leiman (1957) oithogonalized factor model. With the nested model, factors are mutually orthogonal and observed variables can be loaded by multiple factors all of which are at the same level. To compare the two modeling approaches, consider a test of dynamic visual processing (e.g. TPSl), which in Fig. 1 is loaded by the dynamic visual processing factor and has indirect effects of g/WM and processing speed by virtue of its parent factor being dependent on these factors. In Fig. 2 which shows the nested factor model, the same test is loaded directly by the g/WM, processing speed and dynamic visual processing factors. In what follows, we describe our effort to test the fit of these models to correlations among a set of cognitive and perceptual-motor tests and to determine the implications of each model for the prediction of multilimb coordination. METHOD Participants

The sample consisted of 172 civilian participants recruited by newspaper advertisements for paid participation in this study which included about 50 h of flight training using a desktop flight simulator. The participants were between 18 and 30 years of age, were generally healthy according to a medical history questionnaire and had no previous formal training in aviation. Approximately 22% of the sample was female, which is larger than the percentage currently enrolled in Air Force flight training in the U.S.A. Procedure

This study was conducted as part of a larger study concerned with individual differences in flying skill acquisition that was administered in 1.54-h sessions over three weeks. On the first day, three tests (one working memory test and two perceptual-motor tests) were administered as a qualification

606

William C. Time and Karen K. Raouf

Fig. 2. The “g/WM

is primary”

hierarchical

nested model. Error variance are not shown.

terms (E) reflecting

uniqueness

battery. Generally, the top 50% of the candidates recruited for the study were selected for participation. The next two sessions were reserved for aptitude testing and beginning lessons on the Basic Flight Instruction Tutoring System (BFITS). Testing and instruction were conducted for classes of 13. The first 60 cases were tested on 386SX 25 MHz computers, then the study was moved to a lab equipped with 486DX 50 MHz computers. A “slow-down” program was written to achieve a comparable frame rate for BFITS on the faster 486DX computers. No adjustment was needed for the aptitude tests. All data analyzed for this study were collected in the first week of testing. Apparatus

The perceptual-motor tests utilized rudder pedals custom manufactured by Technology Systems Inc. and joysticks (Flightsticks) manufactured by CH Products. These were installed on 386SX 25 MHz and 486DX 50 MHz computers with color VGA monitors located in individual study carrels. Experimental test battery

All tests with the exception of the Wonderlic Personnel Test were administered by computer. Tests were classified as cognitive if correct responses were primarily the result of intellectual effort and if responding required only a keypress or mouse click. Tests were classified as perceptual-motor if good scores required effortful control of flightstick and/or rudder pedal devices. The Wonderlic Personnel Test (E.F. Wonderlic & Associates, 1983) (WPT) is an omnibus measure of general cognitive ability. It consists of 50 diverse items administered in 12 min. This test was scored for number correct. In the reading span measure (WMV2) of working memory for verbal content (or verbal working memory, hence WMV), participants are presented lists of 2-6 sentences each paired with an unrelated word. The participant must respond true/false to the sentence and remember the word. Then at the end of the list, the participant must recall the words in order. This test is a variant of the task

