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The speed-accuracy transition due to task complexity
INTELLIGENCE
22, I I5- I28 (1996)
The Speed-Accuracy Transition Due to Task Complexity KARL SCHWEIZER Albert-Ludwigs-University,
Germany
The transition of speed into accuracy was investigated by studying different degrees of transformation. A task requiring different numbers of simple exchanges indicating different degrees of complexity was designed for this purpose. The correlations between accuracy, represented by the numbers of correct responses, and ability scores indicated that accuracy is associated with cognitive ability to a greater extent in complex tasks, as compared to simple tasks. Mental speed, represented by the reaction time observed for the most simple task demand, correlated with accuracy in the more complex demands. A reduction of the correlations between accuracy and cognitive abilities was observed due to the removal of mental speed. The percentage of reduction in common variance varied between 30% and 40% for the highest degree of complexity.
Before the advent of psychometric tests, attempts were made to measure cognitive ability by means of reaction time tests, because mental speed represented by reaction time was assumed to considerably contribute to cognitive ability (see Berger, 1982). So-called mental tests applied by Galton and other researchers served this purpose. Also, mental speed was regarded as being the source of the correlation between reaction time and performance in tests on cognitive ability (e.g., Peak & Boring, 1926; Thorndike, Bregman, Cobb, & Woodyard, 1927). However, this explanation of the relationship was soon called into question (see McFarland, 1928). Conceptual considerations led to the suggestion that the explanation is restricted to tests that were administered under timed conditions. It could no longer be applied to the relationship between mental speed and test performance observed under untimed conditions, although empirical evidence suggesting such a relationship was made available. Substantial correlations between scores obtained under timed and untimed conditions were observed (e.g., Lord, 1956), as well as between reaction times and test scores observed under untimed conditions (e.g., Vernon & Kantor, 1986; Vernon, Nador, & Kantor, 1985). Despite these findings, the restriction of the argument as to the relationship between reaction time and timed ability test scores has long been a major problem of the speed-ability hypothesis.
The author is very grateful to Arthur R. Jensen and Philip A. Vernon for useful suggestions. Correspondence and requests for reprints should be sent to Karl Schweizer, Psychologisches Institut, Albert-Ludwigs-UniversitPt, Belfortstrape 16, 79106 Freiburg, F.R.G. 115
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SCHWEIZER
Nowadays, a trade-off between mental speed and limitations of the information-processing system is assumed to be the primary source of the correlation between measures of mental speed and test performance observed under untimed conditions. Limited capacity theories that account for this correlation were formulated by various researchers (e.g., Eysenck, 1986, 1987; Jensen, 1982, 1987a, 1992a, 1992b; Kyllonen & Cristal, 1989, 1990; Lehrl & Fischer, 1988; Necka, 1992; Vernon, 1983, 1987). According to all of these theories, limitations of the information-processing system are responsible for the transformation of speed or efficiency into the number of correct responses in a given test performance. The concept of a working memory system, proposed by Baddeley (1986), proved to be especially useful in explaining the transformation. Such a system includes an active part for performing cognitive operations and a passive part for storing information. This concept suggests a trade-off between the amount of information held and the amount processed simultaneously (Vernon, 1983). According to Jensen (1992a, 1992b) there is a race between the speed and efficiency of processing and the rate of decay of information in the working memory system. Individual differences in mental speed are thus transformed into individual differences in accuracy in information processing. Furthermore, individual differences in characteristic features of the information-processing system are assumed to contribute to those observed in reaction time as well as in intellectual ability. These are differences in working memory capacity, in breadth of declarative knowledge, and procedural knowledge (Kyllonen & Christal, 1989). Accordingly, empirical findings show that the efficiency of components of the working memory system correlates with ability test scores (e.g., Kyllonen & Cristal, 1990; Lehrl & Fischer, 1988; Necka, 1992; Vernon, 1983). Although the proposed transformation is not demonstrated by these results, the assumption of a trade-off is supported. This study was designed to provide such a demonstration by showing a gradual transition of speed into accuracy that is represented by the number of correct responses. Such a transition must include several partial transformations of increasing degrees of completeness to make the change obvious. According to the various limited capacity theories, such a demonstration requires one to apply tasks that are capacity demanding to the information-processing system. The speed-accuracy transition should become obvious in tasks that are capacity demanding to different degrees. The concept of complexity helps to differentiate between tasks that are capacity demanding to a greater or lesser degree (Crawford, 199 1). Complex tasks are usually regarded as being more capacity demanding than simple tasks. A transformation is more likely to occur in complex tasks than in simple tasks. Accordingly, Jenkinson (1983) observed that error was only correlated with cognitive ability at complex levels of processing. Furthermore, in experiments including complex tasks, the number of correct responses rather than processing time was used for representing efficiency (e.g., Roberts, Beh, Spilsbury, & Stankov, 1991; Roberts, Beh, & Stankov, 1988). Additionally, a
