Stefan J. Troche
Institute for Psychology, University of Bern, Bern, Switzerland
Petra Bellmann-Knieps
Institute for Psychology, University of Bern, Bern, Switzerland
Thomas H. Rammsayer
Institute for Psychology, University of Bern, Bern, Switzerland
Abstract
The temporal resolution power hypothesis postulates that temporal acuity of the brain is an important mechanism underlying psychometric intelligence. Evidence for this notion can be derived from studies reporting a close association between temporal resolution power and psychometric intelligence. The present study was designed to investigate whether scholastic achievement as a real world correlate of psychometric intelligence can also be predicted by temporal resolution power. For this purpose, the relation between temporal resolution power, assessed by two timing tasks, and scholastic achievement was examined in 40 second-graders, 40 fourth-graders, and 50 sixth-graders. For all three samples, structural equation modelling revealed a reliable positive relationship between a factor “temporal resolution power” and a factor “scholastic performance”. Our findings support the view that temporal resolution power of the brain is not only associated with general psychometric intelligence but also reflects a fundamental mechanism involved in scholastic achievement.
Keywords: temporal resolution power; scholastic performance
Introduction
The mental speed approach to human intelligence has produced converging evidence for a functional relationship between speed of information processing in so-called “elementary cognitive tasks” (ECTs) and psychometric intelligence. Various measures of speed of information processing, such as simple and choice reaction time following the rationale of Hick (1952; for a review see Jensen, 2006), inspection time (Brand & Deary, 1982), short-term memory scanning (Sternberg, 1966), or long-term memory retrieval (Posner & Mitchell, 1967) have been found to be associated with higher psychometric intelligence.
Coefficients of correlation between such measures of speed of information processing and psychometric intelligence were reported to be rather moderate, typically in the range of .20 to .40 (for reviews see Deary, 2000; Jensen, 1982, 1987, 1998; Juhel, 1991; Neubauer, 1997; Vernon, 1987). In case that multiple regression analyses were carried out, in order to predict psychometric intelligence with a battery of various ECTs, the relationship was observed to be increased up to R = .60 (Neubauer, 1995). Critizing those results, Süß (2001) emphasized that it is the speed rather than the capacity component of psychometric intelligence which can be explained by speed-related ECTs. This assumption is supported by the finding of Neubauer and Bucik (1996) who reported that speed of information processing in a battery of ECTs was highly correlated with the intelligence component processing speed (r = .75) as assessed by the Berlin Intelligence Structure Test (BIS, Jäger, Süß, & Beauducel, 1997). Limiting the critics of Süß (2001), however, also the relationship between response times on ECTs and the component of processing capacity of the BIS was fairly high (r = .50).
Most recently, Helmbold, Troche, and Rammsayer (2007) reported that the relationship between response times in the Hick paradigm and psychometric intelligence is mediated by temporal resolution power. Temporal resolution power refers to the notion of a general timing mechanism within the central nervous system that controls speed and efficiency of information processing (Rammsayer & Brandler, 2002, 2007). The higher the oscillation rate of this timing mechanism the more mental operations can be performed in a certain frame of time (see also Jensen, 1982, 2006). Additionally, in case that a mental operation is completed faster, the probability of interfering incidents is decreased (Lindenberger, Mayr, & Kliegl, 1993; Rammsayer & Brandler, 2002; Salthouse, 1991). Thus, higher information processing rate and decreased probability of interfering incidents should lead to faster response times in ECTs as well as to superior performance on tests of psychometric intelligence.
Rammsayer and Brandler (2002, 2007) suggested that psychophysical measures of timing accuracy and temporal sensitivity represent the most direct psychophysical measure of temporal resolution power of the CNS. Empirical evidence for this assumption has been derived from the finding that a compound measure obtained from a broad range of psychophysical timing tasks explained 31% of total variance of a general factor of psychometric intelligence referred to as psychometric g (Rammsayer & Brandler, 2007). Similarly, Helmbold et al. (2007) found a direct path coefficient of .57 from a factor representing temporal resolution power to psychometric g. Since this path coefficient also accounted for the major portion of the correlational relationship between response time measures derived from the Hick paradigm and psychometric g, temporal resolution power has been suggested to represent a general concept underlying the relationship between speed-related ECTs and psychometric intelligence. Furthermore, unlike traditional speed-related ECTs (cf., Neubauer & Bucik, 1996), temporal resolution power has been shown to be closer related to capacity-related than to speed-related aspects of intelligence (Helmbold & Rammsayer, 2006).
