Fitts' law, movement time and intelligence

Person. indixid. Diff: Vol. 23. No. 2, pp. 221-246, 1997 8 1997 Elsevier Science Ltd. All rights reserved

Pergamon

Printed in Great Britain 0191-8X69/97 $17.00+0.00

PII: SO191-8869(97)00038-X

FITTS’ LAW, MOVEMENT

TIME AND INTELLIGENCE

Richard D. Roberts*? Armstrong

Laboratory,

Brooks AFB, San Antonio,

TX 782355352,

U.S.A.

(Received 22 October 1996) Summary-Recently, several published studies have reported an empirical relationship between Movement Time (MT, i.e. the speed associated with sensori-motor control of movement) and intelligence. However, this finding is very much at odds with early research that suggested that there was no relationship between measures of these two constructs, One explanation for this anomaly is that intelligence has generally been imprecisely defined across disparate research programs, often with reference to a single test. Another explanation is that studies currently conducted involve poor operationalization of psychomotor processes, essentially confounding this aspect with other psychological mechanisms (e.g. Decision Time). In short, analyses of MT and intelligence have not been truly representative of these constructs, at least as conceptualized within more widely accepted models of these psychological processes. The present study examined the relationship between MT and intelligence by first selecting tasks in each domain that are representative of established psychological theories. A total of 179 participants performed a psychomotor task conforming to Fitts’ law (an information theory principle relating MT to task difficulty) and a battery of 25 psychometric tests. The latter measures were selected in order to define six broad cognitive ability factors under the framework of Gr/G, theory. Microstructural properties of the psychomotor task were examined in as rigorous a fashion as possible. Evidence indicated adherence to simplex structure, group and intraindividual conformity to Fitts’ law, and a hitherto unreported linear relationship between variability and the pre-scaled function of target distance and width. However, with the notable exception of a well-defined broad speediness function (G,), correlations between psychomotor parameters and psychometric measures were close to zero. These results are discussed in relation to cognitive and biological models of human cognitive abilities. c 1997 Elsevier Science Ltd Kqwords: individual differences; chomotor performance.

cognitive

abilities;

Movement

Time; Decision

Time; Fitts’

law; psy-

INTRODUCTION In studies involving the cognitive correlates approach to intelligence, two dependent variables are generally derived from elementary cognitive tasks (ECTs). One of these variables is Movement Time (the speed associated with sensori-motor control of movement), the other is Decision Time (the time required to determine and initiate an appropriate response to stimuli). However, operationalization of the former measure tends to ignore a considerable experimental literature dealing with this type of performance speed in isolation. As such, recent investigations of the relationship between psychomotor performance and intelligence plausibly have limited generalizability. Acknowledging problems in current perspectives, Carroll (1993, Ch. 13) gives psychomotor factors a separate chapter in his book, The Structure of Human Cognitive Abilities. It would appear from this review that more precise assessment of MT is possible. The present study was designed to explore the relationship between one such measure of psychomotor performance and intelligence. The last two decades have witnessed a concerted effort to investigate the relationship between various chronometric indices and intelligence (Bates & Eysenck, 1993; Carlson & Jensen, 1982; Carlson, Jensen & Widaman, 1983; Carlson & Widaman, 1987; Carroll, 1987; Ford & Keating, 1981; Hunt, Lunneborg & Lewis, 1975; Jenkinson, 1983; Jensen, 1987, 1991, 1993a, 1993b; Keating

*This research was based on the authors Ph.D. dissertation conducted at the University of Sydney, Sydney, Australia. However, the paper was written while the author held a National Research Council Fellowship at the Human Resources Directorate of Brooks AFB, TX, U.S.A. Due acknowledgment is thus given to all relevant institutions. I would like to thank Lazar Stankov, Gerry Pallier, Patrick Kyllonen, Fleur Buffier and an anonymous reviewer for helpful comments on an earlier draft of this manuscript. tTo whom all correspondence should be addressed. 227

228

Richard D. Roberts

& Bobbitt, 1978; Larson & Saccuzzo, 1986, 1989; Matthews & Dorn, 1995; Nettelbeck, 1987; Neubauer, 1990a; Neubauer & Freudenthaler, 1994; Roberts, Beh & Stankov, 1988; Smith & Stanley, 1983, 1987; Vernon, 1983, 1987; Vernon & Jensen, 1984; Vernon, Nador & Kantor, 1985). In general, it is measures of Decision Time (DT) that have tended to provide the impetus for these empirical studies. While original formulations within this research program simultaneously downplayed the importance of Movement Time (MT) (Jensen, 1979, 1982a, 1982b; Jensen & Munro, 1979) more recent results suggest that this approach may have been premature. Thus, there is now a body of evidence that demonstrates a moderate negative correlation between MT and intelligence (Buckhalt, 199 1; Buckhalt & Jensen, 1989; Buckhalt, Reeve & Dornier, 1990; Detterman, 1987; Era, Jokela & Heikkinen, 1986; Frearson & Eysenck, 1986; Houlihan, Campbell & Stelmack, 1994; Jensen, 1987; Neubauer, 1990b; Telzrow, 1983). It would appear that without any clear precedent, MT was considered an irrelevant variable as cognitive correlates approaches to intelligence emerged, but that this position has changed. This proposition finds support in a brief survey of the early literature on psychomotor skills. Researchers often concentrated on developing a taxonomy of psychomotor ability (of which aimed movements is a factor) independent from those of a psychometric nature (e.g. Fleishman, 1954, 1964, 1972; Guilford, 1958; see also Fleishman & Quaintance, 1984; Peterson & Bownas, 1982). This reflected a commonly held view by psychometrists that simple motor tasks should share low to zero correlations with intelligence (e.g. McGeoch, 1942). This position was strengthened by studies that failed to show significant correlations between psychomotor skills and psychometric abilities. These studies were nevertheless flawed, often relying exclusively on psychometric measures involving verbal content (Clark & King, 1960) and/or particularly small sample sizes (Barratt, 1959). Problems associated with inadequate sample size have only recently been addressed in experiments examining correlations between MT variables and measures of cognitive ability. This may, in part, explain contemporary findings. Notwithstanding, similar criticisms could be made of these studies regarding the psychometric instruments employed-generally only a single test is used (Juhel, 1991). However, each of these tests tends to involve over-sampling from the visual-spatial domain (e.g. the Raven’s Progressive Matrices Test). Collectively these empirical studies suggest that provided the sample size is fairly large and measures other than those assessing verbal abilities are employed, correlations between MT and psychometric performance are as high as those involving other elementary cognitive operations (i.e. between -0.35 and -0.50, see in particular, Buckhalt et al., 1990). However, this, in turn, leaves it uncertain whether MT relates to primary mental abilities, a second-order factor (such as fluid intelligence) or psychometric g (cf. Carroll, 1993, p. 647). On balance of the available evidence, it would not be all that surprising if a relationship between MT and a general intelligence factor were found. Within contemporary speed of information processing studies, the correlation between MT and DT is reported to be as high as 0.40 (Jensen, 1982a). This relationship is taken as evidence for a general speed factor (Pierson & Rasch, 1960, 1961; see also Bors & Forrin, 1995; Hale & Jansen, 1994; Miller & Vernon, 1992; Salthouse, 1994, 1996). Because MT and DT both appear to share significant correlations with certain measures of intelligence, it seems reasonable to conclude that this response speed factor is responsible for a significant proportion of variance in general intelligence (or psychometric g). In support of a speed interpretation for these findings, is the magnitude of correlation between MT slope and psychometric performance, which is reported in several studies employing ECTs. Obtained correlations have been taken to represent “the influence of general intelligence on even rather simple types of cognitive operation-such as bit resolution or motor programming-that underlie speeded behavior” (Widaman & Carlson, 1989, p. 168). However, as noted from the outset, cognitive correlate studies have examined the relationship between MT and intelligence virtually by default. Because it is considered conceptually meaningful to differentiate between DT and MT in ECTs (see Jensen, 1979; also Smith, 1989 for an alternative view), some attention is generally afforded to psychomotor constructs, often without ‘theoretical’ justification (Stankov & Roberts, 1997). As a result, individual differences studies have not investigated ‘manipulations’ of the MT variable, and most certainly not of the type evidenced in the experimental literature. For example, by varying target distance (and/or width) it is possible to change the informational demands of a psychomotor task (see Fitts, 1954). This follows from the general formula relating task difficulty and MT, which has come to be known as Fitts’ law:

