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Evidence for an attentional model of human intelligence using the competing task paradigm
Person. indicid. Difl
Vol.
I?. No. 5. pp. 445455.
0191-8869.:91 $3.00 + 0.00 Copyright c 1991 Pergamon Press plc
1991
Printed in Great Britain. All rights reserved
EVIDENCE FOR AN ATTENTIONAL MODEL OF HUMAN INTELLIGENCE USING THE COMPETING TASK PARADIGM RICHARD D. ROBERTS, HELEN C. BEH,* GEORGINA SPILSBURY and
LAZAR STANKOV
Department of Psychology, University of Sydney, Sydney, N.S.W. 2006, Australia (Received
7 August 1990)
Summary-The present study examined competing task performance within an information theory framework. In the first experiment, 72 subjects performed a card-sorting task at four levels of task difficulty (O-bit, l-bit, 2-bit and 3-bit levels) under both single and competing task conditions. Output per 60 set was measured for each task. In the second experiment, estimates of fluid and crystallized ability, as well as short-term acquisition and retrieval, were obtained from 68 subjects who performed the same tasks as the subjects in Experiment 1. The results of the first experiment suggested the rate of processing remains invariant under both single and competing task conditions with the latter condition being readily interpreted as introducing an additional bit of information. The introduction of the competing condition also led to higher correlation between processing parameters and G, (but not G, or SAR) marker tests. The implication of these findings for cognitive models of human ability is discussed.
SPEED
OF
PROCESSING
UNDER SINGLE CONDITIONS
AND
COMPETING
TASK
One of the most consistent features emerging in the recent literature on intelligence is the high status afforded to ‘information’ in disparate research programs. Jensen (1982), for example, has related individual differences in intelligence to differences in the rates in which individuals “process (and hence acquire) the information offered by the environment” (p. 98). Others have implicated the term in linking divided attention and intelligence (e.g. Stankov, 1983) and processing complexity and intelligence (e.g. Vernon & Jensen, 1984). Given the importance of transmitted formation in conceptualizations of intelligence, it is not surprising that much of the current research focuses on disparate means of influencing information load when relating this experimental manipulation with a psychometric measure of intelligence. Typically, information has been manipulated either by increasing or decreasing the stimulus alternatives (as in the Hick paradigm) or by providing the individual with a wider range of sources from which information derives (as in the competing task paradigm). Using the Hick paradigm, researchers have found a linear relationship between the speed of information processing (as measured in bits) and measures of intelligence. Moreover, it has been reported that measures derived from this paradigm are good predictors of performance on cognitive ability tasks (Jensen, 1982, 1988; Jensen & Munro, 1979; Vernon, 1983). In addition, where two complex cognitive tasks are presented simultaneously, placing additional information demands on the individual, performance under such competing task conditions has been found to correlate more highly with measures of intelligence than performance under a single task condition (Fogarty & Stankov, 1982; Hunt, 1980; Stankov, 1983, 1988a). Demonstration of such relationships has advanced our understanding of intelligence, with researchers attempting to link their findings to existing theories of cognitive processing. One of the issues in the area of cognition is the nature of cognitive processing, with various researchers proposing either serial processing models (e.g. Broadbent, 1958), parallel processing models (e.g. Townsend, 1974) or models incorporating both forms of processing (e.g. Kantowitz & Knight, 1976). A study by Roberts, Beh and Stankov (1988), which investigated the relationship between competing task performance and intelligence, throws some light on this issue. Analysis *To whom all correspondence
should be addressed.
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RICHARD D. ROBERTS et al.
for single task performance which was parallel to the regression line for a combined primary-secondary task performance measure under competing task conditions. This finding suggests that parallel processing of the two inputs did not occur under the competing task conditions used in this study because such processing would have resulted in regression lines which were superimposed. Indeed, the findings indicated that the competing task condition resulted in an increase of 500 msec per choice in the primary task (card-sorting). This was reflected in the difference between the intercepts of the regression lines generated by the data from that study. The parallel regression lines obtained by Roberts et al. (1988) imply that the rate of processing remains constant regardless of any increase in processing load imposed by increases in the difficulty of the primary task or by the introduction of the secondary task. In fact, the findings strongly suggested that the addition of each bit of information results in an additional 500 msec of processing time. Because both the slope of the regression lines and the difference in the intercepts imply a difference of approx. 500 msec in processing time, it might be tempting to conclude that the introduction of a secondary task adds one bit (in information theory terms) to the task requirements. This would be in agreement with the common observation that where information theory measures are used, processing time remains constant despite task variations (see for example Hyman, 1953). Correlations of performance with other measures, however, point to a qualitative difference between increasing the processing load by increasing the difficulty level of the primary task and increasing the load by introducing a secondary task. That is, while the competing task situation is associated with an increase in correlation with measures of intelligence, increases in the difficulty level of the primary task are associated with an initial increase in correlation with intelligence measures, followed by a decrease. This observation has led to the suggestion that the introduction of a competing task produces a qualitative change in task demands (or a change in task complexity) while aterations to the characteristics of a specific task produces a quantitative change (or a change in the level of task difficulty) (Roberts et al., 1988; Stankov, 1988b). Because of the relevance of the various implications of the study by Roberts et al. (1988) to the nature of cognitive processing, to the distinction between the concepts of task complexity and task difficulty, and to the understanding of the nature of intelligence, it was considered important that the findings from this study be replicated. It was decided, however, to test the robustness of the original data by using output, rather than speed of performance, as the dependent variable. That is, in the Roberts et al. (1988) study, the time taken to complete a task was the variable of interest, as was the case in other studies involving Crossman’s version of the card-sorting task. While this is a convenient measure of performance under single task conditions, it is less appropriate as a measure where two sorting procedures are used simultaneously since it is unlikely both tasks would take the same amount of time to complete. To overcome this objection to speed as the measure of performance in a competing task situation, output (or items sorted during a specified time) was selected as the dependent variable for the present study. * This measure, while overcoming procedural difficulties, would be expected to yield findings in agreement with speed measures in a single task situation in that a linear relationship should prevail between output and the number of bits of information contained in a task. In addition to conducting a modified application of the Roberts et al. (1988) study, the present study was also designed to investigate further the correlations between processing rate and measures of fluid (G,) and crystallized (G,) intelligence, as well as the short-term acquisition and retrieval (SAR) factor. It was hoped that such measures would yield data which could clarify the relationship between various information manipulations and the broad measures of intelligence.
*While output per 60 set can be transformed to reaction time by way of a reciprocal transformation procedure. the analyses and subsequent inferences to be drawn in this paper, are best couched in terms of output measures. Moreover by taking into consideration all processing that occurs within a specified time period [unlike in Roberts er al. (1988) study] output measures actually provide a more rigorous test of Hick’s Law under competing task conditions.
Competing
task performance
Experiment
447
I
RATIONALE The purpose of this experiment was to replicate the findings of Roberts et al. (1988) regarding parallelism of regression lines for single and competing versions of the card-sorting task and to consider findings in relation to the question of parallel vs serial processing in competing task conditions. METHOD
Subjects Ss (n = 72) were 41 females and 31 males whose ages ranged from 17 to 40 years (mean age = 20.5 yr). Forty-eight of the Ss were first year students from the University of Sydney who participated in order to gain course credit points. The remaining Ss were recruited from sporting organizations (i.e. a IO-pin bowling center and local cricket club). Tasks Curd-sorting tusks. In this series of tasks, based on tasks used by Crossman (1953), Ss were required to sort a deck of Queens Slipper playing cards into specified piles in designated areas. There were four levels of information content used (0, 1, 2, 3 bits), with information being manipulated as follows: O-bit task-Ss were required to sort the cards alternately into two piles as quickly as possible; l-bit task-Ss were required to sort the deck into red suits and black suits; 2-bit task-Ss were required to sort the deck into spades, diamonds, hearts, clubs; 3-bit tasks-Ss were required to sort the deck into eight piles, cards 7 and above and cards 6 and below for each suit. Ss were allowed 60 set to work on each task and the number of items correctly sorted during this period was recorded. For the purposes of the experiment, the card-sorting task was designated as the primary task. Word-classiJication task. This task, designated as the secondary task, consisted of a list of 52 words which fell into one of four semantic categories-sport (e.g. baseball), job (e.g. plumber), color (e.g. brown), personality characteristic (e.g. lazy). There were 13 words in each of the categories and prior to the commencement of the experiment, Ss were allowed to look over the list for 5 min. Five forms of the list were constructed by randomly varying the position of the words in the list. During the experiment, Ss were aurally presented with the words from a list for 60 set and were asked to respond by stating the category to which each word belonged. The number of correct responses during the 60 set test period was scored for each S. Each stimulus word for this was presented immediately following the Ss response to the previous stimulus word. From information theory the difficulty of this task is calculated as 2 bits. Procedure Prior to commencing the experiment, Ss were given practice in the tasks they were to perform. For the card-sorting task, Ss sorted the deck of cards into two piles corresponding to picture cards and number cards. For the word-classification task, Ss were instructed as to the nature of the task, allowed to peruse the words for 5 min and then presented with a list of 52 words to which they gave a verbal response. During the experiment proper, all Ss performed the four conditions of the card-sorting task under both single and competing task conditions. The word-classification task, which served as the secondary task in the competing task conditions, was also presented as a single task. Each S first performed the four card-sorting tasks for 60 set each in one of the 24 possible combinations to which they had been randomly assigned. They then performed the word-classification task for 60 set, after which the four card-sorting tasks were again performed in a random order under dual task conditions for 60 set with the word-classification task as the secondary task. RESULTS
In the present study, the dependent variable was the number of correct decisions made during the 60 set test period. Descriptive statistics for the raw data of this study may be seen in Table 1.