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limited degree of specificity of a transformation can be expected due to individual task characteristics because investigations into the structural properties of reaction times indicated diversity (e.g., Kranzler & Jensen, 1991; Schweizer, 1993, 1994a). Consequently, a task including several experimental treatments corresponding to different degrees of complexity was designed for this study. These levels gave rise to several expectations. First, a decrease in the number of correct responses and an increase in reaction time were expected to occur when the degree of complexity was increased. Second, correct responses observed in complex tasks were expected to show higher correlations with cognitive ability than those observed in simple tasks. Additionally, mental speed, measured in elementary cognitive tasks (Carroll, 1981; Jensen, 1987b) was expected to show a negative relationship with the number of correct responses observed in complex tasks.
METHOD
Participants The sample included 100 university students (55 female and 45 male). The mean age of the sample was 23.4 years of age, with a standard deviation of 2.9. A mean Advanced Progressive Matrices (APM) score of 25.17 (SD = 4.90) was observed. The participants received a financial reward for their participation.
Description of the Exchange Task The experimental task required the participants to compare two lists composed of five figures each, and to determine the number of exchanges necessary for obtaining identical lists. Only pairwise exchanges of neighboring figures were allowed. In the beginning, a fixation point was shown in the middle of a screen. After 800 ms, this point was replaced by the first list. After another 1,000 ms, the second list appeared below the first one. An example of a pair of lists as they were presented on the screen is included in the upper part of Figure 1. In the example, the second, third, and fourth figures of the first and second lists differed. A participant might have mastered this task by mentally exchanging the second and third figures (the vertical line and the cross) of the second list in the first step. As a consequence, the vertical line would now be in the third position. In the next step, the new third and the fourth figures (the vertical line and the equal sign) would be exchanged to finally obtain a second list corresponding to the first list. This way the participant would have found out that two exchanges were necessary. The participants were instructed to determine the number of successive exchanges of neighboring figures as fast as possible, and to press the response key after completing this task. Afterward, the figures were masked by stars and the participants were requested to input the number of exchanges using the keyboard. No feedback on the appropriateness of the trial was provided in order to
SCHWEIZER
118
First Second
x+= Ixl+=-
List List
Treatment (Incomplete 1
+-+
Level Lists)
2
3
4
5
6
X-+ +X-
X-+ +-X
-Xl+ l-+X
x-I+ +X/-
X-I+ +-IX
Figure 1. Complete pair of lists (upper part) and incomplete lists according to the six treatment levels (lower part) (examples).
avoid frustration about erroneous responses in the more demanding treatment levels. There were six treatment levels, each differing in the number of figures that needed to be exchanged and the number of exchanges. Examples of these treatment levels are included in the lower part of Figure 1. These lists are incomplete in order to make the difference between the first and the second lists more obvious. 1.
2.
3.
4.
In the first treatment level, one exchange including two figures was required. This level did not challenge a participant’s information-processing capacity, because there was no alternative but to exchange the two figures. It represented the lowest degree of complexity. The reaction time obtained for this treatment level was selected to represent mental speed. In the second treatment level, two exchanges including three figures were required. However, because there was another level also involving three figures, the participants really had to perform the mental exchanges. This level was regarded as being the second degree of complexity. The third treatment level also required the participant to exchange three figures. However, three exchanges were now needed. It represented the third degree of complexity. The reordering of four figures was necessary in the fourth treatment level. Corresponding lists could be achieved by exchanging three figures. This treatment level was regarded as being the fourth degree of complexity because of the increase in the number of figures required to be reordered.
SPEED-ACCURACY
5. 6.