Fitts’

law,

MT and

intelligence

229

MT = k log,(A/W + 0.5)

(1)

where ‘A’ is the target distance, ‘W’ is the target width and k is the slope constant.* Indeed, given equation (l), analyses involving the MT parameter are essentially misrepresented within cognitive correlate approaches to intelligence. In particular, across a series of choice-reaction-time experiments, Jensen (1982a, 1987) has plotted MT as a function of stimulus information, and in turn, claimed that it is surprising that these performance measures have near zero slope. However, Fitts’ law requires this outcome since neither target distance nor target width is generally manipulated in traditional implementation of ECTs. One consequence of the state of affairs described above is that a number of potentially meaningful indices of psychomotor performance appear never to have been systematically evaluated. Note, in studies involving ECTs, the slope of DT is assumed to reflect the rate at which an individual processes information and that a variety of conceptual models have been postulated on this basis. Investigation of the various empirical properties of the DT measure has subsequently led to a near plethora of studies and theoretical speculation (Barrett, Eysenck & Lucking, 1986; Detterman, 1987; Eysenck, 1987a, 1987b; Jensen, 1979, 1987; Neubauer, 1991; Roth, 1964). No such data on the slope of MT has been reported, though this too is (in principle) of theoretical significance. In this context, analyses of the mean structure of group and ‘intraindividual parameters’ obtained from an information theory manipulation of MT are bound to be informative. While it is well established that group means will exhibit a linear relationship between MT and bits of information (Fitts, 1954; Fitts & Peterson, 1964; Fitts & Radford, 1966; Hancock & Newell, 1985; Knight & Dagnall, 1967; Meyer et al., 1988; Schmidt, Zelaznik & Frank, 1978; Welford, 1968; Welford, Norris & Shock, 1969)t there are no data on the adherence of individual subjects to Fitts’ law, the function describing standard deviation and bits of information, nor are there data concerning the presence (or otherwise) of a simplex pattern within the correlation of MTs at each level of task difficulty. Importantly, each of these types of analyses is viewed as paramount to the interpretative properties of the DT component of almost all ECTs (see in particular, Jensen, 1987). In sum, limitations identified in the literature include not only poor demarcation of an intelligence factor (or factors) and imprecise operationalization of MT, but also failure to establish the validity of psychomotor parameters that would seemingly be of utility. In light of these shortcomings, the present study had two main aims. The first was to determine the various properties of an information theory manipulation of MT. Is it empirically valid, for example, to extract analogous parameters to those that have been obtained with DT indices (e.g. intraindividual MT slope measures)? The second aim of this study was to ascertain whether or not the relationships observed between MT parameters and intelligence are ephemeral. This issue divides itself into two, by no means unrelated, research questions. Is it possible to obtain meaningful correlations between MT and intelligence outside an experimental situation in which DT is also assessed? Secondly, at what point (given ‘oneoff measures of intelligence have previously been employed) does linkage with MT and human cognitive abilities occur? Elsewhere, Carroll (1993) has warned of problems interpreting cognitive correlates approaches that do not sample widely enough across the psychometric domain. It remains plausible that MT shares relationship with lower stratum abilities [perhaps only aspects of a test (i.e. whether it is given within strict time limits)] and not higher stratum constructs such as g.

*Fitts (1954) actually proposed the following and time taken to make hand movements:

equation

as a formulation

for the relationship

between

amplitude,

accuracy

MT=a+blog,(2A/W). However, Welford (1968), modified this equation after demonstrating that it did not always model performance on aimed ballistic tasks effectively (see also Crossman, 1957 as cited in Welford, 1968). The original formulation was found, for example, to cut the zero information line below the origin. It is also worth noting that equation (1) “makes MT dependent upon a kind of Weber Fraction in that the S is called upon to distinguish between the distances to the far and near edges of the target” (Welford, 1968, p. 147). On balance, equation (1) may thus be taken to be more empirically and theoretically sophisticated than Fitts’ original formulation. tThe relationship proposed by Fitts is most robust and has in fact been demonstrated to hold over a wide range of S populations (see e.g. Flowers, 1976; Wade, Newell &Wallace, 1978), in different physical environments (i.e. underwatersee Kerr, 1973), using disparate anatomical units (Langolf, Chaffin & Foulke, 1976), and under microscopic conditions (Hancock, Langolf & Clark, 1973 as cited in Hancock & Newell, 1985).

Richard D. Roberts

230 Table I. Cognitive Variable

ability measures and their hypothetical G

Level measures (number correct) Racen :v Proyre.~sswr Mutrms (RM) 02. Lerter mmtin,q (LC) 03. LeTW sets (SL) 04. Number series-Single (NSS) 05. Number series-Competing (NSC) 06. Letter series-Single (LSS) 07. Letter series-Competing (LSC) 08. Water jars (WJ) 09. ScramhlfYl words (SW) IO. Generul infornmtion (GI) I I. Votuhulur>~ multichoice (VM) 12. Esoteric unal@~~es(EA) 13. Digr/ spun-Forwards (SF) 14. Digit .spun-Burkword.r (SB) 15. Card rnralions (CR) 16. Computer form boards (CFB) 17. Hidden figures Smgle (HFS) IX. Hidden figures-Competing (HFC) 19. Tonal memory-Single (TMS) 20. Tonal memory-Competing (TMC) 21. Speech distortion (SD) 01.

G‘

SAR

structure G

G,

G

X X X X X X X X X X

X X X X X X X X

X X X

Speed measures (msec)

22. 23. 24. 25.

Number comparison Stroop color (SCT) Stung search (SST) Digit .x,vmho/ (DSQ

(NCT)

X X X X

N.B. Tests m italics were given m paper and pencil format. All other tests were administered aspect of design addresses concerns that factors are artifacts of method.

via computer.

