Richard D. Roberts¹
(National Research Council Fellow)
Armstrong Laboratory (AL/HRMA)
Brooks AFB, San Antonio
TX 78235 - 5352
E-mail: roberts@alhrm.brooks.af.mil

Recently, several researchers have focused increasing attention on the empirical status of Movement Time (MT - i.e. the speed associated with sensori-motor control of movement) particularly in its moderate negative relationship with intelligence. However, the results from these studies are very much at odds with early research that suggested that there was no relationship between these two constructs. Possible explanations for this discrepancy lay in the fact that research currently conducted either fails to manipulate the amount of information contained in a psychomotor task or otherwise confounds this aspect of performance with other psychological processes (e.g. decision time). In sum, contemporary analyses of MT are not truly representative of this construct - at least as it is conceptualized outside the individual differences’ realm.

The present study addressed these problems. One hundred and seventy-nine subjects performed a psychomotor task conforming to Fitts' law (an information theory principle relating MT to task difficulty) and a battery of twenty-five psychometric tests. The latter measures were selected in order to define seven broad cognitive ability factors under the framework of Gf/Gc 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 (Gs), 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.

In studies involving the cognitive correlates approach to intelligence, two dependent variables are generally derived from a single elementary cognitive tasks (ECT). One of these is Movement Time (the speed associated with sensori-motor control of movement), the other Decision Time (the time required to determine and initiate an appropriate response to stimuli). However, operationalization of the former psychological 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 have limited generalizability. Acknowledging problems in current perspectives, Carroll (1993, Chapter 13) gives psychomotor factors a separate chapter in his book, The Structure of Human Cognitive Abilities.

The last two decades have witnessed a concerted effort to investigate the relationship between chronometric performance and intelligence (see for example, Carroll, 1993, Chapter 11; A. R. Jensen, 1987; Stankov & Roberts, 1996 for reviews). In so doing, measurement of Decision Time (DT) has tended to provide the generic empirical focus. While original formulations within this research program simultaneously downplayed the importance of Movement Time (MT) (see for example, Carlson & C. M. Jensen, 1982; A. R. Jensen, 1979, 1982a, 1982b; A. R. Jensen & Munro, 1979), more recent results suggest that this might have been premature (Buckhalt, 1991; Buckhalt & A. R. Jensen, 1989; Buckhalt, Reeve & Dornier, 1990; Detterman, 1987; Era, Jokela & Heikkinen, 1986; Frearson & Eysenck, 1986; Houlihan, Campbell & Stelmack, 1994; A. R. Jensen, 1987; Neubauer, 1990; Telzrow, 1983).

A possible explanation for the low status afforded to MT in earlier accounts may be gathered from a brief survey of the 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 (see for example, Fleishman, 1954, 1964, 1972; Guilford, 1958; see also Fleishman & Quaintance, 1984; N. G. Peterson & Bownas, 1982). This reflected a commonly held view by psychometrists that simple motor tasks will share low to zero correlations with intelligence (see for example, McGeoch, 1942). This position was strengthened by studies that failed to show significant correlations between psychomotor skills and psychometric ability. Such studies were nevertheless flawed, often relying exclusively on psychometric measures involving verbal content (see for example, Clark & King, 1960) and/or particularly small sample sizes (see for example, 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. However, similar criticisms could be mounted of these regarding the psychometric instruments employed - generally only a single test is used (Juhel, 1991). Notwithstanding, these tend to involve measures having high visuo-spatial content (e.g., the Raven's Progressive Matrices Test). Thus, provided that the sample size is fairly large and measures other than those assessing verbal abilities are employed, correlations between MT and psychometric performance have been reported to be as high as those involving other elementary cognitive operations (i.e. between -0.35 and -0.50, see for example, Buckhalt et al., 1990).