From a diagnostic point of view, ECTs provide the opportunity to assess intelligence largely unaffecterd by the impact of knowledge, personality, and cultural background. Furthermore, these tasks are so easy that there is no room for intelligent strategic variations. Thus, differences in performance can only be attributed to differences in the speed and accuracy with which stimuli are processed and simple decisions are made (e.g., Anderson, 2001; Jensen, 1998). Süß (2001) urged that, until today, little effort has been made to investigate the construct validity of intelligence measures derived from ECTs. More specifically, if tests are required to measure intelligence, it is not sufficient to demonstrate an association with standard tests of psychometric intelligence. Rather, a similar relationship has also to be established to real-world performances such as scholastic, academic, or job performance. The few available studies addressing this issue emphasize a possible relationship between speed of information processing and scholastic performance (Rindermann & Neubauer, 2001, 2004; Kranzler, Whang, & Jensen, 1994; Luo & Petrill, 1999). Applying structural equation modelling, Rindermann and Neubauer (2004) found an indirect effect of β = .39 from speed of information processing on scholastic performance which was mediated by psychometric intelligence. Furthermore, Luo and Petrill (1999) compared the predictive validity of psychometric g derived from several batteries of intelligence tests and of ECT response-time measures on performance on the Metropolitan Achievement Test Battery (MAT). Their results indicate that ECTs were able to reliably predict MAT performance as well as psychometric intelligence.
Proceeding from the assumption that temporal resolution power represents a basic concept underlying psychometric intelligence and speed of information processing (cf., Helmbold et al., 2007), temporal resolution power should also be able to predict real-world correlates of intelligence. Thus, the present study was designed to investigate whether a small set of psychophysical indicators of temporal resolution power would be able to reliably predict scholastic performance. For this purpose, two timing tasks were applied in a sample of second-, fourth- and sixth-graders. Using structural equation modelling, the relationship between a factor of scholastic achievement and a factor of temporal resolution was investigated.
Method
Participants
Participants were 19 male and 21 female second-graders ranging in age from 7.4 to 9.8 years (mean ± standard deviation: 8.1 ± 0.49 years), 17 male and 23 female fourth-graders ranging in age from 9.1 to 11.3 years (mean age: 10.1 ± 0.51 years), and 24 male and 26 female sixth-graders ranging in age from 11.6 to 13.5 years (mean age: 12.3 ± 0.44 years). All participants were screened for the presence of neurological, developmental, or learning disorders. Four of the second-graders and two of the fourth-graders were reported to suffer from dyslexia. Since there is evidence for the notion that dyslexics exhibit impaired temporal information processing (Farmer & Klein, 1995; Rousseau, Hébert, & Cuddy, 2001; Tallal, Stark, & Mellits, 1985), these children were excluded from analyses.
Scholastic performance
As indicators of scholastic performance in the present study, marks for mathematics, German language, and general knowledge were recorded from last school record. Marks ranged from 1 (very good) to 6 (insufficient) with intermediate grades of ± .3. Marks of 1.0 and 6.0 could only be incremented and decremented, respectively.
Duration discrimination tasks
As a psychophysical indicator of temporal resolution power, performance on duration discrimination in the range of milliseconds and seconds was assessed (cf., Rammsayer & Brandler, 2002, 2007). An experimental session consisted of one block of duration discrimination in the range of milliseconds and one block of duration discrimination in the range of seconds. The millisecond task contained auditory intervals with a base duration of 50 ms, the second task contained auditory intervals with a base duration of 1,000 ms. When participants are asked to compare time intervals, many of them count out the required number of seconds. Since explicit counting becomes a useful timing strategy for intervals longer than approximately 1,200 ms (Grondin, Meilleur-Wells, & Lachance, 1999), the “long” base duration was chosen not to exceed this critical value. The auditory intervals consisted of white-noise bursts presented binaurally through headphones (Vivanco SR85) at an intensity of 67 dB SPL.
The order of the two tasks was counterbalanced across participants. Prior to each task, six practice trials were presented. Each task contained 32 trials, and each trial consisted of a constant standard interval (= base duration) and a variable comparison interval. The order of presentation for the standard interval and the comparison interval was randomized and balanced, with each interval being presented first in 50% of the trials. The two intervals were presented with an interstimulus interval of 900 ms. The duration of the comparison interval varied according to an adaptive rule, the weighted-up-down-procedure (Kaernbach, 1991). ‘Adaptive’ means that stimulus presentation on any given trial is determined by the preceding set of stimuli and responses. Therefore, the comparison interval is varied in duration from trial to trial depending on the participant’s previous response. Correct responding resulted in a decrease of the duration of the comparison interval and incorrect responses made the task easier by increasing the duration of the comparison interval. Participants were not informed that there was a constant standard interval on every trial.