Cognitive and perceptual-motor

abilities

607

introduced by Daneman and Carpenter (I 980). True/false verification time (TFVRT) for the sentences was retained as an indicator of information processing time. The WMV4 is a running memory span measure involving antonyms. A list of 3-7 words is presented sequentially. At the end of the list the participant is directed to recall the last three words presented. If the words were presented in red, the participant is to recall the antonyms (e.g. fast/slow) of the last three words. Participants are allowed 25 s to respond. The spafiul XYZ assignment spatial working memory test (WMS3) presented three pairs of simple line drawings (labeled X, Y, Z) on separate frames. The participant was directed to mentally add or sometimes subtract the drawings to create a third drawing. After the third frame, the participant must recall each generated figure. The task requires temporary maintenance of mental images while doing other spatial processing. In the roratedsymbols test (ROTS, spatial relations), three pairs of abstract symbols are presented in a row. The participant must indicate how many pairs (0,1,2,3) consist of identical symbols rotated in a plane. In the marching planes test (MAP, visualization & multilimb coordination) a model aeroplane must be rotated in three dimensions (pitch, roll and yaw) using flight controls to match the attitude of the target plane (Tirre & Raouf, 1994). The test was scored for percentage correct and solution time. The spatial orientation test (SPO) presents the participant a cube with a chair-like object in the center (Barratt, 1955). The participant is referred to a window on the cube and is asked to select one of six views of the object that would be seen from the given window. The procedure is reversed for the second half of the test. That is, an object is shown below the main figure and the participant must select the window which would provide the given view. The verbal associative learning test (ALV3) first presents eight blocks of 32 matching items. Eight word pairs are presented in a row at the top of the screen (occupation-furniture pairs). A test pair is presented in center of screen. The participant must decide if the word pair is a match or nonmatch. The last two blocks are recognition items: test pairs are presented without opportunity to look up the answer. In the quantitative associative learning test (ALQZ), number pairs (e.g. Flight 263-Gate 41) are presented for 4 s each. After eight pairs are presented, the participant is presented stimulus terms (Flight 263) and must type in response terms (41). Three sets of eight pairs are presented. The spatial associative learning test (ALSI) presents pairs of line figures drawn by connecting dots in a 3 x 3 matrix for 10 s. After the fourth pair the participant is presented the stimulus term and must construct the response term by clicking mouse on dots. Twelve sets of four pairs are presented. The verbulprocedurul learning test (PLV2) has participants learn to apply two rules to word pairs to produce a third. All words pertain to relative time (past, present, future). Participant might be presented BEFORE YESTERDAY. Rule 1 says that if two words refer to the same time, respond with the same time (e.g. future). Rule 2 says if two words refer to different times (BEFORE TOMORROW), respond with the missing time (e.g. present). Response (past, present, future) must be made within I5 s or it is counted wrong. There are 72 items. The quantitative procedural learning test (PLQ3) presents numbers to be classified according to a set of rules. If the number is positive and small (l-9) respond “(Small or Even)“. If the number is positive and big (1 I-19) respond “(Big or Odd)“. If the number is negative and odd (- I, - 3,. . - 19) respond “(Big or Odd)“. If the number is negative and even (- 2, - 4,. . . - 18) respond “(Small or Even)“. Initially participants study rules for I min. Thereafter numbers are presented individually for classification. When misclassifications occur, the participant gets to review the rules. Twelve sets of 32 items are presented. In the rapid serial cfussification test of spatial procedural learning (PLSl), a box divided into quadrants is presented. Lights appear in sequence in the quadrants tracing one of three patterns (Z, X, or C). Participants must classify each sequence as a Z, X, or C within 2 s or be counted wrong. The test consists of 96 items. The Posner and Mitchell (1967) name (AA or Au) vs physical identity (AA or aa) test of processing speed for verbal content (PSV) required same/different responses. Response time was measured and speedy responses without careless mistakes were encouraged. The number comparison task (PSQ) required participants to select the larger of two digits as