Note this

METHOD Participants A total of 179 participants were involved in the present study. A substantial number of these individuals (i.e. 82%) were first year psychology students at the University of Sydney. The remainder were drawn from the genera1 community and, in particular, adult education classes. Of the total, 110 were female. The age of the participants ranged from 17 to 50 years with a mean age of 21.6 yr and a standard deviation of 6.2yr. It should be noted that those participants drawn from outside the university population were generally well educated-holding Bachelors degrees or higher. Design The design was intended to provide a framework for systematically investigating the relationship between an experimental manipulation of psychomotor performance and various second-stratum cognitive abilities. For present purposes, the test battery consisted of 25 tasks that were employed to define psychometric constructs and a single psychomotor task having five levels of task difficulty.* It was envisaged that six broad factors [hypothesized on the basis of G,-/Gc theory (see e.g. Horn, 1988; Stankov, Boyle & Cattell, 1995)] would be obtained from the psychometric tests. Each of these tests (along with the factor for which they serve as a marker) is presented in Table I. As will be noted, there were eight markers of fluid intelligence (G,, Tests l-8), four markers of crystallized intelligence (G,, Tests 9-l 2), two markers of short-term acquisition and retrieval (SAR, Tests 13-I 4), four markers of broad visualization (G,,, Tests 15-l S), three markers of broad auditory function (G,, Tests 19-21) and four markers of clerical-perceptual speed (G,, Tests 22-25). Except for those marker tests hypothetically defining the clerical-perceptual speed factor, the dependent variable was number-correct (i.e. level, see Carroll, 1993, Ch. 11). Fitts’ movement task. For the purpose of this task, five response boards were constructed from wood, corresponding to the five levels of task difficulty manipulated in this paradigm. Each of these

*The study also employed two personality obtained with these additional measures

inventories and 10 other ECTs (see Roberts, are peripheral to the aims of the present paper.

1995). However,

the outcomes

Fitts’ law, MT and intelligence

18-

231

‘j+

9-

Fig. 1. A face view of the stimulus presented in Fitts’ Movement rapidly

tap a probe between the two circular

Table 2. Conditions

Condition 1

2 3 4 5

Time Task. The participants’ targets of equal circumference.

selected for study in Fitts’ Movement Task with the associated derived from information theory Hole wdth (cm) 5.080 3.810 2.540 1.905 1.245

Function

(i.e. A/W+O.S) 1.36 10.11 16.51 25.52 50.50

task was to

bit values

Bits in task 2.88 3.34 4.05 4.62 5.66

N.B. Bits were calculated from the formula: log, (A/W +0.5). In the present case, Target Area (A) is constant (i.e. 30.5 cm). Target Width (W), however, was variable being the difference between the diameters of the hole (which was experimentally manipulated) and the pin (which was constant, i.e. 0.635cm).

boards was placed horizontally in front of the participant at a comfortable arm’s distance. The order of presentation of each condition across participants was random.* The boards consisted of two holes that were set 30.5cm apart from center-point to center-point (see Fig. 1). These holes constituted targets that varied in diameter (i.e. target width) across the five boards. From Fitts’ (1954) formula [i.e. equation (l)] respective bit values were calculated for all five of the treatment conditions. Table 2 gives the parameters relevant to each experimental manipulation. Note that this Table provides values of the untransformed function (Column 3) and the information metric (Column 4) that is hypothesized to share a linear relationship with mean measures of task performance. Both parameters are relevant to analyses conducted in this paper. The participants’ task was to tap a small metal probe (that had a length of 10.00 cm and diameter 0.635 cm) back and forth between the two target holes as quickly and accurately as possible. Prior to each experimental trial they were given 10 set practice on each task condition. Participants were instructed to hold the probe in an upright manner between the thumb and four fingers of their preferred hand. They were also told to refrain from counting the number of times they responded since this might detract from their overall performance. For each test condition the experimenter recorded the number of cycles made by each participant within a 60-set time period. A cycle was defined as the movement of the probe from the origin (the center of the circle on the participants’ right-hand side) and back again. It should be noted that this definition corresponds to the manner in which this construct has previously been assessed in the literature (see e.g. Fitts, 1954). Output was subsequently transformed into the time (measured in msec) it took participants to complete one cycle.?

*No more than two participants performed this task in the same order-120 combinations were possible and all were used. t.Ss were instructed that an error would be recorded against them if the pin was not placed directly into the hole. Whilst relatively infrequent, such errors were subtracted from participants’ performance during the testing phase.

232

Richard

D. Roberts

Table 3. Summary stattstlcs of mean Movement Time (msec) as a function of bits for Fltts’ Movement Task Parameter

Meall

SD

MT,,*

280. I2 304.49 352.72 400.28 497.50 367.12

46.1 I 46.99 41.1 I 53.20 71.48 47.70

MT; MT, MT, MT, MT,

,a /us 62 he

Procedure The tests were generally administered to participants over two sessions. In the first session, paperand-pencil tests were carried out, while in the second session, computerized cognitive ability measures and Fitts’ Movement Task were completed. The latter was administered to each participant on an individual basis by the experimenter. Computerized tests were performed on both Commodore-64 and Amiga microcomputers. Data were stored on the Psychvax mainframe computer for later statistical analysis using the SPSS program (Norusis, 1990).

RESULTS The results of the present study are divided into three sections. The first deals with microstructural aspects of the psychomotor task under investigation. These analyses attempt to establish the validity of various task parameters for individual differences research. The second section is concerned with the factor structure of the psychometric indices. These analyses confirm whether or not the hypothesized factors are replicable in the present data set. The final section examines the relationship between the parameters derived from the psychomotor task and obtained cognitive ability factor scores. An&ses

inoolring Fitts’ mocement

tusk

~es~~~~ti~e ~tiltist~~s. The group means and standard deviations of mean MT as a function of task difficulty (i.e. bits) are presented in Table 3. * This table also contains the mean performance of this task averaged over experimental conditions (i.e. MT,). Table 3 reveals that for each condition of MT (scaled into bits) both mean performance and between-& variability tend to increase as task difficulty increases. Trend analysis yielded a significant linear relationship between MT and bits of information [F( 1,178) = 3010.56; P< 0.011. While analysis involving residual trends also indicated a significant quadratic function [F( I, 178) = 72.55; P < 0.011 neither the cubic nor quadratic trends were significant. The presence of this quadratic trend is something of a problem from a pure information theory perspective. However, because the linear function is in keeping with a well-understood theory of task difficulty (and the quadratic function is not), it was decided to analyze this task further only from the perspective of an information theoretic framework. The signifi~dnt linear trend that was obtained leads logically to resolution of an important empirical question. Does the apparatus and procedure used in this paradigm yield data that conform to Fitts’ law? This question is addressed in the passages that follow, both in terms of the conformity of group means of mean MT data and the adherence of individuals’ mean MTs to Fitts’ law. Parameter values are compared with the current literature and envisaged extensions. Co~~o~~zit~~ofgroup data to Fitts’ law. Equation (I) may be subject to some degree of error (as in fact are all physical measurements, cf. Jensen, 1987). Because of this a more accurate fit to the current data set is provided by the following: MT=a+bX

*For parameters

given in this (and subsequent) the mean over conditions.