TRANSITION
In this treatment level, four figures needed four exchanges. It served as the fifth degree Five exchanges involving four figures were ment level, which posed the highest degree
119
to be reordered by performing of complexity. necessary in the highest treatof complexity.
In summary, only one solution was to be considered in the case where two figures needed to be exchanged, whereas at least two alternatives existed in all the other cases. The number of the treatment level was proportional to either the number of exchanges or the number of figures involved. There were 12 trials per treatment level. The trials were arranged in a quasirandom order. The experimental trials were preceded by 10 practice trials. Each participant received detailed instructions. The experimenter made sure that a proper understanding of the task existed before beginning the experimental trials. Individual measurements of the processing time as well as information on the correctness of the participants’ responses were stored on hard disk. Ability Scales Raven’s (1962) APM and a reasoning were administered to the participants. letters and numbers that were arranged (e.g., 6 8 10 11 14 16 18 20 22). The letter or number.
scale selected from Horn’s (1962) LPS The reasoning scale included series of in a regular manner with one exception participants had to identify the irregular
Procedure The exchange task was presented first. Afterward, the ability scales were applied in the following order: first the reasoning scale and then the APM. The APM was administered for 40 min and the reasoning scale for 8 min (according to the manuals). In order to also have a measure of untimed performance, the reasoning scale was applied a second time. After the end of the first application, the participants were given a colored pencil and instructed go on with this test until no further improvement could be expected. Usually, a participant worked for another 10 minutes on this task. Data Treatment and Statistical Investigation The median of the individual measurements was determined for representing a participant’s reaction time. Because the distributions of most reaction times and the numbers of correct responses were strongly skewed, Spearman-Rank correlations were computed in investigating relationships. Partial correlations were computed by means of the regression analysis of SPSS (Norusis, 1988). However, its application was restricted to the reaction time of the first treatment level
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SCHWEIZER
and the numbers of correct responses of the fifth and sixth treatment because these variables showed the least degree of skewness.
levels,
RESULTS The reaction times were expected to increase when the degree of complexity was increased, whereas numbers of correct responses were expected to decrease, because every increase in complexity should challenge the limitations of the processing system more severely than the previous one. Findings supporting these expectations are included in Table 1. The means showed the expected increase with respect to complexity. Whereas a mean reaction time of 1,695 ms was observed for the first treatment level, a time of 14,3 19 ms for the sixth level was observed. There was an almost linear increase in reaction time. The mean reaction time in the first treatment level was rather slow. This slowness was due to the number of individual figures to be encoded. According to research in preattentive processing, reaction time depends on the amount of material, even if it is presented outside the focus of attention (Schweizer, 1994b, 1995). The mean values of correct responses showed a monotonic decrease with respect to the treatment levels. The mean of the first treatment level, 11.72 correct responses, was quite large because errors were observed for only a few participants. In contrast, in the sixth treatment level, a mean of 7.62 correct responses indicated that a considerable number of participants were unable to identify the correct number of exchanges in several trials. The minimum number of correct responses even indicated that in the third, fifth, or sixth treatment level, at least one participant
Means, Standard
Treatment
Level
TABLE 1 Deviations, Skewnesses, Minimums, and Maximums and Numbers of Correct Responses (n = 100)
M
of Reaction Times,
SD
Skewness
Minimum
Maximum
449 I.526 2,822 4.020 5,861 8,720
I .75 1.06 1.27 2.15 1.15 2.10
I .060 I.855 2.255 2,325 3,260 2,010
3,990 10,400 16,660 30,015 32,170 5 1,455
I .04 1.88 2.88 2.42 3.12 3.42
5.26 2.63 I.87 1.10 .95 .83
4.00 1.00 .oo 2.00 .oo .oo
12.00 12.00 12.00 12.00 12.00 12.00
Reaction Time
I
1,695 4,661 6,502 8,61 I 5 12,014 6 14,319 Number of Correct Responses I I I .72 2 10.72 3 9.84 4 9.71 5 8.33 6 7.62
2 3 4
SPEED-ACCURACY
121
TRANSITION