608

William C. Tirre and Karen K. Raouf

quickly as possible (Moyer & Landauer, 1967). If the larger digit appeared on the right (left), the participant would press the L(D) key with his right (left) forefinger. There were 144 items. In thefigure comparison task (PSS), two hard-to-label figures drawn by connecting dots within a 3 x 3 matrix were presented for comparison. The participant’s task was to decide if they were the same (Like, press the L key) or different (Different, press the D key). The Alertron task (Pieters & van der Ven, 1982) was a variant of the visual inspection time (VIT) task (Vickers, 1970). A 3 x 3 matrix of red dots (each approximately 0.125” diameter) was centered on the screen. Then three, four or five dots were illuminated for a brief time. The dots would then be replaced by a dynamic mask (a rapid sequence of blinking dots appearing within the same matrix). The participant’s task was to respond “odd (3 or 5)” or “even (4)“. This task was programmed to adapt to the participant to estimate his/her perceptual threshold or inspection time. The algorithm would present a trial with the next shorter exposure time if three correct responses were made to trials with a particular exposure time, and a trial with the next longer exposure time if one incorrect response was made. The program terminated when 16 correct responses were obtained for a particular exposure time. This yielded an ordinal score, 1-9, with 1 being the highest level of difficulty or shortest stimulus exposure time. The nine stimulus exposure times were 74, 88, 106, 120, 142, 206, 306, 406 and 1006 ms. Two blocks of trials were administered and the results were averaged for a final score. The complex coordinator (MLCl) task was a simulation of the W.W.11 multilimb coordination task (Melton, 1947) introduced by Mashburn (1934). There were three sets of lights (red targets, green control). An arc of red lights appeared on top, with an arc of green lights below. Green lights were illuminated by roll inputs on the flightstick. Two columns of lights were in the middle of the screen with green lights being illuminated by pitch input on the flight stick. Two rows of lights were on the bottom with green lights being illuminated by rudder input. As soon as the participant matched the configuration of three red lights, a new item would appear. The task was timed (8 min) with the score being the number of matches made. In the ball-centering test of multilimb coordination (MLC2) the participant was instructed to keep a ball (0.625” diameter) centered on a cross in the middle of the screen. The ball was programmed to move vertically and horizontally away from the screen center. Horizontal control of the ball was by reverse rudder input (to move left, step on the right pedal). Vertical control (pitch) was by the flightstick (to move up pull back). The computer kept a record of the amount of time spent in each of 20 concentric circles drawn about the cross. In the balloon pop task (MLC3) participants were presented sets of balloons floating around the screen which they were to pop using flightstick and pedals to position crosshairs on the target. Trials started with a screen showing 2-8 balloons of various colors (1.5 s per balloon). Participant was directed to memorize the order of balloons and pop balloons in the same order. If the participant attempted to pop a balloon out of order, it would not pop but gave auditory feedback to indicate that the balloon was targeted out of order. Elapsed time to pop all balloons was recorded as the dependent variable. In the helicopter target interceptor task (HELTI), a target (a helicopter about 0.75” long) moved across the screen occasionally changing vertical course. The participant was instructed to move the crosshairs on target using rudder and flightstick input and then fire using the trigger. Number of targets destroyed and elapsed time were recorded. The helicopter target tracking task (HELTT) complicated TI by requiring the participant to track the target for 2 s to achieve a target lock. Only after locking on target could the target be destroyed. In addition to number of targets destroyed and elapsed time, total time locked on target was recorded. The laser shoot one task (LSl) involved shooting a plane flying horizontally across the top of the screen by aiming a laser cannon on the bottom center of the screen with pedals and firing by triggering the flightstick (Tirre & Raouf, 1994). Targets came in three sizes and traveled in three speeds at three heights. This was a fairly easy task of 108 trials and early kills were encouraged. Five shots were allowed. This task served as warm-up for a subsequent task, described next. The laser shoot two (or multi-level targeting) task (LS2) complicated LSl by requiring the participant to match his aircraft (which replaced the cannon) to the size of the target (Tirre & Raouf, 1994). Size of the participant’s aircraft was controlled by moving the flightstick forward to decrease and aft to increase. Ten shots were allowed. Multiple scores were available from this test,

Cognitive Table Composite

Label

G/WM

General

PLACC

Procedural

PLRT

Procedural

EPIMEM

Episodic

PROCRT

Processing

SPATIAL

General

Now:

PC in variable

** Response

and perceptual-motor I. Creation

of composite

abilities

609

variables

Formula cognitive

ability/working

memory

GjWM

learning

accuracy*

PLACC

learning

response time**

PLRT

= MEAN(WPTPC,

WMVZPC.

= MEAN(PLQPC.

WMV4PC.

= MEAN(PLQRT,

PLVRT.

ALV3RT)

accuracy

EPIMEM

= MEAN(ALV3PC.

ALSIPC.

response time (median)

PROCRT

= (PSQRT,

PSSRT)

SPATIAL

= MEAN(SPOPC.

memory spatial

ability

name refers to percent

correct

and RT

refers to median

time was based on second half of test for procedural

learning

response time.

WMS3PC)

PLVPC)

PSVRT,

ROTSPC)

*Accuracy

tests and on first 75%

ALQZPC)

was scored on first half of test.

of test for the verbal

associative

learning

task (ALV3).

but for this study we selected LS2XRNG, which is the complement of the distance the target had traversed before destruction (i.e. screen width in pixels minus distance traveled in pixels). The single racer task (temporal processing-spatial or TPSl) presented a line growing horizontally from left to right of the screen. There were three growth speeds and three different lengths a line could grow before disappearing from the screen. The task was to click on the mouse when the line’s leading edge would reach the finish point on the far right of the screen. This test was scored for percent correct, allowing for 0.5 s tolerance. In the double racer tusk (TPS2) two lines grew from left to right each at any of three speeds. The lines could start at the same or different times and could disappear at the 0.25 or 0.50 screenwidth point. The participant’s task was to click on the line that would reach the finish point first. This test was scored for percent correct. Data reduction and analysis procedures