448
R~XAFCD D. ROBERTS er al. Table
I. Mean
number
of items sorted per 6Osec on each task under competing task conditions (n = 72)
Task Single:
SD
109.17 61.90 46.16 30.14
19.96 a.41 5.56 6.05
42.24
4.36
106.21 52.46 38.57 24.39
20.13 9.24 6.49 5.60
41.50 36.50 33.65 26.65
4.32 4.98 4.99 4.34
single and
Task characteristics
card-sorting
O-bit l-bit 2-bit 3-bit Single:
Mean
both
Alternate piles Colors Suits Suits 6 and under/7
and above
word-classification
2-bit Competing:
O-bit l-bit 2-bit 3-bit Competing:
Four semantic
categories
card-sorting
Alternate piles (+ word task) Colors (+ word task) Suits (f word task) Suits 6 and under/7 and above (+ word task)
word-classfication
2-bit 2-bit 2-bit 2-bit
Plus Plus Plus Plus
O-bit l-bit 2-bit 3-bit
card-sort card-sort card-sort card-sort
task task task task
Table 2. Table of mean number of items sorted per 60 set for the card-sorting and word-classification tasks under both single and competing task presentation in Experiments I and 2 Experiment Condition
Bit-value
I
Experiment
2
Mean
SD
Mean
SD
t
151.41 104.14 89.00 72.38
19.61 9.63 1.32 7.68
162.2 I 112.44 94.62 16.32
21.76 13.33 IO.14 10.25
-3.09. -4.24, -3.78. - 2.58.
147.71 88.77 72.22 51.04
20.72 IO.96 9.17 8.17
147.06 92.94 74.85 53.97
27.02 13.62 13.06 IO.17
0.16 -2.00 - I .39 - I.88
Single presentation
2
Word-classification: plus: Card-sort
Competing
0 I 2 3
presentation
Word-classification: plus: Card-sort
2 0
I 2 3 t-values comparing *P < 0.01).
the results from Experiment
I with those from Experiment
2 are also given (d/ = 138,
In order to extend the findings of Roberts et al. (1988), data, the score from each of the single task presentations for card-sorting was added to the score for the word-classification task under the single presentation condition. In addition, the scores on each task obtained during the statistics for the summed competing task condition were summed for each S. * The descriptive scores for the single and competing task presentation conditions are shown in the first two columns of Table 2. These transformations allow assessment of the mean output of all Ss for single and competing conditions at comparable limits of stimulus input. It can be seen in Tables 1 and 2 that the standard deviations for the lowest level single task and competing task conditions are approximately twice as large as the standard deviations for all the other levels. Also, the means for both the single and competing task conditions are very close and their difference is not significant (I = 1.071, df = 71, P > 0.01). From a theoretical point of view, deviant results under the O-bit condition (i.e. simply placing the cards alternately into two piles) are not surprising. This condition simply measures movement time with no decision component while all other conditions involve a definite decision component in that the S has to decide on the basis of stimulus characteristics where to place each particular card. From an empirical point of view, however, such results are unusual because in the Roberts et al. (1988) study both the means and the standard deviations for the O-bit condition were comparable to those obtained for the other conditions. It is difficult to explain the discrepancy between the two studies. However, given that different processing is involved and, more importantly, that regression procedures are appropriate only where heterogeneity of variance is *To verify, it can be seen that the means in Table 2 bear a direct relationship to the means numerical entry (1$1.41) in Table 2 is the sum of 109.17 and 42.24 (from Table 1).
,
in Table
1. Thus,
the first
449
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Fig. 1. (A) Mean correct decisions per 60 set under single and competing task presentation for Experiment I. Values have been derived by adding the appropriate scores for the word-classification and card-sorting tasks. The values on the abscissa have been obtained by adding the bit-value of the word-classification task (2) to the bit-value of the relevant card-sorting tasks. (B) Mean correct decisions per 60 set under competing and single task presentation for Experiment 1 where 1 extra bit has been added to the competing task condition. Values for both the single and competing task conditions have been obtained by adding the scores on the word-classification task to scores on the card-sorting task. For the competing task values, the 2-bit word classification scores have been added to the appropriate card-sorting scores and plotted at a I-bit higher value along the abscissa. (C) and (D) show the corresponding data from Experiment 2.
small, it was decided to exclude the O-bit condition from further statistical analysis. Indeed, treating the O-bit condition in this way (since it reflects pure MT) makes these output data parallel more closely the Roth-Jensen reaction time parameters. The means for the higher level information conditions are plotted against the combined* bit level for the task in Fig. l(A). Using regression analysis it was found that single and competing task conditions were linear for the 3-, 4- and 5-bit levels and that these regression lines are parallel to each other. This finding is in substantial agreement with the results of Roberts et al. (1988). The overall level of performance in the present study is also comparable to the overall level in the study by Roberts et al. (1988). However, data contained in Table 1 and 2 suggest that adding one extra bit of information (either by doubling the number of piles or by introducing the extra task) increases processing time by about 350 msec which is less than the 500 msec suggested by the Roberts et al. (1988) findings. Inspection of Fig. l(A) also reveals an interesting facet of the data in that the competing condition means for the 3- and 4-bit levels are approximately equal to the single condition means *The term combined is used here to refer to the condition where the 2 bits from the word classification task are added to the appropriate number of bits from the card-sorting task.
450
RICHARD D. ROBERTS et nl.
for the 4- and 5-bit levels respectively. This suggests that the effect of performing the tasks under competing conditions is equivalent to adding one more decision requirement to the single condition. In Fig. l(B) the means for the higher level single task conditions are plotted against the total information content (in bits) together with the means of the competing task conditions to which an allowance of one extra bit per condition has been added (e.g. the competing task condition with the card sorting task at the l-bit level and the word-classification task at the P-bit level is plotted against the 4-bit value). From this figure it may be seen that the points for (i) the 4-bit single task and the 3-bit competing task with the additional bit, and (ii) the j-bit single task and the 4-bit competing task with the additional bit, are overlapping. In addition, the points for the 3-bit single condition and 6-bit competing condition points appear to be collinear with these four middle points. The hypothesis that performance on the competing task conditions in the present study is equivalent to performance on the single task conditions at one bit level higher was tested with multiple regression using SP1DA.t This hypothesis would be supported if all points in Fig. l(B) could be shown to lie on a straight line. Following a suggestion in McNeil, Kelly and McNeil (1975) the repeated measures in the design were accounted for by the use of person vectors. The results indicated that this suggested linearity does not hold (F-value for deviation from linearity = 7.8 1.5, P < 0.01). However, when data for the highest level competing task condition [i.e. the 6-bit condition in Fig. l(B)] are excluded from the analysis, linearity does obtain (F-value for deviations from linearity = 0.44, P > 0.01). The regression equation from this latter analyis is E(responses) = 151.848 - 16.015*bits Using this equation the predicted value for 6 bits is 55.758 which is only 4.716 higher than the obtained mean value. Since there are no data for single tasks at a total bit level of 6 with which to compare the highest level competing task data, it is unclear whether the failure to fit the model at this level is a rejection of the hypothesis or is attributable to the breakdown in linearity often reported for data where a large number of decisions is required. Inspection of the means in Table 1 shows, however, that the reason for non-linearity derives from a pronounced drop in performance on the competing word-classification task. That is, the difference in word-classification performance is twice as large between the 2-bit and 3-bit competing task condition as it is between the l-bit and 2-bit condition. Departures from linearity do not depend on changes in the card-sorting task which suggests that perhaps a change in strategy has occurred with the most difficult competing task condition. In particular, Ss may have attempted to maintain what may have been considered to be the appropriate level of card-sorting performance and thus reduced the overall level of word-classification. Whatever the explanation for the relatively small deviation from linearity at the 6-bit level, it is clear that below this level it is reasonable to claim that qualitative change between single and competing task performance corresponds to an increase in one bit of transmitted information. Experiment 2 RATIONALE The main purpose of this experiment was to replicate and extend the findings of Roberts et al. (1988) regarding correlations between the various levels of the experimental task and measures of intelligence. Previous work has indicated that the Raven’s Progressive Matrices test, which is a known marker for the Gr factor in G,/G, theory, shows a systematic relationship with the performance measures used in Experiment 1 (Roberts et al., 1988). However, additional estimates of fluid intelligence were chosen for use in the present study, with measures of both crystallized intelligence and SAR also obtained. These three broad ability measures were selected in order to Statistical
Package
for Interactive
Data
Analysis,
Statistical
Computing
Laboratory,
Macquarie
University.
