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Should we take the shape of reaction time distributions into account when studying the relationship between RT and psychometric intelligence?
Person. inditkf. 01% Vol. 15, No. 3, pp. 357-360. Printed in Great Britain. All rights reserved
1993 Copyright
0191-8869/93 $6.00 + 0.00 IT; 1993 Pergamon Press Ltd
Should we take the shape of reaction time distributions into account when studying the relationship between RT and psychometric intelligence? JACQUES Department
of Psychology, (Received
JUHEL
University qf Rennes 2, 6, Aaenue Gaston Berger, 14 August
1992;
received for publication
35043
15 January
Rennes Cedex,
France
1993)
Summary-The negative correlation between psychometric intelligence and variability of reaction time (RT) in elementary cognitive tasks (ECTs) is now well established. However, there has been relatively little research aimed at describing distributions of RT trials other than with mean, median and standard deviation. The present study was designed to examine the relationship between measured intelligence and parameters yielded by exCaussian analysis of RT distributions. Fifty two subjects were administered a computerized discrimination task and five intelligence tests. Data collected indicated that the skewness of RT was more correlated with psychometric intelligence than intraindividual variability in RT was. In addition, and though the exGaussian analysis provided a good description of RT distributions, the results showed that the parameters of the analysis did not correlate significantly with measured intelligence.
The importance of studying the relationship between measures of reaction time (RT) on elementary cognitive tasks (ECTs) and psychometric intelligence is now well acknowledged by psychologists of intelligence. Numerous studies conducted by Jensen and others have established that RT variables, particularly RTmd (median of the S’s RTs over n trials) and RTSD (intraindividual variability in RT) “are correlated (negatively) with psychometric g, RTSD somewhat more than RTmd” (Jensen, 1992, p.879; see Vernon, 1987 for a sampling of opinions about individual differences in RT). It is also well known that this statistical relationship between psychometric intelligence, RTmd (which is supposed to be an index of speed of processing) and RTSD (as assumed to reflect consistency in processing speed) is of great importance for those who believe that individual differences in intelligence are caused by neurophysiological differences in basic elementary processes (Jensen, 1982; Eysenck, 1986; Hendrickson, 1982: Robinson, 1989). As established several decades ago by researchers using RT (McCormack & Wright, 1964), a problem with RT studies is that RT distributions are manifestly positively skewed. This positive skew in RT distributions appears because “there is a physiological limit to the speed of reaction and no limit on the slowness of reaction (unless imposed by the experimenter)” (Jensen, 1992, p. 870). However, this problem has been rarely considered by researchers interested in studying the relationship between RT and psychometric g (but for Krantzler, 1992). Consequently, systematic use of “traditional” statistics like mean (RTm), median (RTmd) or standard deviation (RTSD) may not always be suitable to summarize measures of RT performance without the risk of giving rise to perhaps serious misinterpretation of the data. For instance, some bias may be associated with individual median RT, particularly when the number of items is small and when the distribution is highly skewed (Miller, 1988). One may of course make the distribution more symmetrical by trimming the data i.e. by eliminating extreme RT trials but this technique is questionable. Trimming data by a priori dropping trials on which RT are three or four SD above RTm means one needs to accept the hypothesis that skew reflects “nuisance” variables even though the worst RT trials seem to be an important source of information in intelligence prediction (Larson & Alderton, 1990). On the other hand, though less frequently applied in intelligence RT research, use of scale or logarithmic transformations questions the meaningfulness of the summary statistics (Wainer. 1977; Heathcote. Popiel & Mewhort, 1991). Two main methods may be used to avoid problems in trimming the data and discarding perhaps valuable information contained in an RT distribution. One way is to describe the distribution’s characteristic shape with higher order moments like RT skewness and kurtosis and then to study the relationship between these moments and psychometric g. For instance, results of a recent study conducted by Krantzler (1992) seem to indicate that there is no relationship between the skewness of RT distributions and psychometric g. But one major drawback of this method is that stability in these higher moments is not achieved unless numerous RT trials contribute to the estimates (Ratcliff, 1979). Thus, one must design RT studies carefully before stating that variation in skewness might be of little theoretical interest in examining the relationship between RT dependent variables and measured intelligence. Another way relatively unexplored by differentialists is to hypothesize an explicit model characterizing the distribution of individual RT scores and to estimate some individual parameters of this model by means of a goodness-of-fit function (Hockley, 1984; Rat&T & Murdock, 1976; Ratcliff, 1979). However, it is necessary that the assumed RT model gives good fits to RT distributions and several models, though distinct in terms of their theoretical assumptions, might look satisfactory (see for instance van Breukelen, 1989). As Heathcote et al. (1991) recently recalled, such a well-fitted mathematical description of the RT distributions has been proposed some 30 years ago (Hohle, 1965). In this normal-plus-exponential or exGaussian model, RT distributions are modeled as the convolution of normal and exponential distributions where p and cr are the mean and standard deviation, respectively, of the normal component and 7 is the parameter of the exponential component. Although in Hohle’s decision theory, the duration of a decision process is assumed to have an exponential distribution when the duration of the residual processes (e.g. nuisance) has a normal distribution, some authors suggest to the contrary that this model does not dispose of a robust underlying theory (van Breukelen, 1989; Heathcote et al., 1991). In fact, the convolution parameters p, 0 and r seem to behave differentially in different tasks (Hockley, 1984). These theoretical interpretations notwithstanding, the exGaussian model provides a good summary of RT distributions. 357
358
NOTES AND
SHORTER
COMMUNICATIONS
It might then be of interest to study the relationship between RT variables and exGaussian parameters obtained in a large number of trials, and psychometric intelligence. This was the aim of the present study in which we collected individual RT scores on a computerized ECT and computed convolution analysis of RT distributions,
METHOD Subjects Ss were I1 male and 41 female students (n = 52) at Rennes 2 University They were aged between 19 and 41 with an average age of 21.6 years. Psychomelric
who participated
in exchange
for course credit.