That moderate correlations between MT and intelligence are observed is not as surprising as it would first appear. Within contemporary speed of information processing studies, the correlation between MT and DT is reported to be as high as 0.40 (see for example, A. R. Jensen, 1982a). Such correlations may be 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). Since 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 some of the individual differences 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 reported in these studies. 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, most contemporary studies examine the relationship between MT and intelligence by default. Since it is considered conceptually meaningful to differentiate between DT and MT in choice RT paradigms (see A. R. Jensen, 1979; also G. A. Smith, 1989 for an alternative view), some attention is generally afforded to this construct, often without theoretical justification (Stankov & Roberts, 1996). As a result, individual difference 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:

where "A" is the target distance, "W" is the target width and "k" is the slope constant². Indeed, given Equation 1, analyses involving the MT parameter are essentially misrepresented within current cognitive correlates approaches to intelligence. For example, across a series of choice reaction time experiments, A. R. Jensen (1982a, 1987) has plotted MT as a function of stimulus information, claiming that it is surprising that these have zero slope. However, Fitts' law requires this outcome since neither target distance nor target width is generally manipulated in traditional implementation of ECTs.

Analyses of the mean structure of group and intraindividual parameters obtained from an information theory manipulation of MT are bound therefore to be informative. While it is well established that group means will exhibit a linear relationship between MT and bits of information (see for example, Fitts, 1954; Fitts & J. R. Peterson, 1964; Fitts & Radford, 1966; Hancock & Newell, 1985; Knight & Dagnall, 1967; Meyer, Abrams, Kornblum, Wright & J. E. K. Smith, 1988; Schmidt, Zelaznik & Frank, 1978; Welford, 1968; Welford, Norris & Shock, 1969)³ 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. Such analyses are viewed as paramount to the interpretative properties of ECTs (see for example, A. R. Jensen, 1987).

The present study was designed to address deficiencies that are apparent in the literature, and, as such, 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 RT 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 "one-off" measures of intelligence have previously been employed) does linkage with MT and human cognitive abilities occur? Elsewhere, Carroll (1993, p.647) 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.

Subjects. A total of 179 subjects was involved in the present study. A substantial number of these (i. e. 82%) were first year Psychology students. The remainder were drawn from the general community. 110 were female. The age of the subjects ranged from 17 to 50 years with a mean age of 21.6 years and a standard deviation of 6.2 years. It should be noted that those subjects 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 twenty-five tests that were employed to define psychometric constructs and a single psychomotor task having five levels of task difficulty.⁴ It was envisaged that six broad factors (hypothesized on the basis of Gf/Gc theory [see for example, Carroll, 1993; 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 1.

As will be noted, there were eight markers of Gf (Tests 1-8), four markers of Gc (Tests 9-12) , two markers of short-term acquisition and retrieval (SAR, Tests 13-14), four markers of broad visualization (Gv, Tests 15-18), three markers of broad auditory function (Ga, Tests 19-21) and four markers of clerical-perceptual speed (Gs, 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, Chapter 11).

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

Fitts' Movement Task. For this task, five response boards were constructed, making for five experimental conditions. Each of these was placed horizontally in front of the subject in various random combinations.⁵ The boards consisted of two holes varying in diameter that were set 30.5 cm apart from centerpoint to centerpoint (see Figure 1). These holes constituted targets that varied in target width across the five boards. From Fitts' (1954) formula (i.e. Equation 1) - bit values were calculated for each of the respective treatment conditions. Table 2 gives the parameters relevant to each treatment condition.

The subjects' task was to tap a small metal probe (of constant diameter 0.635 cm) between the two targets as quickly and accurately as possible. The experimenter recorded the number of cycles made by each subject for each condition within a 60 sec test period. For this purpose a cycle was defined as the movement of the probe from the origin (the center of the circle on the subjects' 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 for example, Fitts, 1954). Output was subsequently transformed into the time (measured in msec) it took subjects to make one cycle.⁶

N.B. Bits were calculated from the formula: log₂ (A / W + 0.5). In the present case, Target Area (A) is constant (i.e. 30.5 cm). Target Width, however, was variable being the difference between the diameters of the hole (which was experimentally manipulated) and the pin (which was constant, i.e. 0.635 cm).

Procedure. The tests were generally administered to subjects over two sessions. In the first, paper and pencil tests were carried out, while in the second, subjects completed the computerized cognitive ability measures and Fitts' Movement Task. The latter was administered 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.

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.

Descriptive statistics. The group means and standard deviations of mean MT as a function of task difficulty (i.e. bits) are presented in Table 3.⁷ This Table also contains the mean performance of this task averaged over experimental conditions (i.e. MT_X).