Competing
task performance
examine whether they have differential relationships manipulation applied in this experiment.*
451
with the various
types of information
METHOD Subjects
Participants (n = 68) in this experiment were 45 female and 23 male first year students from the University of Sydney. Ss, who were aged between 18 and 65 years (2 = 23.87, SD = 9.90), participated in the experiment in order to fulfil course requirements. The mean age of the group is somewhat larger than the average age of the University population because of over-representation from mature-age students in the present sample. Tasks and procedure
The card-sorting tasks were identical to those of Experiment 1. The word-classification task was, on the other hand, changed somewhat by the creation of four new semantic categories-sport (e.g. golf), weapon (e.g. rifle), fruit (e.g. plum) and vehicle (e.g. car). Individual items within these were selected on the basis of Rosch’s work on prototypes (see for e.g. Rosch, 1975), tying this task to a much sounder conceptual framework and allowing results to be extended beyond a single stimulus set. In all other aspects this task followed the set up mentioned in Experiment 1. Regarding general procedure, the Ss first performed the battery of psychometric tests and then performed the experimental tasks in the manner set out in Experiment 1. A slight modification to this was the additional randomization of single/competing task presentation between Ss so that equal numbers of Ss performed the competing task both prior to and after the single task condition. This additional level of randomization served to further reduce the confounding effects of task order. The test battery consisted of four markers for G, (General Information, Esoteric Analogies, Synonyms Vocabulary and Word Associations), five markers for Gr (Raven’s Advanced Progressive Matrices, Cattell’s Matrices, Letter Counting, Letter Series and Concealed Words) and two markers for SAR (Digit Span Foward and Digit Span Backward). The majority of these tests either come from or are a modification of tests found in the Factor References Kit of Ekstrom, French, Harman and Bermen (1976) or are otherwise much used psychometric indices. Correlations between tests in this battery reveal a structure indicative of that obtained in previous research with these tests.
RESULTS The card-sorting and word-classification tasks of this study were analyzed in a manner analogous to Experiment 1. In all important respects, the data from this experiment are similar to that from the previous experiment, the only difference being that the overall speed of sorting in this experiment was somewhat faster. Combined data for this experiment are presented in the right-hand columns of Table 2 and are plotted in Fig. l(C). Comparison of these data with data from Experiment 1 illustrates the differences in output per 60 set between the groups. Ss sorted on average about 5 cards more within the 60 set period than they did in Experiment 1. However, tests between results from Experiment 1 and Experiment 2 revealed that the difference in output per 60 set was statistically significant only for all levels of single task manipulation (see Table 2). *Prior to Experiment 2 a pilot study was run on 24 university students using outlined in Experiment I. Additionally these Ss were given two markers and a marker (Synonyms Vocabulary) for G,. From this pilot study, word-classification tasks resembled closely the results from Experiment competing tasks adding one bit to single task performance at comparable measures with G, were significant for both single and competing conditions, under the 2-bit competing presentation. However correlations between G, competing task presentation almost always approached zero.
the same performance tasks and procedure (Letter Series and Letter Counting) for Gr combined data for the card-sorting and I (i.e. parallelism of regression lines with levels of information). Correlations of these with the highest correlation (0.47) obtained and task performance under both single and
452
RICHARD D. ROBERTS et al. Table 3. Correlations between measures of task performance and estimates of fluid intelligence (G,), crystallized intelligence (G,) and SAR at different bit-levels (n = 68) Task Single:
O-bit l-bit 2-bit 3-bit Single:
G,
0.04 0.07 0.12 0.29
0.34 0.30 0.33 0.55
0.26
0.24
0.07 0.12 0.20 0.26
0.34 0.35 0.39 0.44
0.17 0.09 0.03 0.21
0.20 0.18 0.12 0.31
0.13 0.14 0.24 0.41
-0.02 0.04 -0.06 0.27
0.21 0.19 0.17 0.24
word-classificorion
2-bit Competing:
plus 2-bit I plus 2-bit 2 plus 2-bit 3 plus 2-bit
Competing:
plus 2 plus 2 plus 2 plus
-0.08
card-sorting
0
2
SAR
G, cord-sorting
word-classification
O-bit l-bit 2-bit 3-bit
There is no obvious explanation of why the present sample performed better under single task conditions than the Ss in Experiment 1, although it may be because only university students were used in this experiment, whereas some Ss in Experiment 1 were not enrolled at a tertiary institution. Despite this difference in speed, however, it might be noted that parallelism of regression lines also obtained in this experiment and that the estimated transmission rate, again, is about 300-350 msec per bit of information processed. Moreover, as can be seen in Fig. l(D), the competing-task condition again acts as though it were adding an extra bit of complexity to the processing requirements of all subjects. Table 3 contains correlations between the performance task measures and measures of intelligence. From the earlier findings of Roberts et af. (1988) it was predicted that correlations of competing task performance with Gr would be higher than correlations of Gr with single task presentation. However, while the correlation between card-sorting scores under competing task performance conditions of Gr is slightly higher for tasks containing 1 and 2 bits, the overall difference between correlation coefficients is zero (0.38 for both single and competing task presentation).* This is largely a function of the 3-bit card-sorting task which acts to reduce the overall difference by having lower correlation with Gr under competing task conditions than under single task presentation. Interestingly, for the competing task at 3 bits, the correlation between word-classification performance and Gr rises to significance (i.e. 0.24 for single word-classification vs 0.41 for competing word-classification at 3 bits). The emergence of this correlation may indicate that some Ss adopt a strategy of enhancing performance on the simpler task when faced with excessive information load. Thus at a point where the competing task has greatest complexity, both primary and secondary task measures share common variance with fluid intelligence. The Roberts et al. (1988) data also showed that card-sorting under lower-bit conditions (O-bit and l-bit) have lower correlation with Gr than card-sorting under the 2-bit condition. However, a decrease in correlation at the 3-bit level was also reported. Since it is known that the 3-bit level is more difficult than the 2-bit level, and since the correlations reversed their trend between the 2and 3-bit level, Roberts et al. (1988) argued that manipulations within Hick’s paradigm represented quantitative (difficulty) not qualitative (complexity) manipulations. However, while the present results are in genera1 agreement with previous results for the competing card-sorting condition, they contradict previous findings for the single task condition (i.e. in the present results there is an increase in correlation from the 2-bit to the 3-bit single task). This difference may also have resulted from the use of different samples in the two studies. It is possible that, for the present group of Ss, the single 3-bit condition was within Ss’ level of maximum attentional capacity. Such an explanation is generally consistent with the interpretation of the data contained in Fig. l(B) and l(D). According to these results, the departure from linearity *When age is partialled out from these correlations there is an overall difference between correlation coefficients (0.40 for single task presentation vs 0.43 for competing task presentation). Even then however, the difference is not as large as that reported by Roberts er al. (1988).