tests
Participants were administered five paper-and-pencil tests particularly designed to measure general intelligence: these tests were the Raven Advanced Progressive Matrices test (Raven, 1962) under nonspeeded conditions and, with usual time limits, the Anstey Dominoes test (Kourosky & Rennes, 1970). the Cattell Culture Fair test (Revised scale 3; Cattell & Cattell, 1953), the Bonnardel Verbal Intelligence test (Bonnardel, 1966) and the Binois-Pichot Vocabulary test (Binois & Pichot, 1949). All these tests were administered with standard instructions to groups of 12 Ss during two sessions of 1.5 hr each, RT task
The task used in the present study was adapted from a discrimination task designed to avoid the shortcomings of Jensen’s RT task as emphasized by some authors (Longstreth, 1984; Neubauer, 1991; Widaman & Carlson, 1989). In this task, sets of 2, 4, 8 or 16 parallel vertical lines (8 mm apart and measuring approx. 50 mm high, 2 mm large) were presented. Ss were instructed to indicate as quickly and accurately as possible, if one of the vertical lines of the set was longer (“yes” answer) or was not longer (“no” answer) than the other ones (the length’s difference was 10 mm). Measures of speed (RTmd) and consistency (RTSD) of information processing were so recorded. As expected, results of a preliminary study conducted on a sample of 57 college students (Juhel, 1990) were in agreement with those usually reported in choice RT literature: RTmd and RTSD increased over trials on average as a linear function of the number of lines of the set. In addition, significant negative correlations between mean RTmd (-0.41), mean RTSD (-0.39) and psychometric intelligence as measured by Raven’s test and Anstey’s Dominoes test were observed. Apparatus and materials. The computerized task was administered using Atari 104OST microcomputers with adapted keyboards for response entry as well as high resolution black and white video monitors. Presentation timings of stimulus and items along with response latency and accuracy recordings were achieved with a GFA BASIC program. Unlike the paradigm described above, only sets of 4 parallel vertical lines were presented in the present study (Fig. I). To start each block of trials, Ss pressed the bar with their thumb while holding their finger indexes on the two contiguous response buttons (Fig. 1). After a foreperiod varying randomly between I to 2 set, the item was presented. Ss reacted by pushing the response button with their right finger index (“no”) and with their left finger index (“yes”). RT was the time in milliseconds (msec) between when the stimulus appeared on the screen and when Ss pressed the response button. Procedure. Sixty four items were initially administered to Ss in order to familiarize them with the paradigm and the apparatus. This step was reproduced if necessary until instructions for the task were perfectly understood. The task itself was constituted with 128 items distributed among 8 blocks of 16 items (8 “yes” answers and 8 “no” answers); the items were presented in a spaced condition with a 30 set rest period between every block. Finally, Ss were administered the RT task on a different day to the two psychometric test sessions. RESUL,TS Psychometric
AND
DISCUSSION
tesfs
Since they were of little importance, we will not report the descriptive statistics for the raw scores of the five psychometric tests. Because of restriction in range, these scores were well above average in comparison to the standardized sample. The positive intercorrelations among these tests ranged from 0.116 to 0.643 with a median of 0.398. In order to derive a composite score of general intelligence, a common factor analysis with one factor specified was conducted (Table 1). This
Table
Fig.