Table(s) subscripted

(2)

numbers

refer to bit values, with the symbol ‘x’ denoting

Fitts’ law, MT and intelligence

0

I

2

Task Difficulty

3

233

4

5

6

(Bits of Information)

Fig. 2. Mean Movement Time as a function of stimulus information (i.e. bits) in Fitts’ Movement (N.B. Stimulus information was calculated according to Fitts’ law).

Task.

where ‘a’ represents intercept, ‘b’ the slope constant and ‘X’ task difficulty (i.e. log, [A/W +0.5]) measured in bits of information. A regression equation of the above form was computed from the group mean MTs for 2.88, 3.34, 4.05, 4.62 and 5.66 bits given in Table 3. The obtained regression equation (MT=44.39+ 78.52 log, [A/W +0.5]) was calculated using the Cricket Graph statistical package (Cricket Software Inc., 1991). In addition, this provided the regression line subscribing to this equation (plotted in Fig. 2), as well as the degree of fit to the linear regression of MT on bits of information-indicated by the Pearson Y. The Yobtained is 0.995, a value that suggests an extremely high degree of conformity in the present sample to the underlying psychological model (i.e. Fitts’ law). In keeping with the principles of information theory, equation (2) is particularly useful in calculating the rate of transmission. This is given by the reciprocal of the slope, ‘b’, expressed as bits per unit time (Crossman, 1953; Fitts, 1954; Hick, 1952; Jensen, 1987; Roberts et al., 1988; Roberts et al., 1991b; Roth, 1964; Shannon & Weaver, 1949). Interestingly, Fitts (1954) reports this value as lying within the range of 7.5 and 12.6 bits/set in three experiments involving aimed ballistic movement, two of which incorporate various aspects of the current apparatus and procedure. Since this would appear the only variable with which the present MT paradigm could be compared to Fitts’ original study (Fitts does not report linear functions in any of his experiments), this measure of performance was obtained using the regression equation given in equation (2). The value so calculated-l 2.7 bits/see-is comparable to the upper range of transmission rates given by Fitts. It is also consistent with the upper range of values given in a number of other studies involving MT for which transmission rates were obtained (Fitts & Peterson, 1964; Welford, 1968; Welford et al., 1969). Findings from the present task would thus seem to be consistent with those reported in previous studies. * Conformity of individuals’ MT to Fitts’ law. As the degree of conformity to Fitts’ law evidenced in group data is acceptable, it would seem worthwhile assessing the extent to which individual data

*In terms of modeling this psychomotor task, it should also be noted that Fitts’ original formulation (i.e. MT=a+b log, [2 A/WI) provides a slightly poorer fit for mean MT regressed on bits (where r = 0.994) than that provided by equation (I). In addition, the line of best fit obtained from this earlier formulation (MT= - 17.82+76.16 log, [2 A/W]) provides a negative intercept value. Both features are consistent with previous results presented in the literature (see e.g. Welford, 1968).

Richard D. Roberts

234

Table 4. Summary statistics of Movement Time parameters obtained from Fats’ Movement Task by calculating regression equations for each mdividual Variable

Meall

SD

MTa MTb MTr

45.800 77.950 0.946

75.600 19.800 0.053

Table 5. Percentage of participants having various rank orderings of MT as a function of task difficulty in Fitts’ Movement Task

Rank order Predicted 12.145

% of participants falling into each category

78.77

‘Minor’ violations 1.5-1.5-345 I-2.5-2.545 l-2-3.5- 3.5 5 L-1.5-3.5-3.5-5 13335

7.26 2.79 I.12 0.56 0.56

‘Major’ violations 2-l-345 I-243-5 2-143-5

7.26 I.12 0.56

similarly exhibit this characteristic. Such analyses have been used in determining the degree to which DT measures subscribe to Hick’s law and certain other lawful empirical phenomena (e.g. memory set size effects; see e.g. Sternberg, 1969). However, to date, there are no relevant data on the extent to which intraindividual MTs conform to Fitts’ law.* To this end, regression equations were calculated for each individual by entering their performance at each bit level into the Cricket Graph statistical package. Means and standard deviations of these three ‘new’ parameters [i.e. intercept (MTa), slope (MTb), and fit to model (MTr)] were subsequently calculated using SPSS (Norusis, 1990). These values are given in Table 4. Inspection of Table 4 shows the conformity of Fitts’ law for individual data to be remarkably high, at least as indicated by the mean value of the Pearson correlation of all participants’ MT over task difficulty. Thus, the square of this mean r represents the percentage of variance in MTs accounted for by the regression of these on bits of information, which for individuals performing the present task is approximately 89.5%. In order to get some clearer indication of the ‘types’ of non-conformity to Fitts’ law that occur in the present sample of participants, these data were subsequently analyzed after the fashion described by Jensen (1987). For this purpose, each participant’s various MTs were examined in terms of their rank order with respect to task difficulty. The predicted order according to Fitts’ law is l-2-3&5. The percentage of individuals having this, and different rank ordering of their MTs for 2.88, 3.34, 4.05,4.62 and 5.66 bits of information is given in Table 5. Table 5 indicates the robustness of Fitts’ law for individual data sets. Without taking into account ties, there are 5! (i.e. 120) possible combinations of these rank orderings. Within this context the percentage of ‘major’ violations (in constituting less than 10% of the present sample) are small. By way of comparison, using only three data points in a similar analysis involving Hick’s law, Jensen (1987) found 20% of a sample of 225 college males exhibiting rank orders that were major violations

*An anonymous reviewer has suggested that intraindividual conformity to Fitts’ law be examined using Mokken scaling. This procedure is particularly useful in making assessment of the scalability and reliability of difficulty manipulations (de Gruijter, 1994; Machowski, 1993; Meijer, Sijtsma & Molenaar, 1995; Meijer, Sijtsma & Smid, 1990). Whilst Mokken scaling of the present data set might provide additional information, the analyses presently conducted follow those made extensively in the extant literature on ECTs, and thus allow for more ready comparisons.