Competing
task performance
453
takes place only at what is putatively a 6-bit level which coincidentally, is the level where the correlation with fluid intelligence begins to share common variance with both primary and secondary tasks. Table 3 also contains correlations between task performance and measures of both crystallized intelligence and SAR. While G, shares a similar pattern of correlations with the various performance measures as Gr, coefficients are, by and large, non-significant. Indeed when fluid intelligence is partialled out from these, all correlations between G, and the performance tasks approach zero (0.02 for single task presentation vs 0.06 for competing task presentation).* While this result is not in agreement with a study conducted by Jenkinson (1983) showing similar magnitude of correlation for Grand G, markers with speed of processing parameters, it is consistent with results generated under the competing task paradigm where typically correlations with G, are not greatly affected by complexity manipulations (see, for example, Stankov, 1983). For SAR the absence of correlations with performance parameters and a trend towards reduced correlations under competing task conditions relative to single task presentation was found. This type of pattern has been found elsewhere in chronometric studies (see for e.g. Roberts, Stankov & Walker, 1991). This finding rules out explanation of the high fluid intelligence-task performance correlations in terms of storage components of working memory. DISCUSSION The present study has shown how information theory can provide a quantitative index of attentional load and, by doing so, allow a comparison of alternative models of processing. Serial processing models would predict an invariant transmission rate (i.e. equivalent slope) in situations where similar requirements operate for simultaneously presented tasks, and strict parallel processing models would either predict an increase in the rate of transmission or invariant transmission rate with the added proviso that obtained regression lines be superimposed. The regression lines obtained in the present experiments for single and competing task conditions indicate invariant transmission rate, but since these are not superimposed, these findings favor serial processing models. The finding of parellel regression lines for the primary task scores under single and competing task conditions in the present study not only provides empirical confirmation of the earlier finding by Roberts et al. (1988) but also provides compelling evidence that transmission rate (and hence processing rate) remains invariant under competing task conditions. Taken together, the present results and those of Roberts et al. (1988) show that parallel processing of different inputs does not occur under the conditions employed, but that information is processed serially, with each additional bit of information increasing reaction time to primary task stimuli by 350-500 msec. These findings may also be taken as indicating that Ss are working to maximum capacity under both the single and competing task conditions in the present experiment. That is, if Ss were working below capacity on any one of the single tasks, linearity of response would not be observed. Similarly, if Ss worked below capacity on competing tasks, the regression line for the primary task under competing task conditions would lose its parallelism with the regression line obtained under single task conditions. Kantowitz (1985) and others have lamented that it is not possible to determine working capacity other than on a subjective basis. The present findings suggest that under conditions where input may be measured in bits of information, an objective indication of working capacity is now available. In earlier studies it has sometimes been suggested that the performance decrement observed under competing task conditions may be explained either in terms of inattentiveness or increased arousal. While there is a performance decrement on the primary task in the present data, the equivalence of slope for the two regression lines renders unlikely explanations of deficit in terms of inattentiveness and/or arousal change. In particular, it cannot be argued that attention has wandered under the more demanding competing task conditions nor can it persuasively be *The correlations task performance measures share with fluid intelligence intelligence (or for that matter SAR) are partialled out from these.
are, conversely,
not affected
if crystallized
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RICHARD D. ROBERTS et al
argued that Ss have found these task conditions more arousing because the increase in difficulty should be expected to interact with arousal levels to produce diverging regression lines. Overall, the data attest to the robustness of Hick’s Law. Not only was the law found to hold under competing task conditions, replicating earlier findings, but it held with the present tasks when the direct measure of performance was output rather than time. Of some significance was the finding that when the two experimental conditions were plotted on a single graph in terms of total information content, the obtained regression line obeyed Hick’s Law when the zero bit information condition was excluded from the analysis. The exclusion of this condition seems well justified since the condition is obviously too far removed from a choice reaction time paradigm. The present findings add to the wealth of evidence which now exists to show that Hick’s Law obtains under a wide range of conditions where decision-making is involved. It would also appear that the present data extend the upper limits of Hick’s Law by employing a competing task paradigm. It is commonly observed that with single task presentation, Hick’s Law consistently breaks down at higher levels of information. This may well be because higher levels of information content in the single task condition result in tasks of excessive difficulty. Once difficulty levels (as defined earlier) reach a ceiling, increases in information content by complexity manipulation may permit an extension of Hick’s Law to higher levels of information content. In turn, the presence of systematic correlations between Hick parameters (obtained under single and competing conditions) and fluid measures of intelligence of Experiment 2 mean that each of these findings has ready application to cognitive models of human ability. For example, within the range of complexity used in the present study, it may be imputed that individual differences in processing rate are responsible, at least in part, for individual differences in Gr. Moreover, because competing presentation conditions generate the highest correlations with markers of G,, it would seem reasonable to conclude that a S’s ability to maximize serial processing rate under increasingly complex informational demands, is related to Gr. Because of the observed parallelism of single and competing conditions, differences in GI cannot be explained away via models emphasising the role of inattentiveness/arousal nor can they be explained away by models which place emphasis on differences in a S’s ability to invoke parallel processes. Instead, what should be seen as crucial in generating a cognitive model of Gr, is the fact that the introduction of an extra bit of complexity leads to better prediction of a S’s ability than any other experimental manipulation. The present emphasis on processing rate as a partial explanation for individual differences in G, is enhanced by consideration of popular conceptualisations of this ability. Gr has in recent times been linked to incidental learning (Horn, 1986). Obviously, being able to process information of a novel kind more quickly and efficiently predisposes individuals to perform better on tasks of an incidental nature.* Moreover, the absence of correlations between Hick manipulations and G, abilities, observed in the present study, become meaningful in this light. G, abilities are generally acquired via repetition or through the overlearning of cognitive strategies. Ability to do G, tasks is often an all or none phenomenon. Consequently, being able to process stimuli quickly and efficiently does not necessarily predispose individuals to perform better on tasks containing this component. In summary, the present study provides evidence that information theory indices permit the quantification of attention. The measurement of attention load in terms of stimulus information is of theoretical and practical use to psychometricians interested in couching intelligence within the framework of attentional processes. The views of theoreticians who hold that intelligence is reflected in part by the speed of processing are supported by the present findings. In replicating and extending findings indicating relationships between information load and performance under competing task conditions, evidence for the relationship between intelligence and complexity has also been strengthened. In addition, the present study provides a means of measuring intelligence in terms of attentional load which may be applied over a wide range of task conditions.
*An anomalous
finding for advocates of the speed of processing paradigm is the finding that with extensive task practice the gradient of reaction time on bits approaches zero (Mowbray & Rhodes, 1959). However, within the present framework this result is easily integrated, since when reaction time tasks tap into non-incidental learning they would no longer be expected to share systematic correlations with G,.
Competing Acknowledgements-Our experiment.