Table 3 reveals that for each condition of MT (scaled into bits) both mean performance and between-subjects 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 < 0.01). While analysis involving residual trends also indicated a significant quadratic function (F (1, 178) = 72.55; p < 0.01) 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, especially as the expression describing this (MT = 208.00 - 2.44X + 9.48X² where "X" is bits of information) provides a perfect correlation between response time and task difficulty (r = 1.00). Nevertheless, since 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 from the perspective of an information theoretic approach.

The significant linear trend that was obtained leads naturally to resolution of an important empirical issue. Does the apparatus and procedure used in this task yield data that conform to Fitts' law? This question is addressed in the passages that follow in terms both of the conformity of group means of mean MT data and the adherence of individuals' mean MTs to Fitts' law. Parameter values are compared to the current literature and envisaged extensions.

Conformity of group data to Fitts' law. Since Equation 1 may be subject to some degree of error (as in fact are all physical measurements [c.f. A. R. Jensen, 1987]), a more accurate fit to the current data analyzed is provided by the following:

where "a" represents intercept, "b" the slope constant and "X" task difficulty (i.e. log₂ [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 log₂ [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 Figure 2), as well as the degree of fit to the linear regression of MT on bits of information - indicated by the Pearson r. The r obtained 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, the above equation (i.e. Equation 2) is particularly useful in calculating rate of transmission. This is given by the reciprocal of the slope, "b", expressed as bits per unit time (see for example, Crossman, 1953; Fitts, 1954; Shannon & Weaver, 1949). Interestingly, Fitts (1954) reports this value as lying within the range of 7.5 and 12.6 bits/sec 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 - 12.7 bits/sec - 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 (see for example, Fitts & J. R. Peterson, 1964; Welford, 1968; Welford et al., 1969). Findings from the present task would thus seem consistent with those reported in previous studies.⁸

Conformity of individuals' MT to Fitts' law. As there is such a high degree of conformity to Fitts' law evidenced in group data it would seem worthwhile assessing the extent to which individual data also exhibit this characteristic. Such analyses have been used previously in determining the degree to which RT measures subscribe to Hick's (1952) law (see for example, A. R. Jensen, 1987). However, to date, there are no relevant data on the extent to which intraindividual MT data 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 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 subjects' 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 percent. In order to get some clearer indication of the "types" of non-conformity to Fitts' law occurring in the present sample of subjects, these data were subsequently analyzed after the fashion described by A. R. Jensen (1987) - wherein each subject's MTs were examined in terms of their rank order with respect to task difficulty. The predicted order according to Fitts' law would be 1 - 2 - 3 - 4 - 5. The percentage of individuals having this and different rank order 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 (i.e. one involving Hick's law), A. R. Jensen (1987) found 20% of a sample of 225 college males exhibiting rank orders that were major violations of the underlying model. At the same time, on the basis of this data set, Jensen argued for the robustness of linear function (and hence Hick's law) within individual subjects.

As it happens, a somewhat vexing problem for the individual regression equations provided from Fitts' law is the finding that a substantial percentage of subjects (24.58%) have negative intercept values. These are 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 subject strategies utilized for performing this task. Annett, Golby and Kay (1958) have shown that some subjects 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.⁹

There are thus two types of exception to Fitts' law within intraindividual regression lines - violations in rank order and subjects having negative intercept values. As a consequence of this, consideration should also be given to changes in mean parameter values when such subjects are excluded. Accordingly, the mean intercept value (as expected) increases quite substantially (i.e. from 45.80 to 76.75 msec), while the mean gradient value decreases somewhat (i.e. from 77.95 to 70.80 msec). The average fit of individual data to Fitts' law, however, remains relatively unchanged (i.e. from 0.946 to 0.950). Elsewhere, Roberts (1995) has demonstrated that these obtained exceptions to Fitts' law are not related to other individual differences phenomenon including measures of cognitive ability and personality, as well as other performance speed parameters.

Variability of MT measures. Current administration of Fitts' Movement Task is such that intraindividual variability measures of MT (sdMT) were not able to be obtained. Because of this measure's current conceptual status (see A. R. Jensen, 1992) consideration was given to between-subjects variability (i.e. group standard deviations in MT) in an attempt to understand the nature of this in relationship to task difficulty (c.f. Buckolz & Ruggins, 1978; Wing & Kristofferson, 1973). These are plotted initially as a linear function of information content scaled in bits of information (see Figure 3). This Figure indicates similar curvature to that reported by A. R. 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 - S.D. of mean MT = 16.78 + 8.84 log₂ [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 A. R. Jensen (1987; e.g. the case where intraindividual variability in DT is regressed on bits across 1402 subjects gives r = 0.910).