was incorrect in all of the trials. The third column shows that all distributions were skewed. The lowest degrees of skewness were found for the numbers of correct responses of the fifth and sixth treatment levels (.95 and .83). Adjustments of Reaction Times A short reaction time as well as a maximum number of incorrect responses were observed for a few participants with respect to the sixth treatment level. Obviously, these participants did not really try to identify the correct number of exchanges of figures. They probably felt unable to meet the demands in this treatment level and, consequently, limited their effort. The reaction times of these participants did not represent the processing time that would have been observed in true attempts to solve the task. Therefore, it was decided to eliminate the reaction times of the participants yielding only incorrect responses from further investigations. However, this provision was restricted to the treatment levels for which the maximum number of incorrect responses were observed. Correlations of the Ability Scales The Spearman-Rank correlations of the ability scales and the reaction times, as well as the numbers of correct responses, are included in Table 2. Large correlations of cognitive ability and numbers of correct responses were expected for those conditions of greater complexity. The observed correlations widely corresponded to these expectations, as can be seen in the upper part of Table 2. Marginal correlations were found for the first treatment level and substantial correlations for almost all of the other levels. The low correlations in the first treatment level may reflect little variance due to a small number of errors. The
Spearman-Rank
TABLE 2 of Ability Scales and Reaction Times as Well as Numbers of Correct Responses (n = 100)
Correlations
Number of Exchanges Ability Scale _
1
2
Numbers of Correct Responses APMa - ,003 ,282” Reasoninga -.120 .158 Reasoningb - ,027 .192 Reaction Times APMa - .458** - .408** Reasoninga - ,230’ - ,233’ Reasonineb -.267” -.258** aTimed performance. -p < .05. **p < .Ol.
bWith additional
3
4
.331** ,147 .313** - ,224’ -.191 -.213* unlimited time.
5
,434”’ ,190 ,290” - .206* -.191 -.I33
6
.473** ,366’” ,444” -.I39 -.181 -.I56
.488** .369** ,467” -.016 -.I75 -.059
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SCHWEIZER
corresponding increases in magnitude were almost monotonic with only two exceptions. The highest correlation with APM and with the reasoning scale were obtained for the sixth treatment level (r = .488, ,367 and r = .467). These correlations did not differ very much in magnitude from the correlation between APM and the reasoning scale (r = .466 and .467), each of which was expected to represent general ability. The correlations of the reaction times and the ability scales showed trends that opposed the trends observed for the other correlations. Only marginal correlations were obtained for the fifth and sixth treatment levels, whereas substantial correlations were obtained for the first and second levels. The correlations with APM monotonically decreased from the first to the sixth treatment levels. The correlations with the reasoning scale applied under timed as well as untimed conditions showed corresponding trends although deviations existed. The correlations of the first and second treatment levels were rather low, although significant. This finding was probably due to participants applying either a safety or a risky strategy because winsorization (see Winer, 1971) led to increases in absolute magnitude over 0.30 for the first and second treatment levels. In order to test the hypothesis that there is a reciprocal relationship between the correlation of ability and reaction time and the correlation of ability and the number of correct responses as a function of the complexity of the task (Jensen, 1992a), correlations between the coefficients of the first and fourth, the second and fifth, as well as the third and sixth rows of Table 2 were computed. The correlation between the APM rows is - .90 (Rank-order correlation = - 1.O, p < .05), between the upper reasoning rows - .79 (Rank-order correlation = - .78, ns), and between the lower reasoning rows - .82 (Rank-order correlation = -.83, p < .05). Correlations of Reaction Times and Numbers of Correct Responses The transition of speed into accuracy was expected to modify the relationship between reaction time and number of correct responses. The respective correlations are included in Table 3. In the first treatment level, the reaction time was expected to represent mental speed because the capacity limit of the informationprocessing system should not be challenged by the task demands. Therefore, errors were not assumed to occur as a result of the speed-accuracy transformation in this level. The results supported these expectations. The reaction time and the number of correct responses did not correlate in the first treatment level Y = - .107).Also, the correct responses did not correlate with any of the other reaction times. In contrast, the reaction time substantially correlated with all of the other numbers of correct responses. This finding indicated that every other level leads to a transformation of speed into accuracy. The results of the second treatment level showed some degree of transformation. In this level, a moderate correlation of the reaction time and the number of correct responses was observed (1. = - .387). Additionally, the reaction time
SPEED-ACCURACY
Spearman-Rank
Treatment Level of Correct Responses
I
-.I07 - ,370 p.202 -.317 - ,229 - .339
2 3 4 5 6 .05.