thanks
task performance
go to both John Mond and Don Watts for collecting
455 much of the data used in our second
REFERENCES Broadbent, D. E. (1958). Perception and communicafion. London: Pergamon Press. Crossman, E. R. F. W. (1953). Entropy and choice reaction time: the effect of frequency imbalance on choice-response. The Quarterly Journal of Experimental Psychology, 5, 41-51. Ekstrom, R. B., French, J. E., Harman, H. H. & Bermen, D. (1976). Manualfor Kit ofl;acror References Cognitive Tasks. Princeton, NJ: Educational Testing Service. Fogarty, G. & Stankov, L. (1982). Competing tasks as an index of intelligence. Personality and Individual Differences, 3, 407-422. Horn J. L. (1987). Intellectual ability concepts. In Sternberg, R. J. (Ed.), Advances in the psychology ofhuman inrelligence. Hillsdale, NJ: Erlbaum. Hunt, E. B. (1980). Intelligence as an information processing concept. British Journal of Psychology, 71, 449-474. Hyman, R. (1953). Stimulus information as a determinant of reaction time. Journal of Experimental Psychology, 45, 188-196. Jenkinson, J. C. (1983). Is speed of information processing related to fluid or crystallised intelligence? Intelligence, 7,91-106. Jensen, A. R. (1982). Reaction time and psychometric g. In Eysenck, H. J. (Ed.), A model for intelligence. New York: Springer. Jensen, A. R. (1988). Individual differences in the Hick paradigm. In Vernon, P. A. (Ed.), Speed of informafion-processing and intelligence. New Jersey: Ablex. Jensen, A. R. & Munro, E. (1979). Reaction time, movement time and intelligence. Intelligence, 3, 121-126. Kantowitz, B. H. (1985). Channels and stages in human information processing: a limited analysis of theory and methodology. Journal of Mathematical Psychology, 29, 135-174. Kantowitz, B. H. & Knight, J. L. (1976). Testing tapping timesharing: II Auditory secondary task. Acfa Psychologica, 40, 343-362. McNeil, K. A., Kelly, F. J. & McNeil, J. T. (1975). Testing research hypotheses using multiple linear regression. Carbondale, IL: Southern Illinois University Press. Mowbray, G. H. & Rhodes, M. V. (1959). On the reduction of choice reaction time with practice. Quarterly Journal of Experimental Psychology, I I, 16-23. Roberts, R. D., Beh, H. C. & Stankov, L. (1988). Hick’s Law, competing task performance and intelligence. Infelligence, I‘?, I1 I-131. Roberts, R. D., Stankov, L. & Walker, M. B. (1991). Fitt’s Law, competing task performance and intelligence. Manuscript in preparation. Rosch, E. (1975). Cognitive representations of semantic categories. Journal of Experimental Psychology: General, 104, 192-233. Stankov, L. (1983). Attention and intelligence. Journal of Educational Psychology, 75, 471-490. Stankov, L. (1988a). Single tests, competing tasks and their relationship to broad factors of intelligence. Personality and Individual D@erences, 9, 25-33. Stankov, L. (1988b). The concept of complexity and intelligence. Paper presented at the XXIV Congress of Psychology, Sydney, August 1988. Stankov, L. & Horn, J. L. (1980). Human abilities revealed through auditory tests. Journal of Educational Psychology, 72, 21-44. Townsend, J. T. (1974). Issues and models concerning the processing of a finite number of inputs. In Kantowitz, B. H. (Ed.), Human information processing. Hillsdale, NJ: Erlbaum. Vernon, P. A. (1983). Speed of information-processing and general intelligence. Inrelligence, 7, 53-70. Vernon, P. A. & Jensen, A. R. (1984). Individual and group differences in intelligence and speed of information-processing. Personality and Individual Differences, 5, 4 1I-423.
Vol.
I?. No. 5. pp. 445455.
0191-8869.:91 $3.00 + 0.00 Copyright c 1991 Pergamon Press plc
1991
Printed in Great Britain. All rights reserved
EVIDENCE FOR AN ATTENTIONAL MODEL OF HUMAN INTELLIGENCE USING THE COMPETING TASK PARADIGM RICHARD D. ROBERTS, HELEN C. BEH,* GEORGINA SPILSBURY and
LAZAR STANKOV
Department of Psychology, University of Sydney, Sydney, N.S.W. 2006, Australia (Received
7 August 1990)
Summary-The present study examined competing task performance within an information theory framework. In the first experiment, 72 subjects performed a card-sorting task at four levels of task difficulty (O-bit, l-bit, 2-bit and 3-bit levels) under both single and competing task conditions. Output per 60 set was measured for each task. In the second experiment, estimates of fluid and crystallized ability, as well as short-term acquisition and retrieval, were obtained from 68 subjects who performed the same tasks as the subjects in Experiment 1. The results of the first experiment suggested the rate of processing remains invariant under both single and competing task conditions with the latter condition being readily interpreted as introducing an additional bit of information. The introduction of the competing condition also led to higher correlation between processing parameters and G, (but not G, or SAR) marker tests. The implication of these findings for cognitive models of human ability is discussed.
SPEED
OF
PROCESSING
UNDER SINGLE CONDITIONS
AND
COMPETING
TASK
One of the most consistent features emerging in the recent literature on intelligence is the high status afforded to ‘information’ in disparate research programs. Jensen (1982), for example, has related individual differences in intelligence to differences in the rates in which individuals “process (and hence acquire) the information offered by the environment” (p. 98). Others have implicated the term in linking divided attention and intelligence (e.g. Stankov, 1983) and processing complexity and intelligence (e.g. Vernon & Jensen, 1984). Given the importance of transmitted formation in conceptualizations of intelligence, it is not surprising that much of the current research focuses on disparate means of influencing information load when relating this experimental manipulation with a psychometric measure of intelligence. Typically, information has been manipulated either by increasing or decreasing the stimulus alternatives (as in the Hick paradigm) or by providing the individual with a wider range of sources from which information derives (as in the competing task paradigm). Using the Hick paradigm, researchers have found a linear relationship between the speed of information processing (as measured in bits) and measures of intelligence. Moreover, it has been reported that measures derived from this paradigm are good predictors of performance on cognitive ability tasks (Jensen, 1982, 1988; Jensen & Munro, 1979; Vernon, 1983). In addition, where two complex cognitive tasks are presented simultaneously, placing additional information demands on the individual, performance under such competing task conditions has been found to correlate more highly with measures of intelligence than performance under a single task condition (Fogarty & Stankov, 1982; Hunt, 1980; Stankov, 1983, 1988a). Demonstration of such relationships has advanced our understanding of intelligence, with researchers attempting to link their findings to existing theories of cognitive processing. One of the issues in the area of cognition is the nature of cognitive processing, with various researchers proposing either serial processing models (e.g. Broadbent, 1958), parallel processing models (e.g. Townsend, 1974) or models incorporating both forms of processing (e.g. Kantowitz & Knight, 1976). A study by Roberts, Beh and Stankov (1988), which investigated the relationship between competing task performance and intelligence, throws some light on this issue. Analysis *To whom all correspondence
should be addressed.
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RICHARD D. ROBERTS et al.
for single task performance which was parallel to the regression line for a combined primary-secondary task performance measure under competing task conditions. This finding suggests that parallel processing of the two inputs did not occur under the competing task conditions used in this study because such processing would have resulted in regression lines which were superimposed. Indeed, the findings indicated that the competing task condition resulted in an increase of 500 msec per choice in the primary task (card-sorting). This was reflected in the difference between the intercepts of the regression lines generated by the data from that study. The parallel regression lines obtained by Roberts et al. (1988) imply that the rate of processing remains constant regardless of any increase in processing load imposed by increases in the difficulty of the primary task or by the introduction of the secondary task. In fact, the findings strongly suggested that the addition of each bit of information results in an additional 500 msec of processing time. Because both the slope of the regression lines and the difference in the intercepts imply a difference of approx. 500 msec in processing time, it might be tempting to conclude that the introduction of a secondary task adds one bit (in information theory terms) to the task requirements. This would be in agreement with the common observation that where information theory measures are used, processing time remains constant despite task variations (see for example Hyman, 1953). Correlations of performance with other measures, however, point to a qualitative difference between increasing the processing load by increasing the difficulty level of the primary task and increasing the load by introducing a secondary task. That is, while the competing task situation is associated with an increase in correlation with measures of intelligence, increases in the difficulty level of the primary task are associated with an initial increase in correlation with intelligence measures, followed by a decrease. This observation has led to the suggestion that the introduction of a competing task produces a qualitative change in task demands (or a change in task complexity) while aterations to the characteristics of a specific task produces a quantitative change (or a change in the level of task difficulty) (Roberts et al., 1988; Stankov, 1988b). Because of the relevance of the various implications of the study by Roberts et al. (1988) to the nature of cognitive processing, to the distinction between the concepts of task complexity and task difficulty, and to the understanding of the nature of intelligence, it was considered important that the findings from this study be replicated. It was decided, however, to test the robustness of the original data by using output, rather than speed of performance, as the dependent variable. That is, in the Roberts et al. (1988) study, the time taken to complete a task was the variable of interest, as was the case in other studies involving Crossman’s version of the card-sorting task. While this is a convenient measure of performance under single task conditions, it is less appropriate as a measure where two sorting procedures are used simultaneously since it is unlikely both tasks would take the same amount of time to complete. To overcome this objection to speed as the measure of performance in a competing task situation, output (or items sorted during a specified time) was selected as the dependent variable for the present study. * This measure, while overcoming procedural difficulties, would be expected to yield findings in agreement with speed measures in a single task situation in that a linear relationship should prevail between output and the number of bits of information contained in a task. In addition to conducting a modified application of the Roberts et al. (1988) study, the present study was also designed to investigate further the correlations between processing rate and measures of fluid (G,) and crystallized (G,) intelligence, as well as the short-term acquisition and retrieval (SAR) factor. It was hoped that such measures would yield data which could clarify the relationship between various information manipulations and the broad measures of intelligence.
*While output per 60 set can be transformed to reaction time by way of a reciprocal transformation procedure. the analyses and subsequent inferences to be drawn in this paper, are best couched in terms of output measures. Moreover by taking into consideration all processing that occurs within a specified time period [unlike in Roberts er al. (1988) study] output measures actually provide a more rigorous test of Hick’s Law under competing task conditions.