1. Apparatus
in the discrimination button “yes”).
task
(Ss pressed
I. Loadings
of the psychometrx tests on the common (42.6% of total variance n = 52)
Mental tests
Factor
Raven’s APM test
0.7 I6
Dominoes D70 test Culture-fair test Bonnardel verbal test
0.847 0.637 0.657
Vocabulary test
0.253
factor
NOTES AND SHORTER
Table 2. Descriptive ~MeaIl SD
statistics
Table
(in msec) for the RT task (n = 52)
RTm 552.04
RTmd 512.89 73.51
108.36
common factor constituted 42.6% used for computing the composite
RTSD 178.79 134.78
RTskew 3.35 I .98
359
COMMUNICATIONS
3. Descriptive
statistics (in msec) for the exGaussian ameters p. n and 7 (n = 52) 426.59 47.79
Mean SD
43.71 10.52
of the total variance of the psychometric tests. The factor score, hereafter called intelligence (INT).
regression
par-
125.94 84.52
scores were then
RT task The RT variables measured on each S were RTmd (median), RTm (mean) and RTSD. As a preliminary, one-way ANOVA with “answer” as repeated measures, were performed for RTm, RTmd and RTSD and showed no significant difference between RT variables measured on “yes” and “no” answers [all F(1,51)< I]. Similarly, the results of RT’s trend analyses revealed no significant practice effects (P ~0.05). Consequently, all further analyses were conducted for “yes” and “no” RT trials, as measured on the 128 experimental trials. However, it should be stated that tricls with incorrect RT responses (1.27% on average) were omitted from the analysis. Table 2 displays the descriptive statistics of RTm, RTmd, RTSD and RTskew. This table shows that the distributions of the RT trials were considerably positively skewed. Hence, it was well-founded to obtain a more accurate description of Ss RT distributions. For this purpose, we conducted for each S a distribution analysis performed by means of Heathcote exGaussian analysis program (Heathcote, 1991). In a few words, this program can compute best-fitting parameters for the three exGaussian distribution parameters using a robust optimization technique of log likelihood. When the number of Ss’ RTs is at least 100, as it was in this study, the fit is stable enough and the program gives each best fitting parameter and the final log likelihood value. The program succeeded in fitting the 52 distributions of RT trials, once again indicating that the exGaussian model provides adequate fit to the observed RT distributions. The obtained parameter estimates of p, 0 and t averaged over Ss are presented in Table 3. Correlations (uncorrected for attenuation) between RT variables and exGaussian’s parameter estimates with psychometric intelligence are displayed in Table 4. The correlations of z with RTm, RTmd and RTSD suggest that these three variables partially reflect the same component, larger values of T corresponding to larger tails. On the other hand, correlated only with RTm and RTmd, p could be a more accurate measure of central tendency than these two variables. It must also be remarked that the correlations between RT standard variables and psychometric intelligence were quite moderate in size. But this pattern of correlations was consistent with previous results obtained from university student samples restricted in range [see for instance Jensen’s (1987) review where the size of the mean negative RT-IQ correlation is -0.10 to -0.30]. As would be expected, these correlations indicate that RTSD is better than RTm or RTmd for predicting measured intelligence; obviously, such a superiority of intraindividual variability in predicting psychometric intelligence might support the so-called “good organ” theory (Eysenck, 1987). But a remarkable finding was the significant negative correlation observed between intelligence and RT skewness, suggesting that 5’s most extreme RTs were good predictors of psychometric intelligence (Larson & Alderton, 1990). This result enables one to contradict Krantzler’s (1992) claim that the skewness of the distribution of RT trials “is not a significant correlate of psychometric g” (p. 946). In this study, RT skewness tells one about portions of the distribution that may be of interest. Consequently, and since the unusually long responses may not be accidental, we feel that systematically eliminating RTs that fall more than, for instance, three SDS above the subject RTm, might be a questionable practice when studying the relationship between RT variables and measured intelligence. More troublesome was the finding that none of the correlations between exGaussian’s parameters and psychometric intelligence were significant. One could conjure up several explanations to this contradictory statement, For instance, it could be argued that parameter estimates of p, 0 and ‘I derived using a maximum likelihood estimator were biased and underestimated since, as can be seen in Tables 3 and 4, mean results did not satisfy the equations expressing sample RTm and RTSD as a function of the exGaussian’s parameters derived using the method of moments (e.g. RTm = p + z and RTSD = (0’ + z’)“*; Ratcliff, 1979). Because we did not trim our data, an alternative and perhaps complementary explanation that might also be offered could be the weaker sensitivity of exGaussian’s parameter estimates to outlier RTs, as compared to the one of RTSD (see the correlations of RT skewness with the three exGaussian’s parameters). CONCLUSION
In view of these results, when a large number of observations per S condition is collected, both intraindividual variability in RT and RT skewness, though perhaps differently reflecting Ss’ consisrency in the processing of information, might be used in psychometric intelligence investigations since, as suggested by Larson and Alderton (1990), the correlations between measured intelligence and certain RT variables could mainly appear because of Ss occasional !ong latency responses. Consequently, and as Necka (1992) explains, “it seems fairly possible that RT in tasks such as the so-called Hick paradigm
Table 4. Raw correlations INT INT RTm
RTmd RTSD RTskew P 0 7
between RTm
RT variables, RTmd
exGaussian’s (n = 52) RTSD
parameters
and psychometric
intelligence
RTskew
fi
0
I
I -0.017 -0.216 0.135
I 0.267 0.287’
I 0.417**
I
I -0.206
-0.201 -0.332* -0.396**
-0.145 -0.037 -0.182
‘P < 0.05. **FJ < 0.01.