p i
TABLE 3 Correlations of Reaction Times and Numbers of Correct Responses (n = 100) Treatment Level of Reaction Times
I
,’ i
123
TRANSITION
2 ,051 -.387 -.201 - .350 -.26l -.263
3
4
5
6
~ ,003 -.I23 ,090 .034 - ,092
,106 -.I64 .043 -.I67 -.065
,008 - ,059 ,078 ,033 .019
-.053 - ,020 ,213 .I21 ,075
-.I18
-.I09
- .043
-.008
.Ol
with the numbers of correct responses of higher levels, whereas the number of correct responses of this level only correlated with the reaction time of the first treatment level. The reaction times of the remaining treatment levels showed only one correlation that reached the level of significance. Because only 1 correlation in 20 was considered significant, this result was probably due to chance. In summary, these findings indicate that the main transition occurs between the first and the third treatment levels.
correlated
Partial Correlations of Correct Responses and Ability Scales Partial correlations were computed in order to investigate the contribution of mental speed to the relationship between the number of correct responses and the ability scales. Therefore, the reaction time of the first treatment level was removed from the correlations of the number of correct responses and the APM, as well as from the reasoning scale administered under timed and untimed conditions. The computation was restricted to the fifth and sixth treatment levels, because the skewnesses of the correct responses were comparably low in these levels. Furthermore, the sample was reduced to 90 participants by winsorization (e.g., Winer, 1971) according to the overall number of errors in order to most accurately obtain correlations representing the true relationship. This way participants applying either a safety or a risky strategy were excluded from the sample. The results are included in Table 4. The second, third, and fourth columns include the correlations between intelligence and accuracy as well as reaction time, and between accuracy and reaction time. Some of the correlations reported in this table differ from corresponding correlations included in Tables 2 and 3, because the regression procedure of SPSS yields Pearson correlations and winsorization was also applied to the sample. The partial correlations are included in the fifth column. A comparison of the coefficients included in the second and the fifth
124
Correlations
SCHWEIZER
TABLE 4 and Partial Correlations of Selected Ability Scales (IQ), Number of Correct Responses (NR), and Reaction Times (RT) (n = 90) Correlation
Ability Scale APMa Reasoning= Reasoningb
Exchanges 5 6 5 6 5 6
=Timed performance.
of
NR-IQ
RT-IQ
RT-NR
,504 ,466 ,382 .361 ,461 ,417
- .490 -.490 - .351 -.351 -.330 - .330
-.30 -.32 -.30 - .32 -.30 -.32
bWith additional
Partial Correlation (NR-IQ.RT) .43 .37 .31 .28 .40 .35
Reduction in Common Variance (o/o) 21.2 35.6 34.6 40.5 23.8 30.0
unlimited time
columns indicates that in all cases, partialing out the reaction time led to a reduction in magnitude. The sixth column gives the percentage of the reduction in common variance observed due to this operation. From the numbers it is obvious that between 23% and 40% of the common variance is due to mental speed. In all cases, a stronger reduction in common variance was obtained for the sixth treatment level than the fifth treatment level. The reduction was especially high with respect to the reasoning scale administered under timed conditions. The consistency of the reductions in magnitude was most striking. Therefore, the combination of these results was submitted to a statistical test. At first, the z-differences between the zero order and the partial correlations were computed. The corresponding probabilities were 0.26 and 0.22 for APM, 0.29 and 0.27 for reasoning under timed condition and 0.3 1 and 0.30 for reasoning under untimed condition. Then the investigation was extended to those combinations of results that could be assumed to be independent of each other either due to the treatment levels or to the scales. Accordingly, the results of the APM and the reasoning scale under timed conditions were combined. Also the results of the APM and the reasoning scale under untimed conditions were combined. The probability of the first combination of results (0.26, 0.22, 0.29, 0.27) was smaller than the probability of a combination of events of which the probability was 0.29 (0.29, 0.29,0.29,0,29). According to the bionomial test, the probability of this combination was 0.007 (= 0.294). The respective probability of the results obtained for APM and the reasoning scale under untimed condition was 0.009 (= 0.314).