Competing
task performance
Experiment
447
I
RATIONALE The purpose of this experiment was to replicate the findings of Roberts et al. (1988) regarding parallelism of regression lines for single and competing versions of the card-sorting task and to consider findings in relation to the question of parallel vs serial processing in competing task conditions. METHOD
Subjects Ss (n = 72) were 41 females and 31 males whose ages ranged from 17 to 40 years (mean age = 20.5 yr). Forty-eight of the Ss were first year students from the University of Sydney who participated in order to gain course credit points. The remaining Ss were recruited from sporting organizations (i.e. a IO-pin bowling center and local cricket club). Tasks Curd-sorting tusks. In this series of tasks, based on tasks used by Crossman (1953), Ss were required to sort a deck of Queens Slipper playing cards into specified piles in designated areas. There were four levels of information content used (0, 1, 2, 3 bits), with information being manipulated as follows: O-bit task-Ss were required to sort the cards alternately into two piles as quickly as possible; l-bit task-Ss were required to sort the deck into red suits and black suits; 2-bit task-Ss were required to sort the deck into spades, diamonds, hearts, clubs; 3-bit tasks-Ss were required to sort the deck into eight piles, cards 7 and above and cards 6 and below for each suit. Ss were allowed 60 set to work on each task and the number of items correctly sorted during this period was recorded. For the purposes of the experiment, the card-sorting task was designated as the primary task. Word-classiJication task. This task, designated as the secondary task, consisted of a list of 52 words which fell into one of four semantic categories-sport (e.g. baseball), job (e.g. plumber), color (e.g. brown), personality characteristic (e.g. lazy). There were 13 words in each of the categories and prior to the commencement of the experiment, Ss were allowed to look over the list for 5 min. Five forms of the list were constructed by randomly varying the position of the words in the list. During the experiment, Ss were aurally presented with the words from a list for 60 set and were asked to respond by stating the category to which each word belonged. The number of correct responses during the 60 set test period was scored for each S. Each stimulus word for this was presented immediately following the Ss response to the previous stimulus word. From information theory the difficulty of this task is calculated as 2 bits. Procedure Prior to commencing the experiment, Ss were given practice in the tasks they were to perform. For the card-sorting task, Ss sorted the deck of cards into two piles corresponding to picture cards and number cards. For the word-classification task, Ss were instructed as to the nature of the task, allowed to peruse the words for 5 min and then presented with a list of 52 words to which they gave a verbal response. During the experiment proper, all Ss performed the four conditions of the card-sorting task under both single and competing task conditions. The word-classification task, which served as the secondary task in the competing task conditions, was also presented as a single task. Each S first performed the four card-sorting tasks for 60 set each in one of the 24 possible combinations to which they had been randomly assigned. They then performed the word-classification task for 60 set, after which the four card-sorting tasks were again performed in a random order under dual task conditions for 60 set with the word-classification task as the secondary task. RESULTS
In the present study, the dependent variable was the number of correct decisions made during the 60 set test period. Descriptive statistics for the raw data of this study may be seen in Table 1.
448
R~XAFCD D. ROBERTS er al. Table
I. Mean
number
of items sorted per 6Osec on each task under competing task conditions (n = 72)
Task Single:
SD
109.17 61.90 46.16 30.14
19.96 a.41 5.56 6.05
42.24
4.36
106.21 52.46 38.57 24.39
20.13 9.24 6.49 5.60
41.50 36.50 33.65 26.65
4.32 4.98 4.99 4.34
single and
Task characteristics
card-sorting
O-bit l-bit 2-bit 3-bit Single:
Mean
both
Alternate piles Colors Suits Suits 6 and under/7
and above
word-classification
2-bit Competing:
O-bit l-bit 2-bit 3-bit Competing:
Four semantic
categories
card-sorting
Alternate piles (+ word task) Colors (+ word task) Suits (f word task) Suits 6 and under/7 and above (+ word task)
word-classfication
2-bit 2-bit 2-bit 2-bit
Plus Plus Plus Plus
O-bit l-bit 2-bit 3-bit
card-sort card-sort card-sort card-sort
task task task task
Table 2. Table of mean number of items sorted per 60 set for the card-sorting and word-classification tasks under both single and competing task presentation in Experiments I and 2 Experiment Condition
Bit-value
I
Experiment
2
Mean
SD
Mean
SD
t
151.41 104.14 89.00 72.38
19.61 9.63 1.32 7.68
162.2 I 112.44 94.62 16.32
21.76 13.33 IO.14 10.25
-3.09. -4.24, -3.78. - 2.58.
147.71 88.77 72.22 51.04
20.72 IO.96 9.17 8.17
147.06 92.94 74.85 53.97
27.02 13.62 13.06 IO.17
0.16 -2.00 - I .39 - I.88
Single presentation
2
Word-classification: plus: Card-sort
Competing
0 I 2 3
presentation
Word-classification: plus: Card-sort
2 0
I 2 3 t-values comparing *P < 0.01).
the results from Experiment
I with those from Experiment
2 are also given (d/ = 138,
In order to extend the findings of Roberts et al. (1988), data, the score from each of the single task presentations for card-sorting was added to the score for the word-classification task under the single presentation condition. In addition, the scores on each task obtained during the statistics for the summed competing task condition were summed for each S. * The descriptive scores for the single and competing task presentation conditions are shown in the first two columns of Table 2. These transformations allow assessment of the mean output of all Ss for single and competing conditions at comparable limits of stimulus input. It can be seen in Tables 1 and 2 that the standard deviations for the lowest level single task and competing task conditions are approximately twice as large as the standard deviations for all the other levels. Also, the means for both the single and competing task conditions are very close and their difference is not significant (I = 1.071, df = 71, P > 0.01). From a theoretical point of view, deviant results under the O-bit condition (i.e. simply placing the cards alternately into two piles) are not surprising. This condition simply measures movement time with no decision component while all other conditions involve a definite decision component in that the S has to decide on the basis of stimulus characteristics where to place each particular card. From an empirical point of view, however, such results are unusual because in the Roberts et al. (1988) study both the means and the standard deviations for the O-bit condition were comparable to those obtained for the other conditions. It is difficult to explain the discrepancy between the two studies. However, given that different processing is involved and, more importantly, that regression procedures are appropriate only where heterogeneity of variance is *To verify, it can be seen that the means in Table 2 bear a direct relationship to the means numerical entry (1$1.41) in Table 2 is the sum of 109.17 and 42.24 (from Table 1).
,
in Table
1. Thus,
the first
449
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Fig. 1. (A) Mean correct decisions per 60 set under single and competing task presentation for Experiment I. Values have been derived by adding the appropriate scores for the word-classification and card-sorting tasks. The values on the abscissa have been obtained by adding the bit-value of the word-classification task (2) to the bit-value of the relevant card-sorting tasks. (B) Mean correct decisions per 60 set under competing and single task presentation for Experiment 1 where 1 extra bit has been added to the competing task condition. Values for both the single and competing task conditions have been obtained by adding the scores on the word-classification task to scores on the card-sorting task. For the competing task values, the 2-bit word classification scores have been added to the appropriate card-sorting scores and plotted at a I-bit higher value along the abscissa. (C) and (D) show the corresponding data from Experiment 2.
small, it was decided to exclude the O-bit condition from further statistical analysis. Indeed, treating the O-bit condition in this way (since it reflects pure MT) makes these output data parallel more closely the Roth-Jensen reaction time parameters. The means for the higher level information conditions are plotted against the combined* bit level for the task in Fig. l(A). Using regression analysis it was found that single and competing task conditions were linear for the 3-, 4- and 5-bit levels and that these regression lines are parallel to each other. This finding is in substantial agreement with the results of Roberts et al. (1988). The overall level of performance in the present study is also comparable to the overall level in the study by Roberts et al. (1988). However, data contained in Table 1 and 2 suggest that adding one extra bit of information (either by doubling the number of piles or by introducing the extra task) increases processing time by about 350 msec which is less than the 500 msec suggested by the Roberts et al. (1988) findings. Inspection of Fig. l(A) also reveals an interesting facet of the data in that the competing condition means for the 3- and 4-bit levels are approximately equal to the single condition means *The term combined is used here to refer to the condition where the 2 bits from the word classification task are added to the appropriate number of bits from the card-sorting task.