I 0.931” 0.794.’ 0.098 0.665"
0.443** 0.906**
I 0.575** 0.071 0.863** 0.439” 0.706**
I 0.406**
0.191 0.316 0.910**
360
NOTES AND SHORTER COMMUNICATIONS
(Jensen, 1987) would appear insignificant as a correlate of IQ if the intraindividual variance of RT was properly controlled” (p. 1045). Hence we feel that the psychologist interested in testing the consistency-of-information-processing perspective of human intelligence should give a positive answer to the question asked in the title of this paper. Concerning the distribution analysis of RT trials, it is clear that our finding of a nonsignificant relationship between exGaussian parameter estimates and psychometric intelligence needs replication. The fact that the observed correlations are certainly deflated because of restriction of range might contribute to explain such a result. We think also that it would be interesting to fit RT distributions with other and more substantive models grounded on a better theoretical substratum than the exGaussian one. The “distraction model” for RTs on simple overlearned tasks proposed by Roskam and his colleagues (van Breukelen, Jansen, Roskam. Van der Ven & Smit, 1987) could be used for instance. Further research might then be undertaken to measure the theoretical components explicitly formalized in such a model and determine their relationship to psychometric intelligence. Acknowledgemenr.s-The
author
gratefully
acknowledges
Virginie
Laguitton
for her assistance
in running
this study
REFERENCES
Binois, R. & Pichot, P. (1949). Test de vocabulaire. Paris: ECPA. Bonnardel. R. (1966). Tesr d’intelligence g&&ale BV9. Paris: PUF. van Breukelen, G. J. (1989). Concentration, speed and precision in mental tests: A psychonometric approach. Unpublished doctoral dissertation, University of Nijmegen. van Breukelen, G. J. Jansen, R. W., Roskam, E. E., Van der Ven, A. H. & Smit, J. C. (1987). Concentration, speed and precision in simple mental tasks, In Roskam, E. E. & Suck, R. (Eds), Progress in mathematical psychology (Vol. I, pp. 175193). Amsterdam: Elsevier. Cattell, R. B. & Cattell, A. K. S. (1953). Test d’intelligence de Cattell (&he//e 3,formes A et B). Paris: ECPA. Eysenck, H. J. (1986). The theory of intelligence and the psychophysiology of cognition. In Sternberg, R. J. (Ed.), Advances in the psychology qf human intelligence (Vol. 3, pp. 1-34). Hillsdale, NJ: Erlbaum. Eysenck, H. J. (1987). Speed of information processing, reaction time, and the theory of intelligence. In Vernon, P. A. (Ed.), Speed of information processing and intelligence (pp. 21-67). Norwood, NJ: Ablex. Heathcote, A. (1991). Fitting the exGaussian to RT data. Program for the IBM PC Heathcote, A., Popiel, S. J. & Mewhort, D. J. K. (1991). Analysis of response time distributions: An example using the Stroop task. P.yychological Bulletin, 109, 340-347. Hendrickson, A. E. (1982). The biological basis of intelligence. Part I: Theory. In Eysenck, H. J. (Ed.), A model.for intelligence (pp. 151-196). New York: Springer-Verlag. Hockley, W. E. (1984). Analysis of response time distributions in the study of cognitive processes. Journal ofE.yperimental Psycholog>>: Learning, Memory and Cognition, 6, 598-6 15. Hohle, R. H. (1965). Inferred components of reaction times as functions of foreperiod duration. Journal of E.rperimenta/ Psychology, 69, 382-386. Jensen. A. R. (1982). Reaction time and psychometric ,e. In Eysenck, H. J. (Ed.), A model fir infelligence (pp. 93 -132). New York: Springer-Verlag. Jensen. A. R. (1987). Individual differences in the Hick paradigm. In Vernon, P. A. (Ed.), Speed of informationprocessing and intelligence (pp. lOlll75). Norwood, NJ: Able;. Jensen, A. R. (1992). The importance of intraindividual variation in reaction time. Personality and Indicidual Di@-ewes, 13, 869-88 1, Juhel, J. (1990). Etude structurale des relations entre parambtres de traitement de l’information et intelligence psychometrique (Structural analysis of the relationships between information processing parameters and psychometric intelligence). Research Report, Differential Psychology Research Group, University of Rennes 2. Kourosky, F. & Rennes, P. (1970). Test D 70. Paris: ECPA. Krantzler. J. H. (1992). The skewness of the distribution of RT trials does not correlate with psychometric x. Personality, and Individual Differences. 13, 945-946. Larson. G. E. & Alderton. D. L. (1990). Reaction time variabilitv and intelligence. A “worst performance” analysis of individual differences. Intel/&&e, 12, 309-325. Longstreth, L. E. (1984). Jensen’s reaction-time investigations of intelligence. A critique. Intelligence, X, 139 160. McCormack, P. & Wright, N. (1964). The positive skew observed in reaction time. Canadian Journal of P,~~~cho/o,q. 18, 43-51. Miller, J. (1988). A warning about reaction time. Journal qfExperimenta/ P.ychology: Human Perception and Pe[fiwmance, 14, 539-543. Necka, E. (1992). Cognitive analysis of intelligence: The significance of working memory processes. Personalit~~ and Individual D&vences, 13, 103 I 1046. Neubauer, A. C. (1991). Intelligence and RT: A modified Hick paradigm and a new RT paradigm. Intelligence, 15, 175 192. Ratcliff. R. (1979). Group reaction time distributions and an analysis of distribution statistics. P.~,vcho/ogica/ BuNetm. X6, 446-461. Ratcliff, R. & Murdock, B. B. (1976). Retrieval processes in recognition memory. P.vyho/ogical Review, X3. 190 214. Raven, J. C. (1962). Advanced Progressire Matrices. Set II. London: H. K. Lewis. Robinson, D. L. (1989). The neurophysiological bases of high IQ, International Journal of Neuroscience, 46, 209~ 234. Vernon, P. A. (Ed.) (1987). Speed of information processing and intelligence. Norwood, NJ: Ablex. Wainer, H. (1977). Speed vs reaction time as a measure of cognitive performance. Memory, and Cognition, 5, 278-280. Widaman, K. F. & Carlson, J. S. (1989). Procedural effects on performance on the Hick paradigm: Bias in reaction time and movement time parameters. Intelligence, 13, 63-85.
1993 Copyright
0191-8869/93 $6.00 + 0.00 IT; 1993 Pergamon Press Ltd
Should we take the shape of reaction time distributions into account when studying the relationship between RT and psychometric intelligence? JACQUES Department
of Psychology, (Received
JUHEL
University qf Rennes 2, 6, Aaenue Gaston Berger, 14 August
1992;
received for publication
35043
15 January
Rennes Cedex,
France
1993)
Summary-The negative correlation between psychometric intelligence and variability of reaction time (RT) in elementary cognitive tasks (ECTs) is now well established. However, there has been relatively little research aimed at describing distributions of RT trials other than with mean, median and standard deviation. The present study was designed to examine the relationship between measured intelligence and parameters yielded by exCaussian analysis of RT distributions. Fifty two subjects were administered a computerized discrimination task and five intelligence tests. Data collected indicated that the skewness of RT was more correlated with psychometric intelligence than intraindividual variability in RT was. In addition, and though the exGaussian analysis provided a good description of RT distributions, the results showed that the parameters of the analysis did not correlate significantly with measured intelligence.