DISCUSSION The transition of speed into accuracy was investigated by exposing participants to task demands that were characteristic of working memory tasks. Preliminary results were to be produced and stored for further use in later steps both before
SPEED-ACCURACY
TRANSITION
12.5
and after pairs of items were reordered by the central processor. The efficiency of this system was probably challenged more by the storing and the retrieving of the preliminary results than by the individual exchanges. A trade-off between mental speed and limitations of the information-processing system was assumed to occur when several items were to be stored and retrieved. Different numbers of exchange operations were required by the various treatment levels except in the fourth level. The mean reaction times of the treatment levels showed corresponding increases. The working memory system provides various opportunities for errors to occur. Preliminary results may be lost or inaccurately remembered. Furthermore, inappropriate exchanges may occur. This type of error is probably rare, because these operations are quite efficient due to their frequent use. Loss or inappropriate retrieval are ordinarily due to decay, which happens when the system is too slow. Therefore, the occurrence of error can be assumed to depend on mental speed. These considerations are supported by the results. The reaction time obtained for the first treatment level negatively correlates with the numbers of correct responses of the higher treatment levels. Obviously, in the higher levels the task demands enforce the transformation of individual differences in mental speed into individual differences in the number of correct responses. The main part of the transformation of speed into accuracy occurs between the first and third treatment levels. Although the efficiency of the transformation increases up to the sixth level, the initial effect is more dramatic than the effects of higher levels. No transformation is observed in the first treatment level. In this case, the storing of preliminary results is not required. In contrast, storage operations are required due to the task demands of the other levels. Obviously, the additional operations greatly enhance the probability of errors. The correlations of the numbers of correct responses and the ability scales observed in the third, fourth, fifth, and sixth treatment levels support these expectations. The considerations concerning the working memory system suggest that there is no fundamental difference in processing due to ability testing under timed and in processing under untimed conditions. The individual tasks included in an ability scale are to be regarded as being rather independent challenges to the working memory system. In each case, mental speed as well as the limitations of the system substantially contribute to the likelihood of finding a correct solution as long as enough testing time is available. Otherwise, the difficulty of a task would be of no importance and a participant would always arrive at the correct solution within the limits of testing time. Furthermore, the difficulty of an individual task cannot be predicted from its position within a series of tasks in mental testing. Processing in a reaction time task seems to be more similar to processing under untimed conditions as compared to timed conditions because time is not restricted. Therefore, it is not surprising that slightly larger correlations between the reasoning scale and reaction time as well as accuracy were obtained for untimed than for timed conditions.
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SCHWEIZER
Furthermore, a cautionary note concerning “timed” and “untimed” testing needs to be added. A definite testing time (e.g., 10 minutes) can be defined as timed testing for one participant but as untimed testing for another participant who is more capable. Additionally, motivation needs to be considered. When the testing time is very long, the motivation for an additional effort is usually quite low. Both these arguments are to be considered in planning a study. In this study, the APM as well as the reasoning scale were applied according to the guidelines of the manuals, thus guaranteeing comparability with the results of other studies. However, some participants did not require all of the provided time for completing APM. Furthermore, participants do not usually spend much more time on completing the APM when additional time is made available, probably because of lack of motivation. In contrast, in applying the reasoning scale for a second time, as done in this study, motivation is not a problem, because the testing time according to the manual is only 8 minutes. In this case, the subjects spent a lot more time on this test so the results of the second administration are really due to power testing. Therefore, the procedure selected for this study possesses the advantage that the results can be compared with the test norms and that in the untimed conditions the limits are really tested. Finally, the substantial reduction in the amount of common variance due to the elimination of mental speed needs to be emphasized. Through this observation, it is clear that speed is really transformed into accuracy. The degree of transformation shows an increase from the fifth to the sixth treatment level, the latter of which is more demanding to the working memory system. Although the reduction is considerable, it is incomplete. Obviously, individual differences in mental speed are not the only sources of individual differences in performance on ability tests. As already indicated in the introductory section, further contributions can be expected from individual differences in capacity limitation, in declarative knowledge and in procedural knowledge. Additionally, it needs to be indicated that the reduction in common variance due to mental speed is incomplete. In comparing the percentage in reduction with the percentage of the variance of ability test scores predicted by reaction time composites in independent studies (e.g., Kranzler & Jensen, 1991; Schweizer, 1994a; Vernon, 1983), it becomes obvious that the transformation of speed into accuracy is incomplete. Task demands requiring other mental operations can be considered to yield the additional transformation. REFERENCES Baddeley, A. (1986). Working memory. Oxford: Clarendon Press. Berger, M. (1982). The “scientific approach” to intelligence: An overview of its history with special reference to mental speed. In H.J. Eysenck (Ed.), A model for intelligence.New York: Springer. Canoll, J. B. (198 I). Ability and task difficulty in cognitive psychology. Educarional Researcher. IO. 11-21.