450
RICHARD D. ROBERTS et nl.
for the 4- and 5-bit levels respectively. This suggests that the effect of performing the tasks under competing conditions is equivalent to adding one more decision requirement to the single condition. In Fig. l(B) the means for the higher level single task conditions are plotted against the total information content (in bits) together with the means of the competing task conditions to which an allowance of one extra bit per condition has been added (e.g. the competing task condition with the card sorting task at the l-bit level and the word-classification task at the P-bit level is plotted against the 4-bit value). From this figure it may be seen that the points for (i) the 4-bit single task and the 3-bit competing task with the additional bit, and (ii) the j-bit single task and the 4-bit competing task with the additional bit, are overlapping. In addition, the points for the 3-bit single condition and 6-bit competing condition points appear to be collinear with these four middle points. The hypothesis that performance on the competing task conditions in the present study is equivalent to performance on the single task conditions at one bit level higher was tested with multiple regression using SP1DA.t This hypothesis would be supported if all points in Fig. l(B) could be shown to lie on a straight line. Following a suggestion in McNeil, Kelly and McNeil (1975) the repeated measures in the design were accounted for by the use of person vectors. The results indicated that this suggested linearity does not hold (F-value for deviation from linearity = 7.8 1.5, P < 0.01). However, when data for the highest level competing task condition [i.e. the 6-bit condition in Fig. l(B)] are excluded from the analysis, linearity does obtain (F-value for deviations from linearity = 0.44, P > 0.01). The regression equation from this latter analyis is E(responses) = 151.848 - 16.015*bits Using this equation the predicted value for 6 bits is 55.758 which is only 4.716 higher than the obtained mean value. Since there are no data for single tasks at a total bit level of 6 with which to compare the highest level competing task data, it is unclear whether the failure to fit the model at this level is a rejection of the hypothesis or is attributable to the breakdown in linearity often reported for data where a large number of decisions is required. Inspection of the means in Table 1 shows, however, that the reason for non-linearity derives from a pronounced drop in performance on the competing word-classification task. That is, the difference in word-classification performance is twice as large between the 2-bit and 3-bit competing task condition as it is between the l-bit and 2-bit condition. Departures from linearity do not depend on changes in the card-sorting task which suggests that perhaps a change in strategy has occurred with the most difficult competing task condition. In particular, Ss may have attempted to maintain what may have been considered to be the appropriate level of card-sorting performance and thus reduced the overall level of word-classification. Whatever the explanation for the relatively small deviation from linearity at the 6-bit level, it is clear that below this level it is reasonable to claim that qualitative change between single and competing task performance corresponds to an increase in one bit of transmitted information. Experiment 2 RATIONALE The main purpose of this experiment was to replicate and extend the findings of Roberts et al. (1988) regarding correlations between the various levels of the experimental task and measures of intelligence. Previous work has indicated that the Raven’s Progressive Matrices test, which is a known marker for the Gr factor in G,/G, theory, shows a systematic relationship with the performance measures used in Experiment 1 (Roberts et al., 1988). However, additional estimates of fluid intelligence were chosen for use in the present study, with measures of both crystallized intelligence and SAR also obtained. These three broad ability measures were selected in order to Statistical
Package
for Interactive
Data
Analysis,
Statistical
Computing
Laboratory,
Macquarie
University.
Competing
task performance
examine whether they have differential relationships manipulation applied in this experiment.*
451
with the various
types of information
METHOD Subjects
Participants (n = 68) in this experiment were 45 female and 23 male first year students from the University of Sydney. Ss, who were aged between 18 and 65 years (2 = 23.87, SD = 9.90), participated in the experiment in order to fulfil course requirements. The mean age of the group is somewhat larger than the average age of the University population because of over-representation from mature-age students in the present sample. Tasks and procedure
The card-sorting tasks were identical to those of Experiment 1. The word-classification task was, on the other hand, changed somewhat by the creation of four new semantic categories-sport (e.g. golf), weapon (e.g. rifle), fruit (e.g. plum) and vehicle (e.g. car). Individual items within these were selected on the basis of Rosch’s work on prototypes (see for e.g. Rosch, 1975), tying this task to a much sounder conceptual framework and allowing results to be extended beyond a single stimulus set. In all other aspects this task followed the set up mentioned in Experiment 1. Regarding general procedure, the Ss first performed the battery of psychometric tests and then performed the experimental tasks in the manner set out in Experiment 1. A slight modification to this was the additional randomization of single/competing task presentation between Ss so that equal numbers of Ss performed the competing task both prior to and after the single task condition. This additional level of randomization served to further reduce the confounding effects of task order. The test battery consisted of four markers for G, (General Information, Esoteric Analogies, Synonyms Vocabulary and Word Associations), five markers for Gr (Raven’s Advanced Progressive Matrices, Cattell’s Matrices, Letter Counting, Letter Series and Concealed Words) and two markers for SAR (Digit Span Foward and Digit Span Backward). The majority of these tests either come from or are a modification of tests found in the Factor References Kit of Ekstrom, French, Harman and Bermen (1976) or are otherwise much used psychometric indices. Correlations between tests in this battery reveal a structure indicative of that obtained in previous research with these tests.
RESULTS The card-sorting and word-classification tasks of this study were analyzed in a manner analogous to Experiment 1. In all important respects, the data from this experiment are similar to that from the previous experiment, the only difference being that the overall speed of sorting in this experiment was somewhat faster. Combined data for this experiment are presented in the right-hand columns of Table 2 and are plotted in Fig. l(C). Comparison of these data with data from Experiment 1 illustrates the differences in output per 60 set between the groups. Ss sorted on average about 5 cards more within the 60 set period than they did in Experiment 1. However, tests between results from Experiment 1 and Experiment 2 revealed that the difference in output per 60 set was statistically significant only for all levels of single task manipulation (see Table 2). *Prior to Experiment 2 a pilot study was run on 24 university students using outlined in Experiment I. Additionally these Ss were given two markers and a marker (Synonyms Vocabulary) for G,. From this pilot study, word-classification tasks resembled closely the results from Experiment competing tasks adding one bit to single task performance at comparable measures with G, were significant for both single and competing conditions, under the 2-bit competing presentation. However correlations between G, competing task presentation almost always approached zero.
the same performance tasks and procedure (Letter Series and Letter Counting) for Gr combined data for the card-sorting and I (i.e. parallelism of regression lines with levels of information). Correlations of these with the highest correlation (0.47) obtained and task performance under both single and
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RICHARD D. ROBERTS et al. Table 3. Correlations between measures of task performance and estimates of fluid intelligence (G,), crystallized intelligence (G,) and SAR at different bit-levels (n = 68) Task Single:
O-bit l-bit 2-bit 3-bit Single:
G,
0.04 0.07 0.12 0.29
0.34 0.30 0.33 0.55
0.26
0.24
0.07 0.12 0.20 0.26
0.34 0.35 0.39 0.44
0.17 0.09 0.03 0.21
0.20 0.18 0.12 0.31
0.13 0.14 0.24 0.41
-0.02 0.04 -0.06 0.27
0.21 0.19 0.17 0.24
word-classificorion
2-bit Competing:
plus 2-bit I plus 2-bit 2 plus 2-bit 3 plus 2-bit
Competing:
plus 2 plus 2 plus 2 plus
-0.08
card-sorting
0
2
SAR
G, cord-sorting
word-classification
O-bit l-bit 2-bit 3-bit
There is no obvious explanation of why the present sample performed better under single task conditions than the Ss in Experiment 1, although it may be because only university students were used in this experiment, whereas some Ss in Experiment 1 were not enrolled at a tertiary institution. Despite this difference in speed, however, it might be noted that parallelism of regression lines also obtained in this experiment and that the estimated transmission rate, again, is about 300-350 msec per bit of information processed. Moreover, as can be seen in Fig. l(D), the competing-task condition again acts as though it were adding an extra bit of complexity to the processing requirements of all subjects. Table 3 contains correlations between the performance task measures and measures of intelligence. From the earlier findings of Roberts et af. (1988) it was predicted that correlations of competing task performance with Gr would be higher than correlations of Gr with single task presentation. However, while the correlation between card-sorting scores under competing task performance conditions of Gr is slightly higher for tasks containing 1 and 2 bits, the overall difference between correlation coefficients is zero (0.38 for both single and competing task presentation).* This is largely a function of the 3-bit card-sorting task which acts to reduce the overall difference by having lower correlation with Gr under competing task conditions than under single task presentation. Interestingly, for the competing task at 3 bits, the correlation between word-classification performance and Gr rises to significance (i.e. 0.24 for single word-classification vs 0.41 for competing word-classification at 3 bits). The emergence of this correlation may indicate that some Ss adopt a strategy of enhancing performance on the simpler task when faced with excessive information load. Thus at a point where the competing task has greatest complexity, both primary and secondary task measures share common variance with fluid intelligence. The Roberts et al. (1988) data also showed that card-sorting under lower-bit conditions (O-bit and l-bit) have lower correlation with Gr than card-sorting under the 2-bit condition. However, a decrease in correlation at the 3-bit level was also reported. Since it is known that the 3-bit level is more difficult than the 2-bit level, and since the correlations reversed their trend between the 2and 3-bit level, Roberts et al. (1988) argued that manipulations within Hick’s paradigm represented quantitative (difficulty) not qualitative (complexity) manipulations. However, while the present results are in genera1 agreement with previous results for the competing card-sorting condition, they contradict previous findings for the single task condition (i.e. in the present results there is an increase in correlation from the 2-bit to the 3-bit single task). This difference may also have resulted from the use of different samples in the two studies. It is possible that, for the present group of Ss, the single 3-bit condition was within Ss’ level of maximum attentional capacity. Such an explanation is generally consistent with the interpretation of the data contained in Fig. l(B) and l(D). According to these results, the departure from linearity *When age is partialled out from these correlations there is an overall difference between correlation coefficients (0.40 for single task presentation vs 0.43 for competing task presentation). Even then however, the difference is not as large as that reported by Roberts er al. (1988).