Elsewhere, A. R. 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 for example, A. R. Jensen, 1982a, 1992). While this is not possible to directly determine 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", these provided 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 Figure 4). The obtained regression equation (S.D. of mean MT = 39.91 + 0.61 [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 into 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 A. R. Jensen's (1987) meta-analysis, the mean r for the regression of intraindividual variability in DT on bits is 0.990.

Within the overall context of this study, the lawfulness of variability measures to pre-scaled information theory units (i.e. A / W + 0.5) quite clearly requires some explanatory model, particularly if the present results were shown to apply equally well to the regression of sdMT on pre-scaled information units. Notwithstanding, the present result would seem consistent with a motor-output variability hypothesis first put forward by Schmidt, Zelaznik, Hawkins, Frank and Quinn (1979). In this model it is claimed that:

This model shares a number of similarities with concepts expounded by H. J. Eysenck (1987a, 1987b) regarding the conceptual status of intraindividual variability in decision time (sdDT). Eysenck argues within-subject 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 explain the empirical relationship between sdDT and both its linear relationship with set size and subsequent correlation with intelligence (i.e. "neural oscillation" [see for example, A. R. Jensen, 1979, 1992, 1993]) 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 A. R. Jensen, 1982a).¹⁰

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 levels. While the predominant foci of the present analyses are on mean structure, an examination of intercorrelation within the various levels of task difficulty (i.e. bits of information) is also warranted. These indicate whether or not the variables are ordered in terms of task complexity (see for example, Guttman, 1955). For this purpose MTs for the five information levels (i.e. 2.88 to 5.66 bits) were intercorrelated. These were also correlated with mean MT over all conditions (i.e. MT_X). 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 from 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 (see for example, A. R. Jensen, 1987; Roberts, Beh & Stankov, 1988).¹¹

Having conducted the above microstructural analyses of the experimental task, attention is directed to the cognitive ability measures. Means and standard deviations for each of the psychometric 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 employ these tests (see for example, Anstey, Stankov & Lord, 1993; Horn, 1988; Roberts, Stankov, Pallier & Dolph, 1996; 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 7.¹² A solution employing root-one criterion yielded seven factors. With these seven factors, the goodness-of-fit Chi-square test was satisfactory (Chi-square = 144.43; d.f. = 146; p = 0.521). These seven factors were then rotated to an oblique (i.e. oblimin) solution. The ±.10 hyperplane count of this solution was 61.1%, suggesting adequate attainment of simple structure (c.f. Boyle, Stankov & Cattell, 1995). The resulting oblimin factor pattern solution, along with its factor intercorrelation matrix, is presented in Table 8.

N.B. For Tests 1 to 21, the dependent variable is number correct from all items in the test - whether attempted or not. For Tests 22 to 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 Gs).

As explicated in detail elsewhere, this factor structure unfolds predominantly as anticipated (see Roberts, 1995; Roberts, Pallier & Stankov, 1996; Roberts & Stankov, 1995). However, a noteworthy divergence from the hypothesized structure may be seen with the Gf marker tests sharing salient loading both on this and an additional factor 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 (see for example, Stankov et al., 1995).

N.B. All loadings above 0.20 are in bold font. To provide some idea of the correspondence between the hypothetical and obtained factor structure, loadings in line with expectations are underlined. The factor intercorrelation matrix is given below.

Correlations between cognitive ability factors and MT parameters
Commonly a subject’s performance on an ECT is correlated with a single psychometric index (Juhel, 1991). In the present study, a number of intelligence factors have been defined. According to Carroll (1993) this allows for sound theorizing regarding the substantiative meaning of obtained correlations between a given experimental measure and intelligence. Thus, on the basis of the factor analytic solution given in Table 8, factor scores corresponding to each broad cognitive ability were calculated using the BART technique (Norusis, 1990). These 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 (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 later 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 cognitive complexity (see for example, 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 account for the results obtained with RT indices.