Each participant was seated at a table with a keyboard and a computer monitor in a sound-attenuated room. The participant’s task was to decide which of the two intervals was longer and to indicate his or her decision by pressing one of two designated keys on the computer keyboard. One key was labeled “First interval longer” and the other was labeled “Second interval longer”. The instructions to the participants emphasized accuracy; there was no requirement to respond quickly. After each response, visual feedback (“+”, i.e., correct; “–”, i.e., false) was displayed on the computer screen. The next trial started 900 ms after offset of the feedback. An experimental session lasted approximately 15 minutes.
As a measure of performance, 75% difference thresholds were determined in relation to the 50- and 1,000-ms standard intervals, respectively. With this measure, better performance on duration discrimination is indicated by smaller threshold values.
Results
Descriptive statistics of school marks and performance on the psychophysical timing tasks are given in Table 1 for second-, fourth-, and sixth-graders, respectively. The 75% difference thresholds for durations in the range of milliseconds were found to be significantly higher in second-graders compared to fourth-graders [t(78) = 2.74; p < .01; d = .61] and sixth-graders [t(68.97) = 4.53; p < .001; d = .98] as well as in fourth-graders compared to sixth-graders [t(88) = 2.16; p < .05; d = .46]. These differences indicate a continuous improvement of time perception in the range of milliseconds with increasing age. It should be noted that Levene’s test of equality of variances indicated larger variability of the 75% difference threshold in the range of milliseconds for second- compared to sixth-graders [F = 4.54; p < .05]. Therefore, the respective t value and degrees of freedom were adjusted accordingly. Also for duration discrimination in the range of seconds, the 75% difference threshold was higher in second-graders than in fourth-graders [t(78) = 3.66; p < .001; d = .82] and sixth-graders [t(88) = 2.15; p < .05; d = .46]. The difference between fourth- and sixth-graders, however, did not yield statistical significance [t(78) = -.87; p = .39; d = -.19]. Hence, performance improved just from second to fourth grade whereas from fourth to sixth grade there was no further performance increment.
Intercorrelations among marks in mathematics, German language, and general knowledge were of statistical significance (see Table 2) indicating a common latent variable referred to as “Scholastic Performance”. Similarly, 75% difference thresholds for duration discrimination in the range of seconds and milliseconds were significantly correlated in all three samples providing evidence for the existence of a latent variable constituting “Temporal Resolution Power” (see Table 2). Proceeding from these results, structural equation models (SEMs) were calculated to investigate the prediction of the factor “Scholastic Performance” by the factor “Temporal Resolution Power”. The factor “Scholastic Performance” was obtained from marks in mathematics, German language, and general knowledge. The factor “Temporal Resolution Power” was derived from the 75% difference thresholds for duration discrimination of intervals in the range of milliseconds and seconds, respectively. Within SEM, the regression from “Temporal Resolution Power” on “Scholastic Performance” was calculated (see Figure 1). SEMs were based on z-standardized variables. In a first step, data of second-, fourth-, and sixth-graders were analysed separately. Finally, data of all three groups were combined for a more comprehensive view on the relation between scholastic performance and temporal resolution power. This resulted in a total sample size of 130 participants.
As can be seen from see Table 3, for second-graders, the theoretical structural equation model suited the empirical data rather well as indicated by statistically insignificant χ² value and a high comparative fit index (CFI). Although the root mean square error of approximation (RMSEA) did not yield statistical significance, the lower bound of the 90% confidence interval for RMSEA included 0. According to this model the regression coefficient from “Temporal Resolution Power” on “Scholastic Performance” was β = .45 (p < .01; R2 = .20) in second-graders.
Even somewhat better was the model fit for fourth-graders. The χ² value was again statistically insignificant, the CFI was 1.00 and the RMSEA was of statistical significance (see Table 3). The regression coefficient from the factor “Temporal Resolution Power” on the factor “Scholastic Performance” was .42 (p < .01) indicating that 18% of total variability in “Scholastic Performance” could be explained by “Temporal Resolution Power”.
For sixth-graders, fit of the structural equation model was not as good as for fourth-graders (see Table 3). Nevertheless, χ² value did not yield statistical significance, CFI exceeded .90 and lower bound of the 90% confidence interval for RMSEA included 0. Also in sixth-graders, the portion of variance of “Scholastic Performance” explained by “Temporal Resolution Power” (R² = .15) was of statistical significance (β = .38; p < .01).