The cognitive tests described above which yielded mean error rates of 20% or more were treated as power tests and were scored for percent correct. The processing speed tests were scored for median response time over all items. To achieve a desirable examinee-to-variable ratio, we reduced the number of observed variables by creating composites corresponding to factors we have previously found. For example, g/WM was the mean of Wonderlic Personnel Test and three working memory tests, i.e. WPT, WMV2, WMV4 and WMS3 (Table 1). Seventeen variables were reduced to six composite variables resulting in a total of 19 variables for 172 examinees, an examinee to variable ratio of 9 : 1. A ratio of 10 : 1 is desirable. * The perceptual-motor and visual perception tests (e.g. VIT, TPSl, TPS2, PLSl) were kept as separate variables in the correlation matrix to serve as indicators for the multilimb coordination and dynamic visual processing factors, respectively.

RESULTS

The ability test scores were modestly intercorrelated (see Appendix Table A2). The strongest cognitive correlates of the multilimb coordination tests were the dynamic visual processing tests (mean r = 0.28) and the spatial ability composite (mean r = 0.29). The weakest correlates were the indicators of processing speed (mean r = 0.19) and g/working memory (mean r = 0.20). Bear in mind that these correlations are between observed variables without correction for attenuation or for restriction in range.

*Because of the small number of females in our sample, we chose not to examine the factor structures

separately for males and females. Previously, Carretta and Ree (1997) reported negligible differences between the factor structures for cognitive and psychomotor tests for males and females; but we agree with one reviewer of this article, that this issue merits further attention.

610

William C. Tirre and Karen K. Raouf Table 2. Path model standardized

Measurement equations

s/WM PLACC EPIMEM SPATIAL MATCHPLN PROCRT PLRT TFVRT VIT TPSI TPS2 PLSI MLCI MLCZA MLC2B LS2XRNG MLC3 HELTI HELTT Construct equations PROCSPD DYNVISUAL MLCOORD

s/WM

Processing speed

Dynamic visual

0.840 F 0.748 0.747 0.593 0.315

Multilimb coordination

0.421 0.529

F

-0.536 0.509 0.540 0.684 F 0.317

0.266 -0.186

0.219 0.272

0.350 -0.618 -0.654 0.252 -0.591 0.607 0.733 F

0.177 n.s. -0.305

0.258

0.616

x2 with I35 degrees of freedom Probability x=ldf Bentler-Bonett normed fit index Bentler-Bonett Non-normed fit index Comparative fit index Root mean square error of approximation (RMSEA) Average absolute standardized residuals Average off-diagonal absolute standardized residuals Now: All loadings are significant