The importance of studying the relationship between measures of reaction time (RT) on elementary cognitive tasks (ECTs) and psychometric intelligence is now well acknowledged by psychologists of intelligence. Numerous studies conducted by Jensen and others have established that RT variables, particularly RTmd (median of the S’s RTs over n trials) and RTSD (intraindividual variability in RT) “are correlated (negatively) with psychometric g, RTSD somewhat more than RTmd” (Jensen, 1992, p.879; see Vernon, 1987 for a sampling of opinions about individual differences in RT). It is also well known that this statistical relationship between psychometric intelligence, RTmd (which is supposed to be an index of speed of processing) and RTSD (as assumed to reflect consistency in processing speed) is of great importance for those who believe that individual differences in intelligence are caused by neurophysiological differences in basic elementary processes (Jensen, 1982; Eysenck, 1986; Hendrickson, 1982: Robinson, 1989). As established several decades ago by researchers using RT (McCormack & Wright, 1964), a problem with RT studies is that RT distributions are manifestly positively skewed. This positive skew in RT distributions appears because “there is a physiological limit to the speed of reaction and no limit on the slowness of reaction (unless imposed by the experimenter)” (Jensen, 1992, p. 870). However, this problem has been rarely considered by researchers interested in studying the relationship between RT and psychometric g (but for Krantzler, 1992). Consequently, systematic use of “traditional” statistics like mean (RTm), median (RTmd) or standard deviation (RTSD) may not always be suitable to summarize measures of RT performance without the risk of giving rise to perhaps serious misinterpretation of the data. For instance, some bias may be associated with individual median RT, particularly when the number of items is small and when the distribution is highly skewed (Miller, 1988). One may of course make the distribution more symmetrical by trimming the data i.e. by eliminating extreme RT trials but this technique is questionable. Trimming data by a priori dropping trials on which RT are three or four SD above RTm means one needs to accept the hypothesis that skew reflects “nuisance” variables even though the worst RT trials seem to be an important source of information in intelligence prediction (Larson & Alderton, 1990). On the other hand, though less frequently applied in intelligence RT research, use of scale or logarithmic transformations questions the meaningfulness of the summary statistics (Wainer. 1977; Heathcote. Popiel & Mewhort, 1991). Two main methods may be used to avoid problems in trimming the data and discarding perhaps valuable information contained in an RT distribution. One way is to describe the distribution’s characteristic shape with higher order moments like RT skewness and kurtosis and then to study the relationship between these moments and psychometric g. For instance, results of a recent study conducted by Krantzler (1992) seem to indicate that there is no relationship between the skewness of RT distributions and psychometric g. But one major drawback of this method is that stability in these higher moments is not achieved unless numerous RT trials contribute to the estimates (Ratcliff, 1979). Thus, one must design RT studies carefully before stating that variation in skewness might be of little theoretical interest in examining the relationship between RT dependent variables and measured intelligence. Another way relatively unexplored by differentialists is to hypothesize an explicit model characterizing the distribution of individual RT scores and to estimate some individual parameters of this model by means of a goodness-of-fit function (Hockley, 1984; Rat&T & Murdock, 1976; Ratcliff, 1979). However, it is necessary that the assumed RT model gives good fits to RT distributions and several models, though distinct in terms of their theoretical assumptions, might look satisfactory (see for instance van Breukelen, 1989). As Heathcote et al. (1991) recently recalled, such a well-fitted mathematical description of the RT distributions has been proposed some 30 years ago (Hohle, 1965). In this normal-plus-exponential or exGaussian model, RT distributions are modeled as the convolution of normal and exponential distributions where p and cr are the mean and standard deviation, respectively, of the normal component and 7 is the parameter of the exponential component. Although in Hohle’s decision theory, the duration of a decision process is assumed to have an exponential distribution when the duration of the residual processes (e.g. nuisance) has a normal distribution, some authors suggest to the contrary that this model does not dispose of a robust underlying theory (van Breukelen, 1989; Heathcote et al., 1991). In fact, the convolution parameters p, 0 and r seem to behave differentially in different tasks (Hockley, 1984). These theoretical interpretations notwithstanding, the exGaussian model provides a good summary of RT distributions. 357
358
NOTES AND
SHORTER
COMMUNICATIONS
It might then be of interest to study the relationship between RT variables and exGaussian parameters obtained in a large number of trials, and psychometric intelligence. This was the aim of the present study in which we collected individual RT scores on a computerized ECT and computed convolution analysis of RT distributions,
METHOD Subjects Ss were I1 male and 41 female students (n = 52) at Rennes 2 University They were aged between 19 and 41 with an average age of 21.6 years. Psychomelric
who participated
in exchange
for course credit.