Finally, the three groups were combined to investigate the relation between “Temporal Resolution Power” and “Scholastic Performance” in the total sample consisting of 130 participants. Also for the combined sample, the theoretical model was supported by the empirical data with the χ² value being statistically insignificant, CFI very close to 1.00 and RMSEA of statistical significance (see Table 3). The regression coefficient from the factor “Temporal Resolution Power” on the factor “Scholastic Performance” was again statistically significant (β = .35; p < .01; R2 = .12).
Figure 1. Structural equation model for the relationship between the factor “Temporal Resolution Power” derived from performance on duration discrimination in the range of milliseconds (DD1) and seconds (DD2) as indicated by 75% difference thresholds and the factor “Scholastic performance” obtained from grades for mathematics (Maths), German language (German) and general knowledge (Gen. Knowl.). The respective values for the factor loadings (FL), residual variances (Res) and the regression coefficient β are given in Table 4.
Discussion
The present study was designed to investigate whether temporal resolution power as a predictor of psychometric intelligence has construct validity with respect to real world criteria measured as scholastic performance. The outcome of the present study indicates a reliable relation between temporal resolution power and scholastic performance in second-, fourth-, and sixth-graders. The results obtained for the three age-groups were corroborated by a SEM on the total sample. These findings support the assumption that temporal resolution power is not only involved in performance on intelligence tests as indicated by previous studies (Helmbold & Rammsayer, 2006; Helmbold et al. 2006, 2007; Rammsayer & Brandler, 2002, 2007) but also in real world performances. The fact that total time to complete the duration discrimination tasks was only about 15 minutes emphasizes that these psychophysical tasks are not only valid, but also highly efficient in predicting scholastic performance.
Although latent variables of temporal resolution power and scholastic performance were reliably associated, coefficients of simple correlations between 75% difference thresholds and marks were much smaller and less consistent across the three samples. Low reliability of the psychophysical tasks and/or school marks can be considered a likely reason for low correlations between the manifest variables investigated in the present study. Reliability of the duration discrimination tasks used in this study has been investigated by Rammsayer (1992; 1994) and found to be adequately high. Therefore, it seems to be rather unlikely that unreliability of 75% difference thresholds accounted for the low correlations. For school marks and teacher judgments, however, low objectivity and reliability were reported frequently (e.g., Carter, 1952; Finley, 1966; Gipps, 1994; Ingenkamp, 1989; Kleber, Meister, Schwarzer, & Schwarzer, 1976; Murphy, 1982). This weakness of school marks could be responsible for the low correlations with 75% difference thresholds. The factor “Scholastic Performance” derived from the common variance of school marks does not comprise the error variance of school marks. As a consequence, the regression from the latent variable “Scholastic Performance” on the latent variable “Temporal Resolution Power” had a better chance of becoming higher and more consistent than the correlations between manifest variables which were much more prone to error variance.
Although the correlations between psychophysical measures and school marks were inconsistent and rather low at the level of manifest variables, a considerable relation between marks in German language and performance on duration discrimination was obtained in second- and fourth-graders but not in sixth-graders. It should be noted that in elementary schools learning of reading and writing are central aspects of the school subject German language. Mechanisms underlying the acquisition of reading and writing are impaired in individuals suffering from dyslexia. Most interestingly, previous studies pointed out that dyslectic persons have significant deficits in temporal resolutions tasks (e.g., Farmer & Klein, 1995; Rousseau, Hébert, & Cuddy, 2001; Tallal, Stark, & Mellits, 1985; Wolff, 1993). Against the background of these results, the association between marks in German language and temporal resolution power in second- and fourth-graders can be assumed to be based on the crucial role which temporal resolution plays in the acquisition of reading and writing skills. In higher classes, interpretation of texts becomes a more important topic whereas reading and writing represent more or less overlearnt skills which do not considerably contribute to interindividual variability in scholastic performance on German language among students. Therefore, it can be assumed that the relation between marks in German language and temporal resolution power was less pronounced in sixth-graders compared to second- and fourth-graders due to a shift of the contents of the subject “German language”.