Visuo-spatial

0.1 I I ns -0.745 -0.643 -0.482

0.446 0.746 0.355

solution

= = = = = = = = =

RSQ 0.706 0.559 0.558 0.529 0.446 0.445 0.413 0.233 0.288 0.259 0.291 0.467 0.445 0.382 0.623 0.188 0.471 0.368 0.538

0.199 0.606 0.646

178.408 0.00731 I .322 0.859 0.950 0.960 0.044 0.0428 0.0470

with P c 0.05 unless marked “n.s.“;. F = fixed parameter

The results of the structural equation analysis for the two models are shown in Tables 2 and 3. The models were evaluated on the basis of four fit indices: x2 divided by degrees of freedom (x2/@), the mean residual correlation, the comparative fit index (CFI) (Bentler, 1993), and root mean square error of approximation (RMSEA) (Browne & Cudeck, 1993; Joreskog & Sorbom, 1993).* The models are not nested (i.e. one embedded in the other); thus, we cannot compare them statistically with the x2 difference test. Recall that the variables used to predict other factors in the path analysis were always mutually orthogonal. This was accomplished by using the disturbance term, i.e. the part of the factor uncorrelated with its predictors. The “g/working memory is primary” path model (Table 2) resulted in a x2/df of 1.322, a mean residual r = 0.047, a CFZ of 0.960, and a RMSEA of 0.044. Nearly all the hypothesized paths were significant. It is interesting to note how strong the relationship was between dynamic visual processing and g/working memory (p = 0.746, Z = 6.96). Processing speed also explained a small a statistical test of model fit such that non-significant values (P > 0.05) are desirable. For large N samples it is easy for the data to deviate from the model. As Anderson & Gerbing (1988) note “. . . the value of the x2 likelihood ratio statistic is directly dependent on sample size. Because of this, with large sample sizes, significant values can be obtained even though there are trivial discrepancies between the model and the data”. Several alternative measures of fit have been investigated. A simple alternative involves dividing x2 by its df to yield an index that goes to unity (1.00) for a perfect fit. This measure adjusts for the fact that models with many parameters will appear to fit the data better than models with few parameters. Values between 1.OOand 2.00 are desirable. The comparative fit index (CH) varies between 0 and I, with I denoting the perfect fit. Values above 0.9 are desirable. The Bentler-Bonett normed and non-normed fit indices (NFI and NNFI, respectively) are interpreted in the same manner. We prefer the CFI because it does not underestimate fit as often as the NFI for small samples, and has less sampling variability than NNFI (Bentler, 1988). The RMSEA (root mean square error of approximation) is an index of discrepancy per degree of freedom. Its acceptable range (reasonable errors of approximation in the population) is 0.03 to 0.08, with 0.05 being the target value. Values below 0.03 indicate overftt; and values greater than 0.08 indicate underfit. Another index of model fit is the mean standardized residual or residual correlation, which is simply the difference between the observed correlation and the reproduced correlation. Of course, small residual correlations are desirable.

*x2 provides

Cognitive and perceptual-motor abilities Table Measurement equations

.q/WM

3. Nested

model

standardized

611

solution

Processing

Dynamic

Multilimb

Visuo-

Target

speed

visual

coordination

spatial

tracking

RsQ

BP’M

0.834

PLACC EPIMEM

0.748

SPATIAL

0.597

0.356

0.483

MATCHPLN

0.371

0.543

0.432

F

0.696 0.560

0.757

0.573

PROCRT

-0.285

-0.689

PLRT

-0.331

-0.527

TFVRT

-0.181

-0.457

VIT

-0.390

-0.129

TPSI

0.279

TPS2

0.45

PLSI

0.551

I

F

0.556 0.387 0.242 -0.342

n.s.

0. I54 n.s.

0.521

0.031

“.S.

0.312

0.137

“.S.

0.266

0.286 0.373 0.302 0.421

0.167 0.615

MLCI

0.378

-0.774

MLCZA

-0.731

MLCZB

-0.280

0.613 0.172

-0.541

-0.234

MLC3

F

0.269

0.315

LSZXRNG

0.599

-0.188

0.383

HELTI

0.517

0.574

0.597

HELTT

0.63 I

0.544

0.694

Construct

equations

TARGET

TRACK

0.111

0.334 0.441

0.602

0.422

MLCOORD

=

190.473 0.001

X’il

< =

Bentler-Bonett

=

0.850

x1 with

I28 degrees of freedom

Probability normed

Bender-Bonett Comparative Root

Average All

loadings

are significant

fit index

Non-normed

fit index

fit index

mean square error

Average

Now:

0.736

absolute

off-diagonal with

of approximation

standardized absolute

(RMSEA)

residuals standardized

P < 0.05 unless marked

residuals

“n.s.“.

I.488

=

0.924

=

0.943

=

0.054

=

0.0450

=

0.0491

F = fixed parameter.

amount of variance in dynamic visual processing (j? = 0.22, Z = 2.23). Consistent with the model, g/working memory predicted processing speed (/3 = 0.446, Z = 4.40) but the relationship was not as strong. The standardized equation relating multilimb coordination to the cognitive variables explained 64.6% of the criterion variance with contributions from dynamic visual processing (j? = 0.616, Z = 3.62), g/WM (/3=0.355, Z = 3.59) processing speed (/? = 0.272, Z = 2.39), and visuo-spatial processing (b = 0.258, Z = 1.94). The corresponding nested model (Table 3) fared only slightly less well in goodness of fit, resulting in a x2/df of 1.488, a mean residual r = 0.045, a CFI of 0.943 and a RMSEA of 0.054. This model became more complicated in that a target-tracking factor was added to reduce a substantial residual correlation between the two helicopter tracking tasks. The balloon popping task, which also involved intercepting a target with stick and rudder input, provided a third marker for this factor. Contrary to expectations given the path model, processing speed did not load any of the dynamic visual tasks significantly. In the nested model, the cognitive predictors accounted for 73.6% of the variance in multilimb coordination with contributions from dynamic visual processing (/I = 0.602, Z = 3.20) g/WM (a = 0.422, Z = 4.23) and visuo-spatial processing (/I = 0.441, Z = 3.84). Processing speed did not have a significant path coefficient and was deleted from the model. Notice that more of the criterion variance was explained by the cognitive predictors in this nested model than in the path model (73.6% vs 64.6%). We do not attach much importance to this discrepancy. We simply conclude that about 69% of the variance in multilimb coordination is explained by cognitive factors. DISCUSSION