tests
Participants were administered five paper-and-pencil tests particularly designed to measure general intelligence: these tests were the Raven Advanced Progressive Matrices test (Raven, 1962) under nonspeeded conditions and, with usual time limits, the Anstey Dominoes test (Kourosky & Rennes, 1970). the Cattell Culture Fair test (Revised scale 3; Cattell & Cattell, 1953), the Bonnardel Verbal Intelligence test (Bonnardel, 1966) and the Binois-Pichot Vocabulary test (Binois & Pichot, 1949). All these tests were administered with standard instructions to groups of 12 Ss during two sessions of 1.5 hr each, RT task
The task used in the present study was adapted from a discrimination task designed to avoid the shortcomings of Jensen’s RT task as emphasized by some authors (Longstreth, 1984; Neubauer, 1991; Widaman & Carlson, 1989). In this task, sets of 2, 4, 8 or 16 parallel vertical lines (8 mm apart and measuring approx. 50 mm high, 2 mm large) were presented. Ss were instructed to indicate as quickly and accurately as possible, if one of the vertical lines of the set was longer (“yes” answer) or was not longer (“no” answer) than the other ones (the length’s difference was 10 mm). Measures of speed (RTmd) and consistency (RTSD) of information processing were so recorded. As expected, results of a preliminary study conducted on a sample of 57 college students (Juhel, 1990) were in agreement with those usually reported in choice RT literature: RTmd and RTSD increased over trials on average as a linear function of the number of lines of the set. In addition, significant negative correlations between mean RTmd (-0.41), mean RTSD (-0.39) and psychometric intelligence as measured by Raven’s test and Anstey’s Dominoes test were observed. Apparatus and materials. The computerized task was administered using Atari 104OST microcomputers with adapted keyboards for response entry as well as high resolution black and white video monitors. Presentation timings of stimulus and items along with response latency and accuracy recordings were achieved with a GFA BASIC program. Unlike the paradigm described above, only sets of 4 parallel vertical lines were presented in the present study (Fig. I). To start each block of trials, Ss pressed the bar with their thumb while holding their finger indexes on the two contiguous response buttons (Fig. 1). After a foreperiod varying randomly between I to 2 set, the item was presented. Ss reacted by pushing the response button with their right finger index (“no”) and with their left finger index (“yes”). RT was the time in milliseconds (msec) between when the stimulus appeared on the screen and when Ss pressed the response button. Procedure. Sixty four items were initially administered to Ss in order to familiarize them with the paradigm and the apparatus. This step was reproduced if necessary until instructions for the task were perfectly understood. The task itself was constituted with 128 items distributed among 8 blocks of 16 items (8 “yes” answers and 8 “no” answers); the items were presented in a spaced condition with a 30 set rest period between every block. Finally, Ss were administered the RT task on a different day to the two psychometric test sessions. RESUL,TS Psychometric
AND
DISCUSSION
tesfs
Since they were of little importance, we will not report the descriptive statistics for the raw scores of the five psychometric tests. Because of restriction in range, these scores were well above average in comparison to the standardized sample. The positive intercorrelations among these tests ranged from 0.116 to 0.643 with a median of 0.398. In order to derive a composite score of general intelligence, a common factor analysis with one factor specified was conducted (Table 1). This
Table
Fig.
1. Apparatus
in the discrimination button “yes”).
task
(Ss pressed
I. Loadings
of the psychometrx tests on the common (42.6% of total variance n = 52)
Mental tests
Factor
Raven’s APM test
0.7 I6
Dominoes D70 test Culture-fair test Bonnardel verbal test
0.847 0.637 0.657
Vocabulary test
0.253
factor
NOTES AND SHORTER
Table 2. Descriptive ~MeaIl SD
statistics
Table
(in msec) for the RT task (n = 52)
RTm 552.04
RTmd 512.89 73.51
108.36
common factor constituted 42.6% used for computing the composite
RTSD 178.79 134.78
RTskew 3.35 I .98
359
COMMUNICATIONS
3. Descriptive
statistics (in msec) for the exGaussian ameters p. n and 7 (n = 52) 426.59 47.79
Mean SD
43.71 10.52
of the total variance of the psychometric tests. The factor score, hereafter called intelligence (INT).