Fitts’ law, MT and intelligence

235

of the underlying model. At the same time Jensen used this data set to argue for the robustness of linear function (and hence Hick’s law) within individual participants. As it happens, a somewhat vexing problem for the individual regression equations provided from Fitts’ law, is the finding that a substantial percentage of participants (24.58%) has negative intercept values. This outcome is of course suspect from the point of view of modeling intraindividual performance. Conceptually, however, these exceptions to Fitts’ law may simply indicate individual differences in the strategies s’s utilized for performing this task. Annett, Golby, and Kay (1958) have shown that some participants change effective pin diameter by applying the pins to a given hole at an angle. This in turn reduces the amount of information transmitted within the movement cycle. Moreover, this effect is more pronounced at smaller information values, which would have the subsequent effect of reducing the intercept parameter of any given individual who used this strategy. * There are thus two types of exception to Fitts’ law within intraindividual regression linesviolations in rank order and participants having negative intercept values. As a consequence of this finding, consideration should also be given to changes in mean parameter values when such participants are excluded. Accordingly, the mean intercept value (as expected) increases quite substantially (i.e. changes from 45.80 to 76.75msec), while the mean gradient value decreases somewhat (i.e. changes from 77.95 to 70.80 msec). The average fit of individual data to Fitts’ law, however, remains relatively unchanged (i.e. increases from 0.946 to 0.950). Elsewhere, Roberts (1996) has demonstrated that these obtained exceptions to Fitts’ law are not related to other individual differences phenomena including measures of cognitive ability and personality, as well as other performance speed parameters. This is noteworthy in the context of speculation that Eysenck (1987a, 1987b) has entered into concerning the psychological meaning of outlying scores. It would appear that ‘S non-conformity’ to Fitts’ law is not a reliable individual differences phenomenon. Vuriahility of’MTmeasures. Current administration of Fitts’ Movement Task is such that intraindividual variability measures of MT (sdMT) could not be obtained. Because of these parameters elevated conceptual status (see Jensen, 1992) consideration was given to between-& variability (i.e. group standard deviations in MT) in an attempt to understand the nature of this parameter in relationship to task difficulty (cf. Buckolz & Ruggins, 1978; Wing & Kristofferson, 1973). These are plotted initially as a linear function of information content scaled in bits of information (see Fig. 3). This figure indicates similar curvature to that reported by Jensen (1979) for the regression of variability in ‘Decision Time’ on bits, implying that a linear function may be inappropriate. Indeed, the equation describing this relationship-SD of mean MT= 16.78 + 8.84 log, [A/W +0.5]-results in a particularly shallow slope. As for previous regression equations, a measure of model fit was obtained. The value of this (r =0.907) is comparable to that reported in various studies conducted by Jensen (1987); (e.g. the case where intraindividual variability in DT is regressed on bits across 1402 participants gives r=0.910). Elsewhere, Jensen has argued that measures of variability in DT share a much stronger relationship with n, the number of stimuli from which to respond (see e.g. Jensen, 1982a, 1992). While it is not possible to directly determine this for MT assessed in the current manner, an analogous situation exists within this data set-the function of target distance and target width before measures are scaled into information units (i.e. bits). To determine whether, like the regression of variability in DT on n, this function provides a better fit for consistency measures, the group standard deviation of MTs were regressed on the values of (A/W +0.5) obtained from the five levels of this task (see Fig. 4). The obtained regression equation (SD of mean MT= 39.9l-tO.61 [A/W +0.5]) provides a measure of fit (r=0.986) which is not only highly adequate but turns out to be superior to that obtained with scaling onto bits (i.e. r= 0.907). Furthermore, the obtained goodness-of-fit measure is comparable to previous results within an information theory framework. For example, within *The use of this strategy by some participants may also have contributed to the significance of the quadratic trend reported in the analysis of mean structure. These results collectively suggest that more accurate assessment of this facet of performance is required. The use of a video camera in the fashion of Annett et al. (1958) is seemingly an expedient procedure in achieving this end. Note, however, that while this task could also be computerized (for example, by having participants use a joystick to move a cursor between two targets) the movement would then appear to require finer control, and hence probably would involve a different type of psychomotor ability.

Richard D. Roberts

236 X0

r

70

10

0

0

I

I

I

I

I

I

1

2

3

4

5

6

Task Difficulty Fig. 3. Standard

deviation information

of group Movement calculated according

(Bits of Information)

Time plotted as a function of task difficulty to Fitts’ Law) for Fitts’ Movement Task.

(i.e. bits of

80

70

10

0 0

Fig. 4. Standard

10

deviation

20

30

40

50

60

(A/W+0.5) of group Movement Time as a function of target width and target distance A/W + 0.5) for Fitts’ Movement Task.

Jensen’s (1987) meta-analysis, the bits is 0.990. Within the overall context of information theory units (i.e. A/W if the present results were shown information units. Notwithstanding,

mean r for the regression

of intraindividual

variability

(i.e.

in DT on

this study, the lawfulness of variability measures to pre-scaled +0.5) quite clearly requires some explanatory model, particularly to apply equally well to the regression of sdMT on pre-scaled the present result would seem to be consistent with a motor-

Fitts’ law, MT and intelligence

237

Table 6. Table showmg simplex pattern among the mean Movement Time measures of Fitts‘ Movement Task Parameter MT, 14 MT,or MT, 61 MT, 60 MT,

output that:

variability

hypothesis

MT, RX 0.89 0.84 0 71 0.63 0 89

MT,,,

MT, (ii

MT1*2

0.85 0.77 0.68 0.92

0.80 0.72 0.93

0.73 0.89

first put forward

by Schmidt

MT,,

0.86

ef al. (1979). In this model it is claimed

tr. running a motor program results in muscle contractions (in turn. causing a particular pattern of movement). and that the mechanisms involved in this chain of events introduce noise (~~ithin-subject variability)... limitations in a subject‘s capacity to move quickly is an indirect result of the variability produced by the force- and time-production mechanisms (Schmidt et ai., 1979, p. 416.424). This model shares a number of similarities with concepts expounded by Eysenck (1987a, 1987b) regarding the conceptual status of intraindividual variability in decision time (sdDT). Eysenck argues that within-S variability in DT is largely a function of noise (or errors) in neural transmission in the brain. How the current findings might be incorporated into an alternative model, which aims to expiain the empirical relationship between sdDT and both its linear relationship with set size and subsequent correlation with intelligence (i.e. ‘neural oscillation’; Jensen, 1979, 1992, 1993a) is, however, difficult to fathom. The types of processes represented here (simple movements) do not seem to fit easily within the ‘hierarchical binary tree’ proposed as an integral part of the neural oscillation model (see Jensen, 1982a; cf. also Brody, 1992)” One other implication stemming from this finding is that variability in MT is influenced saliently only by target width and/or target distance. Consequently, it may not be affected by the number of stimulus alternatives presented in a visual array. While very little attention has been given to this variable in chronometric studies, this may at least provide an additional means of ensuring that only MT is assessed in any chronometric task purportedly measuring this independently. Thus, if changes in sdMT are observed as a function of set size (providing target width and target distance are constant), it may be inferred that some decision process has entered the MT phase of a choice reaction task. Correlations between MTs across difficulty lecels. While the predominant foci of the present analyses are on mean structure, an examination of intercorrelation within the various levels of task difficulty is also warranted. This analysis indicates whether or not the variables are ordered in terms of task complexity (Guttman, 1955). For this purpose, MTs for the five information levels (i.e. 2.885.66 bits) were intercorrelated. These parameters were also correlated with mean MT over all conditions (i.e. MTx). The results of these analyses are presented in Table 6. Table 6 shows the MT measures exhibiting simplex structure. Thus, values close to the main diagonal are large and taper off at the diagonal to the bottom left-hand corner of the matrix. The presence of simplex structure implies that the MT variables of this task are ordered in terms of complexity in individual differences (Jensen, 1987; Roberts cf al., 1988).t Ana(vses qfpsychometric variables Having conducted the above microstructural directed to the cognitive ability measures. Means

analyses of the experimental task, attention is and standard deviations for each of the psycho-

*If errors in neural transmission are causally related to intelligence the question remains as to why seemingly more direct procedures for assessing this (i.e. tasks devised by Schmidt et al., 1979) have not been implemented. Much research involving RT paradigms has noted the poor reliability of intraindividual variability measures with many assumptions required to link these with neural transmission. Arguably, Schmidt et a/.‘~ tasks might shed light on this relationship in an ostensibly more valid and reliable manner. tWhile it would be highly desirable to obtain some indication of this tasks reiiability, procedures adopted for deriving the dependent variable prohibited knowledge of this psychometric property.