Both models imply that multilimb coordination has multiple cognitive determinants or components. Among these are dynamic visual processing, working memory capacity, and visuo

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spatial processing. None of the predictors captured the “lion’s share” of the variance in multilimb coordination, though it is possible that the variance explained by g/working memory could decrease with practice on the perceptual-motor tasks. It is also possible that processing speed, not significantly related to multilimb coordination in the nested model reported here, could become a significant predictor in a later phase of training. Ackerman (1987, 1988, 1990) proposed a theory of how performance of novel tasks would correlate with ability constructs as a function of practice. Initial performance in the declarative phase of learning would be a controlled process dependent on g, which reflects the amount of attentional resources the learner can bring to bear. Subsequently, in the associative or knowledge compilation phase, conscious mediation would drop out as the learner increases the strength and efficiency of stimulus-response associations. In this phase, performance would be predicted by perceptual speed ability, as this reflects how quickly the learner can acquire simple procedural skills. In the autonomous phase, the subject fine tunes performance components until there is a minimal draw on resources. During this phase, performance is predicted by simple reaction time and motor speed. Ackerman’s theory applies to simple tasks which have consistent mapping of stimuli onto responses. If tasks are more complex and the stimulus-response mappings are not consistent, these predictions are not borne out (Ackerman, 1992). A simulation of the Complex Coordinator used in Fleishman & Hempel(1954), a fairly complicated task, was used as a subtest in the present study’s battery. This test and other tests with comparable multilimb coordination requirements appear to require controlled processing, and may demonstrate stable correlations with g/working memory. Other tasks which are indicators of Fleishman’s response orientation and rate control factors may demonstrate steeper acquisition curves and patterns of correlation more consistent with Ackerman’s theory. Another issue meriting study concerns the role of gender on factorial structure and domain overlap. Males and females differ in ability profiles. For example, females generally perform better on tests of perceptual speed and accuracy and verbal fluency, and males perform better on tests of spatial visualization and mathematical reasoning (Halpern, 1986). Within the perceptual-motor domain there is some evidence that females perform better on tests of manual dexterity (Kimura & Hampson, 1994) and that males perform better on tests of multilimb coordination (Tirre & Raouf, 1994). Gender differences in abilities might be mediated by physiological (e.g. hormonal) variables or by experience and socialization variables. Either way, gender might affect how the participant approaches task performance and thus affect how task parameters intercorrelate. Gender effects on factorial structure can be examined using multi-group structured means analysis (Bentler, 1993). The question is whether gender effects in perceptual-motor performance can be accounted for by differences in mean performance on the factors or whether different factors underlie performance. In conclusion, the results of the present study suggest that multilimb coordination ability is not simply another manifestation of general cognitive ability, but instead the result of several abilities including dynamic visual processing and visuo-spatial processing as well as working memory. An understanding of the nature of these component abilities would require more detailed research. Furthermore, we believe that the relationship between perceptual-motor and cognitive abilities merits additional study, especially with respect to the roles of practice, experience and gender. Acknowledgements-We would like to thank Scott Chaiken and Patrick Kyllonen for their helpful comments on all phases of the research and Janice Hereford, Richard Walker, Henry Clark. Cynthia Garcia, Brennan Underwood, Wayne Crone and David Hartman for their assistance in programming tests, collecting data, and creating data files, and Ginger Goff for helpful advice on structural equation modeling.