regression
par-
125.94 84.52
scores were then
RT task The RT variables measured on each S were RTmd (median), RTm (mean) and RTSD. As a preliminary, one-way ANOVA with “answer” as repeated measures, were performed for RTm, RTmd and RTSD and showed no significant difference between RT variables measured on “yes” and “no” answers [all F(1,51)< I]. Similarly, the results of RT’s trend analyses revealed no significant practice effects (P ~0.05). Consequently, all further analyses were conducted for “yes” and “no” RT trials, as measured on the 128 experimental trials. However, it should be stated that tricls with incorrect RT responses (1.27% on average) were omitted from the analysis. Table 2 displays the descriptive statistics of RTm, RTmd, RTSD and RTskew. This table shows that the distributions of the RT trials were considerably positively skewed. Hence, it was well-founded to obtain a more accurate description of Ss RT distributions. For this purpose, we conducted for each S a distribution analysis performed by means of Heathcote exGaussian analysis program (Heathcote, 1991). In a few words, this program can compute best-fitting parameters for the three exGaussian distribution parameters using a robust optimization technique of log likelihood. When the number of Ss’ RTs is at least 100, as it was in this study, the fit is stable enough and the program gives each best fitting parameter and the final log likelihood value. The program succeeded in fitting the 52 distributions of RT trials, once again indicating that the exGaussian model provides adequate fit to the observed RT distributions. The obtained parameter estimates of p, 0 and t averaged over Ss are presented in Table 3. Correlations (uncorrected for attenuation) between RT variables and exGaussian’s parameter estimates with psychometric intelligence are displayed in Table 4. The correlations of z with RTm, RTmd and RTSD suggest that these three variables partially reflect the same component, larger values of T corresponding to larger tails. On the other hand, correlated only with RTm and RTmd, p could be a more accurate measure of central tendency than these two variables. It must also be remarked that the correlations between RT standard variables and psychometric intelligence were quite moderate in size. But this pattern of correlations was consistent with previous results obtained from university student samples restricted in range [see for instance Jensen’s (1987) review where the size of the mean negative RT-IQ correlation is -0.10 to -0.30]. As would be expected, these correlations indicate that RTSD is better than RTm or RTmd for predicting measured intelligence; obviously, such a superiority of intraindividual variability in predicting psychometric intelligence might support the so-called “good organ” theory (Eysenck, 1987). But a remarkable finding was the significant negative correlation observed between intelligence and RT skewness, suggesting that 5’s most extreme RTs were good predictors of psychometric intelligence (Larson & Alderton, 1990). This result enables one to contradict Krantzler’s (1992) claim that the skewness of the distribution of RT trials “is not a significant correlate of psychometric g” (p. 946). In this study, RT skewness tells one about portions of the distribution that may be of interest. Consequently, and since the unusually long responses may not be accidental, we feel that systematically eliminating RTs that fall more than, for instance, three SDS above the subject RTm, might be a questionable practice when studying the relationship between RT variables and measured intelligence. More troublesome was the finding that none of the correlations between exGaussian’s parameters and psychometric intelligence were significant. One could conjure up several explanations to this contradictory statement, For instance, it could be argued that parameter estimates of p, 0 and ‘I derived using a maximum likelihood estimator were biased and underestimated since, as can be seen in Tables 3 and 4, mean results did not satisfy the equations expressing sample RTm and RTSD as a function of the exGaussian’s parameters derived using the method of moments (e.g. RTm = p + z and RTSD = (0’ + z’)“*; Ratcliff, 1979). Because we did not trim our data, an alternative and perhaps complementary explanation that might also be offered could be the weaker sensitivity of exGaussian’s parameter estimates to outlier RTs, as compared to the one of RTSD (see the correlations of RT skewness with the three exGaussian’s parameters). CONCLUSION
In view of these results, when a large number of observations per S condition is collected, both intraindividual variability in RT and RT skewness, though perhaps differently reflecting Ss’ consisrency in the processing of information, might be used in psychometric intelligence investigations since, as suggested by Larson and Alderton (1990), the correlations between measured intelligence and certain RT variables could mainly appear because of Ss occasional !ong latency responses. Consequently, and as Necka (1992) explains, “it seems fairly possible that RT in tasks such as the so-called Hick paradigm
Table 4. Raw correlations INT INT RTm
RTmd RTSD RTskew P 0 7
between RTm
RT variables, RTmd
exGaussian’s (n = 52) RTSD
parameters
and psychometric
intelligence
RTskew
fi
0
I
I -0.017 -0.216 0.135
I 0.267 0.287’
I 0.417**
I
I -0.206
-0.201 -0.332* -0.396**
-0.145 -0.037 -0.182
‘P < 0.05. **FJ < 0.01.
I 0.931” 0.794.’ 0.098 0.665"
0.443** 0.906**
I 0.575** 0.071 0.863** 0.439” 0.706**
I 0.406**
0.191 0.316 0.910**
360
NOTES AND SHORTER COMMUNICATIONS
(Jensen, 1987) would appear insignificant as a correlate of IQ if the intraindividual variance of RT was properly controlled” (p. 1045). Hence we feel that the psychologist interested in testing the consistency-of-information-processing perspective of human intelligence should give a positive answer to the question asked in the title of this paper. Concerning the distribution analysis of RT trials, it is clear that our finding of a nonsignificant relationship between exGaussian parameter estimates and psychometric intelligence needs replication. The fact that the observed correlations are certainly deflated because of restriction of range might contribute to explain such a result. We think also that it would be interesting to fit RT distributions with other and more substantive models grounded on a better theoretical substratum than the exGaussian one. The “distraction model” for RTs on simple overlearned tasks proposed by Roskam and his colleagues (van Breukelen, Jansen, Roskam. Van der Ven & Smit, 1987) could be used for instance. Further research might then be undertaken to measure the theoretical components explicitly formalized in such a model and determine their relationship to psychometric intelligence. Acknowledgemenr.s-The
author
gratefully
acknowledges
Virginie
Laguitton
for her assistance
in running
this study
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