238

Richard D. Roberts Table 7. Means and standard deviatmns of cognitive ability variables Test

Mean

~ewl measures (number

Standard deviation

Number of items

(.ow~L.I)

01, Progressive matrices (RM) 02. Letter counting (LC) 03. Letter sets (SL) 04. Number series-Single (NSS) 05. Number series~Comuetine (NSC) 06. Letter series&ingle (‘LSS)07. Letter series-competing (LSC) 08. Water jars (WJ) 09. Scrambled words (SW) 10. Genera1 information (Gl) 11. Vocabulary multichoice (VM) 12. Esoteric analogies (EA) 13. Digit Span-Forwards (SF) 14. Digit span-Backwards (SB) 15. Card rotations (CR) 16. Computer form boards (CFB) 17. Hidden figuresG%ngle (HFS) 18. Hidden figures-Competing (HFC) 19. Tonal memory-Single (TMS) 20. Tonal memory-competing (TMC) 21. Speech distortion (SD)

50.04 6.90 10.99 19.38 11.07 13.85 8.32 38.94 7.30 10.03 10.31 IS.42 9.80 9.18 51.31 10.44 13.18 14.63 13.74 13.16 IS.50

5.79 3.83 2.46 3.77 3.78 4.03 3.00 14.23 4.90 3.85 3.14 3.82 2.10 2.38 13.41 3.52 3.96 3.99 3.39 3.65 1.70

60 15 IS 24 30 24 30 15 25 20 18 24 14 14 80 20 20 20 20 20 24

3000.97 1724.92 1165.94 1351.99

903.87 604.45 333.18 222.43

48 80 90 90

Speed measures (msec)

22. Number comparison time (NCT) 23. Stroop (color) time @CT) 24. String search time (SST) 25. Digit symbol time (DST)

N.B. For Tests l-21, the dependent variable IS the number correct from all items in the test; whether attempted or not. For Tests 22-25 the dependent variable is average time per item (see Stankov. 1988; Stankov, Roberts & Spilsbury, 1994 for the rationale underlying this with computerized markers of G,).

metric variables given in Table 1 are reported in Table 7. Generally, the values of these descriptive statistics are remarkably close to those obtained in previous studies that have employed many of these measures (Anstey, Stankov & Lord, 1993; Horn, 1988; Roberts et al., submitted; Stankov & Crawford, 1993). In order to determine the structure underlying the psychometric variables, maximum likelihood analysis was performed on the psychometric measures given in Table 7.* A solution employing root-one criterion yielded seven factors. With these seven factors, the goodness-of-fit chi-square test was satisfactory (X-square= 144.43; d.f. = 146; P=O.521). These seven factors were then rotated to an oblique (i.e. oblimin) solution. The 20.10 hyperplane count of this solution was 61.1%, suggesting adequate attainment of simple structure (Boyle, Stankov & Cattell, 1995). The resulting oblimin factor pattern solution, along with its factor intercorrelation matrix, is presented in Table 8. As explicated in detail elsewhere, this factor structure unfolds predominantly as anticipated (Roberts, 1995; Roberts et al., 1996; Roberts & Stankov, 1995). However, a noteworthy divergence from the hypothesized structure may be seen with some of the Gf marker tests having salient loading on a Gf factor, whilst others load on an additional factor that may be readily identified as Induction (I). Nevertheless, the factor intercorrelation between Gf and I is sufficiently high to indicate that these two factors are closely related. Moreover, almost all of the other factor intercorrelations are of a magnitude that would be expected from previous research conducted within the framework of Gf/Gc theory (Stankov et al., 1995). Correlations between cognitive ability factors and MTparameters Commonly an individual’s (Juhel, 1991). In the present to Carroll (1993) this allows correlations between a given

*The interested psychometric

reader is referred indices.

performance on an ECT is correlated with a single psychometric index study, a number of intelligence factors have been defined. According for sound theorizing with regard to the substantive meaning of obtained experimental measure and intelligence. Thus, on the basis of the factor

to Roberts,

Pallier,

and Stankov

(1996) for the 25 x 25 correlational

matrix

of these

Fitts’ law, MT and intelligence Table 8. Oblimin Test 01. Ravens matrices 02. Letter counting 03. Letter sets 04. Number series-Single 05. Number series-Competing 06. Letter series-Single 07. Letter series-competing 08. Water jars 09. Scrambled words 10. General information I 1. Vocabulary 12. Esoteric analogies 13. Digit span forward 14. Digit span backward 15. Card rotations 16. Form boards 17. Hidden figures-Single 18. Hldden figures-Competing 19. Tonal memory-Single 20. Tonal memory-Competing 21. Speech distortion 22. Number comparison 23. Stroop color 24. String search 25. Digit symbol N.B. All loadings

factor

pattern matrix

G, G‘ SAR G\ G, G,

1

of psychometric

tests

Fl (G,)

F2 (G,)

F3 (SAR)

F4 (C,)

F5 (G,)

F6 (GJ

F7 (I)

h’

0.94 0.39 0.55 0.07 0.08 0.00 -0.01 -0.01 0.17 -0.03 0.02 0.09 0.04 0.01 0.02 0.31 0.04 0.06 0.18 -0.08 0.01 0.00 -0. I I 0.00 -0.03

0.14 -0.10 0.05 -0.02 -0.10 0.05 0.07 0.08 0.29 0.76 0.76 0.81 0.10 0.09 -0 ox 0.02 0.09 -0.04 0.02 0.03 0.00 0.00 0.01 -0. I5 0.12

-0.24 0.16 0.15 0.15 0.1 I 0.04 0.08 -0.19 0.29 -0.04 0.10 0.04 0.71 0.48 0.12 -0.07 0.07 -0.05 0.06 0.1 I 0.26 0.00 0.10 0.1 I -0.16

0.12 -0.15 0.02 -0.05 -0.06 0.13 0.08 0.08 0 01 -0. I6 0.06 0.14 -0.05 0.04 0.34 0.24 0.71 0.83 -0.03 0.25 0.08 0.01 0.07 -0.03 -0 I2

0.01 0.07 0.05 0.01 -0.08 0.02 0.25 0.03 -0.08 0 07 -0.07 0.06 0.22 0.19 0.08 0.10 -0.04 0.13 0.67 0.71 -0.02 0.05 -0.29 0 02 0.05

0.02 -0.10 -0. I I -0.06 -0.02 0.03 0.06 -0.06 -0. I3 -0.05 0.13 -0.09 0.18 0.02 -0.22 0.20 -0.01 0.04 0.02 -0.14 -0.06 0.75 0.69 0.66 0.57

0.04 0.13 -0.03 0.64 0.52 0.60 0.43 0.40 0.12 0.00 -0.01 -0.04 0.07 0.18 -0.09 0.09 0.12 0.08 -0.05 0.10 0.03 0.00 -0.07 -0.14 0.07

0.99 0.30 0.44 0.53 0.31 0.45 0.39 0.22 0 33 0.57 0.61 0.77 0.68 0.44 0.24 0.27 0.61 0.82 0.55 0.79 0.09 0.56 0.62 0.49 0.42

above 0 20 are in bold font. The factor intercorrelatlon

Factor

239

matrix is given below

G

G

SAR

G,

;.21 0.25 0.24 0.37 -0.18 0.41

;.03 0.13 0.18 0.04 0.28

lYl2 0.21 -0.17 0.24

;.30 -0.16 0.23

G,

I

-0Yl5

.