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APPENDIX Table Al. Means and standard Variable

Mea”

SD

GWM PLACC EPIMEM SPATIAL MATCHPLN PROCRT PLRT TFVRT VIT TPSI TPSZ PLSI MLCI MLCZA MLCZB LSZXRNG MLC3 HELTI HELTT

50.02 50.01 50.01 50.0 I 2.92 49.96 49.9s 2.8 I 6.44 24.07 70.19 58.45 22.1 I 113.85 218.31 56.51 3.10 16.63 3.34

7.48 8.55 7.61 8.08 2.03 7.81 7.87 0.66 I.16 14.30 13.81 18.00 10.04 40.10 41.29 62.55 0.20 7.18 3.43

Norr. N =

deviations

of ability scores

Vartable description General cognitive ability /working memory composite (T-score) Procedural learning accuracy composite (T-score) Episodic memory composite (T-score) Spatial composite Matching planes (Number correct) Processing response time (T-score) Procedural learning response time composite (T-score) True/Pdlse verification response time (seconds) Visual inspection time difficulty level achieved (I is most difficult, 9 is least difficult) Percent correct in time-to-contact estimation PCA-Double Lines ALL w/unanticipated RT Percent correct in identifying serially presented patterns Number of patterns matched on complex coordination Mean distance from center on x-axis center-the-ball task Mean distance from center on x-y vector center-the-ball task Laser shoot II Screen width minus distance traversed (pixels) Log of elapsed time to “pop” balloons Number of helicopters intercepted and destroyed Number of helicopters intercepted. tracked, and destroyed

172. Table AZ. Correlation

GWM

PLACC

GWM PLACC EPIMEM SPATIAL MATCHPLN PROCRT PLRT TFVRT VIT TPSI TPS2 PLSI MLCI MLCZA MLCZB LSZXRNG MLC3 HELTI HELTT

I .ooo 0.624 0.603 0.499 0.340 -0.312 -0.307 -0.329 -0.359 0.282 0.364 0.493 0.315 -0.284 -0.276 0.156 -0.253 0.186 0.220

TFVRT VIT TPS I TPS2 PLSI MLCI MLCZA MLCZB LS2XRNG MLC3 HELTl HELTT

TFVRT I.000 0.133 -0.072 0.01 I -0.100 0.034 0.028 -0.00s -0.137 0.050 -0.136 -0.012

MLC2B LS2XRNG MLC3 HELTI HELTT

MLCZB I.000 -0.209 0.453 - 0.466 -0.548

matrix

EPIMEM

SPATIAL

MAPTCO

PROCRT

I.000 0.626 0.477 0.273 -0.170 -0.174 -0.085 -0.208 0.155 0.272 0.327 0. IS2 -0.125 -0.142 0.034 -0.145 0.096 0.098

1.000 0.405 0.232 -0.241 -0.346 -0.065 -0.295 0.153 0.413 0.432 0.214 -0.245 -0.231 0.198 -0.260 0.196 0. I52

I.000 0.442 -0.145 -0.117 -0.022 - 0.289 0.242 0.320 0.428 0.381 -0.266 -0.391 0.209 -0.189 0.243 0.289

1.000 -0.136 -0.104 0.038 -0.076 0.184 0.228 0.306 0.326 -0.243 -0.431 0.203 -0.230 0.266 0.266

VIT

TPSI

TPS2

PLSI

I .ooo -0.303 -0.296 -0.412 - 0.309 0.23 I 0.260 -0.163 0.233 -0.185 -0.226

I.000 0.314 0.3 I5 0.337 -0.380 -0.322 0.202 -0.38X 0.217 0.298

1.000 0.294 0.367 -0.293 -0.247 0.223 -0.290 0.135 0.262

I.000 0.393 -0.312 -0.370 0.274 -0.339 0.319 0.355

MLC3

HELTI

HELTT

LSZXRNG 1.000 -0.315 0.207 0.271

I.000 -0.437 -0.516

Now N = 172, Critical value for Pearson r (IX= 0.05. 2-tailed) = 0.149.

I.000 0.651

1.000

PLRT

I .ooo 0.451 0.413 0.228 -0.248 -0.213 -0.236 -0.225 0.131 0.215 -0.283 0.337 -0.303 -0.265 MLCI

1.000 -0.417 -0.486 0.253 -0.427 0.345 0.433

I.000 0.312 0.251 -0.181 -0.182 -0.362 -0.144 0.143 0.160 -0.241 0.315 -0.161 -0.195 MLCZA

I.000 0.706 -0.183 0.367 -0.409 - 0.466