The relation between marks in mathematics and performance on duration discrimination was somewhat inconsistent with reliable relations in second- and sixth-graders but weaker association in fourth-graders. In neither group, marks in general knowledge were reliably associated with psychophysical measures of temporal resolution power. This latter finding provides evidence for the notion that temporal resolution power is related to fluid rather than crystallized intelligence (Rammsayer & Brandler, 2002). Furthermore, performance on duration discrimination was better in fourth- than in second-graders and, for duration discrimination of intervals in the range of milliseconds, better in sixth- than in fourth-graders. On the one hand, this finding is in line with previous studies demonstrating improved temporal information processing with increased age (e.g., Droit-Volet, Clement, & Wearden, 2001; McCormack, Brown, Maylor, Darby, & Green, 1999; McCormack, Wearden, Smith, & Brown, 2005; Pouthas, 1993). On the other hand, the age-dependent improvement of temporal resolution power found in the present study bears amazing resemblance to the finding that fluid intelligence increases during childhood until the age of about 15 years (e.g., Fry & Hale, 2000; Raven, Court, & Raven, 1983). Thus, the similar time course in the development of temporal information processing and fluid intelligence may indicate that temporal resolution power represents a fundamental mechanism underlying fluid intelligence. This statement, however, is highly tentative as fluid intelligence has not been directly assessed in the present study. Further research, therefore, should aim on investigating the significance of temporal resolution power for the development of fluid intelligence.
At the level of latent variables, we demonstrated reliable associations between “Scholastic Performance” and “Temporal Resolution Power” ranging from β = .35 to β = .45. The tasks applied in the present study to assess temporal resolution power were discrimination tasks and our finding that sensory discrimination tasks are correlated with scholastic performance is in line with early results of Spearman (1904). Spearman reported surprisingly high correlations between performance on pitch discrimination and “school cleverness” in two samples of children at an English village school. For boys from a high-class preparatory school, Spearman (1904) observed correlation coefficients between performance on several school subjects and pitch discrimination as high as r = .89. Mean age of these boys was about 11 years so that this sample is comparable with the sample of fourth-graders in the present study. Since there is evidence for the notion that performance on discrimination of duration- and frequency-related information has almost the same power to predict psychometric intelligence (Helmbold, Troche, & Rammsayer, 2006), the β coefficients found in the present study seem to be within a plausible range.
Finally, construct validity of temporal resolution power with regard to scholastic performance seems to be in a similar range as the relation between scholastic performance and speed of information processing which has been reported to be β = .39 (Rindermann & Neubauer, 2004). Neubauer and Bucik (1996) found speed of information processing to be more strongly related to the intelligence component “processing speed” than to the component “processing capacity”. The results of Helmbold and Rammsayer (2006), however, indicated that temporal resolution power is more closely associated with capacity- than speed-related components of psychometric intelligence. Given that scholastic performance is rather determined by capacity- than speed-related components of intelligence (Süß, 2001), temporal resolution power accounts for a qualitatively different aspect of scholastic achievement than speed of information processing.
To sum up, in second-, fourth-, and sixth-graders a functional relationship between temporal resolution power and scholastic achievement could be established. The relatively small sample sizes are an obvious limitation of the present study. Although analyses on the total sample consisting of 130 students confirmed the results obtained for each group of students separately, we caution against a premature overestimation of the relationship between temporal resolution power and scholastic performance. Nevertheless, the results may have a strong heuristic value encouraging further research on the construct validity of temporal resolution power as a psychophysical indicator of general intelligence. Especially, the concurrent application of psychometric intelligence tests, temporal information processing tasks, and tasks assessing speed of information processing could reveal to what extent these measures account for unique and shared portions of variance of scholastic performance.
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Biographical Notes
Stefan Troche is Doctor of Psychology at the University of Bern, Switzerland. He received his degrees from the University of Göttingen, Germany. His main research interests are relations between intelligence and sensory information processing. Further topics are inhibition processes in elderly adults and patients suffering from Parkinson’s disease.
Petra Bellmann-Knieps holds a Diploma degree in Psychology. She is currently undergoing counselling training at the Clinic of Psychiatry and Psychotherapy at the University of Göttingen, Germany.
Thomas Rammsayer is professor of psychology at the University of Bern, Switzerland. He is trained in experimental, biological, differential, and clinical psychology and received his degrees from the Universities of Tübingen and Giessen, Germany. His research interests lie in experimental and biological psychology, including temporal information processing, pharmacopsychology, the biological basis of individual differences, and research on intelligence.
Correspondence concerning this article should be addressed to:
Dr. Stefan Troche
Institute for Psychology
University of Bern
Muesmattstr. 45
CH-3000 Bern 9, Switzerland
Phone: +41 31 631 40 33
Email: stefan.troche@psy.unibe.ch