G,<

J.09 0.28

analytic solution given in Table 8, factor scores corresponding to each broad cognitive ability were calculated using the BART technique (Norusis, 1990). These factor scores were subsequently correlated with the parameters obtained from Fitts’ Movement Task. The results of this cognitive correlates analysis are presented in Table 9. Inspection of Table 9 shows that virtually all ‘level’ second-order abilities (i.e. factors defined purely by accuracy scores) share low to near zero correlation with the MT parameters obtained from a ‘pure’ psychomotor task. This outcome is similarly observed when a third-stratum factor (having almost exclusive loadings from ‘level’ tests) is extracted from the second-order factors of the test battery (see final column of Table 9). Interestingly, while most of the correlations with these cognitive ability factors are (as expected) negative in sign, there is a tendency for these to decrease as a function of stimulus information. This latter trend is the obverse to that found with RT parameters. Typically a linear increase is observed between intelligence measures and RT tasks as a function of task difficulty (Vernon & Weese, 1993). This result is curious given the simplex structure reported in Table 6. One possible explanation is that this task is so well automated that it fails to tap the working memory capacity of the individual-the hypothetical construct assumed to

Table 9. Correlations Factor MT, x8 MT, 14 MT,,, MT, 6: MT%66 MT,

between MT as a function

of task dlfficultv and obtained

coenitwe

abihtv factor scores

Gf

G,

SAR

G,

G,

G,

I

G

-0.04 -0.04 -0.07 0.05 0.06 -0.00

-0.09 -0.06 -0 08 -0.03 -0.02 -0.06

-0.13 -0.12 -0. I6 -0. I1 -0.03 -0.10

-0 I2 -0.05 -0.03 -0.02 0.05 -0.03

-0.14 -0.17 -0.13 -0.06 -0.06 -0.12

0.30 0.35 0.30 0.32 0.23 0.33

0.10 0.10 0.12 0.11 0.03 0.10

-0 16 -0.13 -0.15 -0.02 0.02 -0.08

240

Richard D. Roberts

account for the results obtained with RT indices. Note also that several researchers have argued that it is complexity per se (rather than task difficulty) that is responsible for the correlation between elementary cognitive operations and intelligence (Larson & Saccuzzo, 1989; Roberts et al., 1988; Snow, 1989; Spilsbury, 1992; Stankov & Crawford, 1993). The present results would seem consistent with this theoretical postulate. Notwithstanding, MT shares significant correlation with the one psychometric factor presently defined by speed measures, G,. Elsewhere, several commentators have argued that the correlation between chronometric performance and intelligence cannot be accounted for by the fact that many psychometric tests are given under strict time limits (see Vernon & Kantor, 1986; Vernon et al., 1985). In the present study, with the exception of markers of G,, time limits for cognitive tests were liberal. Equally, it has been suggested that “highly speeded tasks in which the task requirements per se are quite simple, such as clerical checking, letter cancellation and the like, are among the poorest psychometric correlates of IQ or g, and they also show the weakest correlations with RT” (Jensen, 1987, p. 417, italic mine). This is obviously not the case with the correlation between MT and G,. At an intuitive level this result makes sense. Clerical-perceptual speed tests, such as Digit Symbol, are notably dependent on fast movement speed for optimal performance. Under the strict time restrictions placed on these types of psychometric test, advantages in performing a single psychomotor act are multiplied by the number of such acts that are completed. In accordance, faster movement speed leaves more time available for the individual to devote to additional cognitive requirements (such as error monitoring), or otherwise allows the individual to devote more time to the search component underlying the test (Roberts, 1995).* In total, these findings suggest a critical re-appraisal of previous theories offered to account for the correlation between MT and intelligence factors. In the ensuing discussion several explanatory models of intelligence are systematically evaluated in light of the present findings. However, attention is directed initially to the implications of the lawfulness of the MT parameter.

DISCUSSION Microstructural analyses of Fitts’ Movement Task indicate that when experimentally manipulated in an appropriate fashion, MT shares a linear relationship with task difficulty. This outcome is evidenced in analysis of mean trends of both group and intraindividual data and is supported also by the simplex structure of intercorrelations between manipulations on the MT variable. The robustness of Fitts’ law within each participant is impressive; renders calculation of intraindividual parameters such as intercept and slope possible, and allows these measures to be related to other psychological variables. From the perspective of previous research within this paradigm, the results are similarly impressive-the transmission rate obtained, while in the upper range reported-would nonetheless seem comparable to established values.? Moreover, features found by Jensen to occur with regularity in RT data (e.g. simplex in measures of central tendency as a function of bits) are found to hold for an information theory manipulation of a MT task. In turn, this bears testament to the potential generality of principles by which diverse ECTs should be validated. The present findings have interesting implications for those working within the areas of human factors and personnel assessment. For example, it has been suggested that psychomotor measures provide incremental validity to cognitive aptitude tests for predicting, in particular, pilot performance (for a recent review see Griffin & Koonce, 1996). The microstructural analyses conducted with Fitts’ Movement Task establish additional parameters that may be useful for such purposes. It remains to be demonstrated whether entering a variety of these parameters into some form of multiple regression procedure will improve the incremental validity still further. Of theoretical importance, the demonstrated lawfulness of the MT paradigm makes the present

*Low to near zero correlations are also observed between each of the intraindividual regression parameters and ‘level’ cognitive abilities. This is despite the correlations between MTa and MT, (r=0.25), and MTb and MT, (r=0.33), being indicative of relatively independent constructs. TThis correspondence is particularly impressive if it is recalled that in Fitts’ original study, each participant was given only 15 set to perform each task, while in the present task each participant was given 60 set, making this later measure potentially more reliable.