Competing
task performance
453
takes place only at what is putatively a 6-bit level which coincidentally, is the level where the correlation with fluid intelligence begins to share common variance with both primary and secondary tasks. Table 3 also contains correlations between task performance and measures of both crystallized intelligence and SAR. While G, shares a similar pattern of correlations with the various performance measures as Gr, coefficients are, by and large, non-significant. Indeed when fluid intelligence is partialled out from these, all correlations between G, and the performance tasks approach zero (0.02 for single task presentation vs 0.06 for competing task presentation).* While this result is not in agreement with a study conducted by Jenkinson (1983) showing similar magnitude of correlation for Grand G, markers with speed of processing parameters, it is consistent with results generated under the competing task paradigm where typically correlations with G, are not greatly affected by complexity manipulations (see, for example, Stankov, 1983). For SAR the absence of correlations with performance parameters and a trend towards reduced correlations under competing task conditions relative to single task presentation was found. This type of pattern has been found elsewhere in chronometric studies (see for e.g. Roberts, Stankov & Walker, 1991). This finding rules out explanation of the high fluid intelligence-task performance correlations in terms of storage components of working memory. DISCUSSION The present study has shown how information theory can provide a quantitative index of attentional load and, by doing so, allow a comparison of alternative models of processing. Serial processing models would predict an invariant transmission rate (i.e. equivalent slope) in situations where similar requirements operate for simultaneously presented tasks, and strict parallel processing models would either predict an increase in the rate of transmission or invariant transmission rate with the added proviso that obtained regression lines be superimposed. The regression lines obtained in the present experiments for single and competing task conditions indicate invariant transmission rate, but since these are not superimposed, these findings favor serial processing models. The finding of parellel regression lines for the primary task scores under single and competing task conditions in the present study not only provides empirical confirmation of the earlier finding by Roberts et al. (1988) but also provides compelling evidence that transmission rate (and hence processing rate) remains invariant under competing task conditions. Taken together, the present results and those of Roberts et al. (1988) show that parallel processing of different inputs does not occur under the conditions employed, but that information is processed serially, with each additional bit of information increasing reaction time to primary task stimuli by 350-500 msec. These findings may also be taken as indicating that Ss are working to maximum capacity under both the single and competing task conditions in the present experiment. That is, if Ss were working below capacity on any one of the single tasks, linearity of response would not be observed. Similarly, if Ss worked below capacity on competing tasks, the regression line for the primary task under competing task conditions would lose its parallelism with the regression line obtained under single task conditions. Kantowitz (1985) and others have lamented that it is not possible to determine working capacity other than on a subjective basis. The present findings suggest that under conditions where input may be measured in bits of information, an objective indication of working capacity is now available. In earlier studies it has sometimes been suggested that the performance decrement observed under competing task conditions may be explained either in terms of inattentiveness or increased arousal. While there is a performance decrement on the primary task in the present data, the equivalence of slope for the two regression lines renders unlikely explanations of deficit in terms of inattentiveness and/or arousal change. In particular, it cannot be argued that attention has wandered under the more demanding competing task conditions nor can it persuasively be *The correlations task performance measures share with fluid intelligence intelligence (or for that matter SAR) are partialled out from these.
are, conversely,
not affected
if crystallized
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RICHARD D. ROBERTS et al
argued that Ss have found these task conditions more arousing because the increase in difficulty should be expected to interact with arousal levels to produce diverging regression lines. Overall, the data attest to the robustness of Hick’s Law. Not only was the law found to hold under competing task conditions, replicating earlier findings, but it held with the present tasks when the direct measure of performance was output rather than time. Of some significance was the finding that when the two experimental conditions were plotted on a single graph in terms of total information content, the obtained regression line obeyed Hick’s Law when the zero bit information condition was excluded from the analysis. The exclusion of this condition seems well justified since the condition is obviously too far removed from a choice reaction time paradigm. The present findings add to the wealth of evidence which now exists to show that Hick’s Law obtains under a wide range of conditions where decision-making is involved. It would also appear that the present data extend the upper limits of Hick’s Law by employing a competing task paradigm. It is commonly observed that with single task presentation, Hick’s Law consistently breaks down at higher levels of information. This may well be because higher levels of information content in the single task condition result in tasks of excessive difficulty. Once difficulty levels (as defined earlier) reach a ceiling, increases in information content by complexity manipulation may permit an extension of Hick’s Law to higher levels of information content. In turn, the presence of systematic correlations between Hick parameters (obtained under single and competing conditions) and fluid measures of intelligence of Experiment 2 mean that each of these findings has ready application to cognitive models of human ability. For example, within the range of complexity used in the present study, it may be imputed that individual differences in processing rate are responsible, at least in part, for individual differences in Gr. Moreover, because competing presentation conditions generate the highest correlations with markers of G,, it would seem reasonable to conclude that a S’s ability to maximize serial processing rate under increasingly complex informational demands, is related to Gr. Because of the observed parallelism of single and competing conditions, differences in GI cannot be explained away via models emphasising the role of inattentiveness/arousal nor can they be explained away by models which place emphasis on differences in a S’s ability to invoke parallel processes. Instead, what should be seen as crucial in generating a cognitive model of Gr, is the fact that the introduction of an extra bit of complexity leads to better prediction of a S’s ability than any other experimental manipulation. The present emphasis on processing rate as a partial explanation for individual differences in G, is enhanced by consideration of popular conceptualisations of this ability. Gr has in recent times been linked to incidental learning (Horn, 1986). Obviously, being able to process information of a novel kind more quickly and efficiently predisposes individuals to perform better on tasks of an incidental nature.* Moreover, the absence of correlations between Hick manipulations and G, abilities, observed in the present study, become meaningful in this light. G, abilities are generally acquired via repetition or through the overlearning of cognitive strategies. Ability to do G, tasks is often an all or none phenomenon. Consequently, being able to process stimuli quickly and efficiently does not necessarily predispose individuals to perform better on tasks containing this component. In summary, the present study provides evidence that information theory indices permit the quantification of attention. The measurement of attention load in terms of stimulus information is of theoretical and practical use to psychometricians interested in couching intelligence within the framework of attentional processes. The views of theoreticians who hold that intelligence is reflected in part by the speed of processing are supported by the present findings. In replicating and extending findings indicating relationships between information load and performance under competing task conditions, evidence for the relationship between intelligence and complexity has also been strengthened. In addition, the present study provides a means of measuring intelligence in terms of attentional load which may be applied over a wide range of task conditions.
*An anomalous
finding for advocates of the speed of processing paradigm is the finding that with extensive task practice the gradient of reaction time on bits approaches zero (Mowbray & Rhodes, 1959). However, within the present framework this result is easily integrated, since when reaction time tasks tap into non-incidental learning they would no longer be expected to share systematic correlations with G,.
Competing Acknowledgements-Our experiment.
thanks
task performance
go to both John Mond and Don Watts for collecting
455 much of the data used in our second
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