Notwithstanding, MT shares significant correlation with the one psychometric factor presently defined by speed measures - Gs. Elsewhere, several commentators have argued that the correlation between chronometric performance and intelligence can not be accounted for by the fact that many psychometric tests are given under strict time limits (see Vernon & Kantor, 1986; Vernon, Nador & Kantor, 1985). In the present study, with the exception of markers of Gs, 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 (A. R. Jensen, 1987, p. 417, underline mine). This is obviously not the case with the correlation between MT and Gs. In total, these findings suggest a critical re-appraisal of previous theories offered to account for the correlation between MT and intelligence factors.¹³

Microstructural analyses of Fitts' Movement Task indicate that when experimentally manipulated in an appropriate fashion MT shares linear relationship with task difficulty. This 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 subject is impressive - rendering calculation of intraindividual parameters such as intercept and slope possible and allowing these to be related to other psychological variables. From the perspective of previous research within this paradigm the results are also impressive - the transmission rate obtained, while in the upper range of values reported, would nonetheless seem comparable to these.¹⁴ Moreover, features found by A. R. 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 - testifying to the potential generality of principles by which such tasks should be validated.

These 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 this paradigm makes the present findings obtained within the cognitive correlates approach compelling. Elsewhere, the psychological processes captured during the MT phase of performance have seemingly been confounded with DT (see for example, G. A. Smith, 1989; G. A. Smith & Carew, 1987). Equally, the cognitive ability factors with which MT variables have previously been correlated have been poorly defined. The present 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 is systematically evaluated in the passages below.

1. Motor response programming and execution. A. R. Jensen (1982a) has argued that MT and intelligence correlations may be accounted for by incomplete programming of the ballistic response in lower intelligence subjects as they leave the home button of an ECT. 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).
2. Hovering strategies. G. A. Smith and Carew (1987) maintained that some subjects leave the home button prior to decision - thus confounding the measurement of MT (and DT) in many chronometric tasks. 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 have suggested.
3. An interaction with level of arousal. Buckhalt et al. (1990) cite a paper by Lindley, W. R. Smith and Thomas (1988) which showed that brighter subjects were more motivated to respond quickly. This proposition would seem inconsistent with the present findings. The current psychomotor task was particularly monotonous yet no significant correlations were established with intelligence across any of its experimental conditions.
4. Developmental phenomenon. This remains a plausible hypothesis especially in light of studies conducted with young children that have shown fairly substantial correlations with MT and cognitive ability marker tests (especially those assessing Gf, see Beh, Roberts and Pearse, 1991; see also Telzrow, 1983). The present sample was very much restricted with respect to the age variable.
5. Automatisation of ballistic response. Widaman and Carlson (1989) have addressed the issue of automatisation 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 nonexistent) when sufficient practice allows for the full automatisation of a subject's response. Accordingly, in the case of typical experiments conducted using the Roth-Jensen apparatus, subjects may not have performed a sufficient number of practice trials to automatise 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.
6. Neurophysiological differences. Buckhalt et al. (1990) conclude their study by noting their evidence is consistent with studies showing that nerve conduction velocity is correlated with speed of information processing and general intelligence. Accordingly, more able subjects both process information faster and move faster due to central underlying physiological differences affecting DT and MT (see for example, Reed & A. R. Jensen, 1991, 1993; Vernon & Mori, 1989). The present findings render such an explanation most unlikely.
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.¹⁵ 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 [Short-Form]). 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 results.¹⁶ 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 period. In attempting to replicate this with a larger battery, which contained a mix of time limited and nonspeeded psychometric tests, most of these correlations tended towards zero.

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. The results are perhaps indicatory of the need to draw distinctions between different types of cognitive speed and the different physiological processes underlying each of these. Moreover, it should be noted that the present task is a marker of one psychomotor factor. Whether all such constructs fail to show significant correlations with intelligence remains an empirical issue.

The present results also establish that the role played by automatisation 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, Carter, Kennedy, Harbeson & Krause, 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 individual differences psychology moves towards computerized testing of all performance measures.

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 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 directed at this finding if the psychometric tests with which MT parameters are correlated have been given within strict time limits.

Moreover, in a recent paper, Stankov and Roberts (1996) 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 factors. Until the taxonomy underlying mental speed is more clearly delineated, researchers should be more cautious in postulating explanatory models of intelligence.

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