Fitts’ law, MT and intelligence

241

findings that were obtained within the cognitive correlates approach, compelling. Elsewhere, the psychological processes captured during the MT phase of performance have seemingly been confounded with DT (Smith, 1989; Smith & Carew, 1987). Equally, the cognitive ability factors with which MT variables have previously been correlated have been poorly defined. The current results, obtained with a broad sampling of the cognitive abilities domain and valid psychomotor indices, are essentially negative. In reviewing the then extant literature, Buckhalt et al. (1990) proffer a number of explanatory hypotheses to account for the relationship between MT and intelligence. In light of the present findings, each of these explanations is evaluated in the passages below. 1. Motor response programming and execution. Jensen (1982a) has argued that MT and intelligence correlations may be accounted for by incomplete programming of the ballistic response in lower intelligence participants, as they leave the home button of certain ECTs. This explanation seems most unlikely given the low ‘positive’ correlation obtained with Fitts’ Movement Task and intelligence factors at ‘higher’ levels of task difficulty (see Table 9). That is, in the 5.88-bit condition, where programming of the ballistic response is most crucial to fast performance, slower speed is (weakly) associated with higher cognitive ability scores. 2. Hovering strategies. Smith and Carew (1987) have suggested that some participants leave the home button prior to decision and that as a consequence the measurement of MT (and DT) in many chronometric tasks is confounded. The failure to obtain significant correlations between MT and intelligence in the present study provides further support for this proposition. Note that this, in turn, implies that previous studies may have incorrectly located the ‘source’ of a given cognitive (or motor) processes correlation with intelligence. This reiterates a sentiment first espoused by Detterman (1987)-RT tasks are by no means as ‘simple’ as the majority of commentators suggest. This proposition is undoubtedly true also of psychomotor tasks such as the one presently employed. 3. An interaction with level of arousal. Buckhalt et al. (1990) cite a paper by Lindley, Smith, and Thomas (1988) that showed that brighter participants were more motivated to respond quickly. This proposition would seem inconsistent with the present findings. The current psychomotor task was particularly monotonous for many of the participants. However, no significant correlations were established with intelligence level across any of the experimental conditions of Fitts’ Movement Task. 4. Developmental phenomenon. This explanation remains a plausible hypothesis given that the present sample was restricted with respect to the age variable. Note that elsewhere, studies conducted with young children have shown fairly substantial correlations with MT and cognitive ability marker tests (especially those tests assessing Gr, see Beh, Roberts, and Pearse, 1991; see also Telzrow, 1983). It would also appear that psychomotor performance correlates more highly with intelligence when older participants (aged 70 and above) are included in the sample (cf. Bors & Forrin, 1995). 5. Automatization of ballistic response. Widaman and Carlson (1989) have addressed the issue of automatization in their investigations of the Hick paradigm and procedural effects. Based on experiments conducted to examine practice effects, they predict that correlations between DT and MT with intelligence will be reduced (or non-existent) when sufficient practice allows for the full automatization of a participant’s response. Accordingly, in the case of typical experiments conducted using the so-called Roth-Jensen apparatus (Jensen, 1987), participants may not have performed a sufficient number of practice trials to automatize the MT component-with this arguably exacerbated by the different movements required in each trial block (Buckhalt et al., 1990). As the present task involves psychomotor movements that are already highly automatic, this explanation would seem consistent with the obtained magnitude of correlation reported in Table 9. dijfirences. Buckhalt et al. (1990) conclude their study by noting their evidence 6. Neurophysiological is consistent with studies showing that nerve conduction velocity is correlated with speed of information processing and general intelligence. Accordingly, more able participants both process information and move faster due to central underlying physiological differences affecting DT and MT (Reed & Jensen, 1991, 1993; Vernon & Mori, 1989). The current findings render such an explanation most unlikely, particularly when it is recalled that the physiological measures

242

Richard D. Roberts

previously employed under this reductionist framework (nerve conduction velocity in the arm) should have a direct bearing on the hand movement speed that is presently assessed. 7. Timed measures of intelligence account for observed relationships with MT. Although no formal explanation of this type is offered in the literature, it is quite conceivable that correlations between MT parameters occur only in those studies that have included timed psychometric tests in the experimental design.* For example, Buckhalt et al. (1990) employed a fairly diverse battery of psychometric indices that nonetheless involved tests given under strict time requirements (e.g. Matrices and Speed of Information Processing subtests from the British Ability Scales, shortform). They then based their correlational analyses upon the composite obtained from these various tests, thereby not ruling out this possibility as an explanation for obtained resu1ts.t Equally, Roberts, Stankov, and Walker (1991) found significant correlations between Ravens (Standard) Progressive Matrices performance and Fitts’ Movement Task when the former was given within a (recommended) 20 min time. In attempting to replicate this with a larger battery, which contained a mix of time-limited and non-speeded psychometric tests, most of these correlations tended towards zero. This interpretation is consistent with the findings obtained in the present study. Tests sharing salient loadings on each of the level abilities are not heavily biased towards speed of responding. Thus, only a small percentage of participants failed to complete all items of marker tests given in this study within the time allotted. Indeed, it is worth noting that only those tests involving clerical/perceptual speed were strictly linked to timed performance, and that these measures alone shared significant correlation with MT. As mentioned previously, fast movement speed on such tasks is clearly important. Not only would it give an individual more time to devote to error checking and the like, it should also give them more time to actually search the array to complete additional items. In sum, the lack of correlation established with each of the ‘level’ abilities defined in this study does not support several explanatory models offered in the literature. These results highlight the need to draw distinctions between different types of cognitive speed and the different physiological processes underlying each of these constructs (Stankov & Roberts, 1997). Moreover, it should be noted that the present task is a marker of one psychomotor factor. Whether all such constructs fail to exhibit significant correlations with intelligence remains an empirical issue. The present results also establish that the role played by automatization in a given task needs to be given very careful consideration when interpreting results. This reiterates several cautionary comments made in the literature surrounding the stabilization times of various ECTs (see in particular, Bittner et al., 1986). In many such paradigms, the possibility can not be ruled out that adaptation to the experimental situation, rather than performance, is related to intelligence (Carroll, 1993, p. 506). Resolution of this issue would seem important as the psychology of individual differences moves towards computerized testing of all performance measures.

CONCLUSION In reviewing the literature, it was suggested that there has been a recent flurry of research activity generated by a possible link between MT and general intelligence. However, by and large, this measure has been obtained de facto. Failure to replicate these findings using a traditional experimental task and a wide battery of psychometric tests should be viewed as compelling, particularly in light of the validity established for the former. Two implications for chronometric research should be noted. Unless it is fully demonstrated that movement is all that is embellished within the ‘psychomotor phase’ of an ECT, studies reporting significant correlation between MT parameters and intelligence should be viewed with suspicion. A similar degree of skepticism should also be

*Although never examined with respect to the MT parameter, this possibility has been dismissed in a number of studies that examine the relationship between timed and untimed psychometric indices and measures of DT (see in particular, Vernon & Kantor, 1986; Vernon et al., 1985) tunfortunately, Buckhalt et al. (1990) do not present the correlations obtained for each individual test, which would allow a more definitive test of this proposition.

Fitts’

law, MT and intelligence

243

directed at this finding, if the psychometric tests with which MT parameters are correlated with, have been given within strict time limits. Moreover, in a recent paper, Stankov and Roberts (1997) argue that mental speed is not basic. The impetus for this paper derives from the finding that ‘speeded’ tasks have as complex a factorial structure as do level abilities. A similar notion was entertained by Carroll (1993) in his survey of the existing factor analytic literature. The present findings are indicative of the fact that one such speed construct is minimally related to ‘level’ cognitive ability factors. Until the taxonomy underlying mental speed is more clearly delineated, researchers should be particularly cautious in postulating explanatory models of intelligence.

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