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Crawford, J.D. (1991). Intelligence, task complexity and the distinction between automatic and effortful mental processing. In H.A.H. Rowe (Ed.), Inrelligence: Reconceprualizurion and measurement. Hillsdale. NJ: Erlbaum. Eysenck, H.J. (1986). The theory of intelligence and the psychophysiology of cognition. In R.J. Stemberg (Ed.), Advances in psychology of human intelligence (Vol. 3). Hillsdale, NJ: Erlbaum. Eysenck, H.J. (1987). Speed of information processing, reaction time, and the theory of intelligence. In P.A. Vernon (Ed.), Speed of information-processing and inrefligence. Norwood. NJ: Ablex
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Schweizer, K. (1995). The effect of task demand and stimulus relevance on preattentive processing. Perceptual and Motor Skills. 80, 1I23- 1128. Thorndike, E.L., Bregman, E.O., Cobb, M.V., & Woodyard, E. (1927). The measurement of intelligence. New York: Teachers College Press. Vernon, P.A. (1983). Speed of information processing and general intelligence. Intelligence, 7, 5370. Vernon, P.A. (1987). New developments in reaction time research. In P.A. Vernon (Ed.), Speed of information-processing and intelligence. Norwood, NJ: Ablex. Vernon, P.A., & Kantor, L. (1986). Reaction time correlations with intelligence test scores obtained under either timed or untimed conditions. Intelligence. 10. 315-330. Vernon, P.A., Nador, S., & Kantor, L. (1985). Reaction times and speed-of-processing: Their relationship to timed and untimed measures of intelligence. Intelligence, 9, 357-374. Winer, B.J. (1971). Statistical principles in experimental designs (2nd ed.). New York: McGrawHill.
22, I I5- I28 (1996)
The Speed-Accuracy Transition Due to Task Complexity KARL SCHWEIZER Albert-Ludwigs-University,
Germany
The transition of speed into accuracy was investigated by studying different degrees of transformation. A task requiring different numbers of simple exchanges indicating different degrees of complexity was designed for this purpose. The correlations between accuracy, represented by the numbers of correct responses, and ability scores indicated that accuracy is associated with cognitive ability to a greater extent in complex tasks, as compared to simple tasks. Mental speed, represented by the reaction time observed for the most simple task demand, correlated with accuracy in the more complex demands. A reduction of the correlations between accuracy and cognitive abilities was observed due to the removal of mental speed. The percentage of reduction in common variance varied between 30% and 40% for the highest degree of complexity.
Before the advent of psychometric tests, attempts were made to measure cognitive ability by means of reaction time tests, because mental speed represented by reaction time was assumed to considerably contribute to cognitive ability (see Berger, 1982). So-called mental tests applied by Galton and other researchers served this purpose. Also, mental speed was regarded as being the source of the correlation between reaction time and performance in tests on cognitive ability (e.g., Peak & Boring, 1926; Thorndike, Bregman, Cobb, & Woodyard, 1927). However, this explanation of the relationship was soon called into question (see McFarland, 1928). Conceptual considerations led to the suggestion that the explanation is restricted to tests that were administered under timed conditions. It could no longer be applied to the relationship between mental speed and test performance observed under untimed conditions, although empirical evidence suggesting such a relationship was made available. Substantial correlations between scores obtained under timed and untimed conditions were observed (e.g., Lord, 1956), as well as between reaction times and test scores observed under untimed conditions (e.g., Vernon & Kantor, 1986; Vernon, Nador, & Kantor, 1985). Despite these findings, the restriction of the argument as to the relationship between reaction time and timed ability test scores has long been a major problem of the speed-ability hypothesis.
The author is very grateful to Arthur R. Jensen and Philip A. Vernon for useful suggestions. Correspondence and requests for reprints should be sent to Karl Schweizer, Psychologisches Institut, Albert-Ludwigs-UniversitPt, Belfortstrape 16, 79106 Freiburg, F.R.G. 115
116
SCHWEIZER
Nowadays, a trade-off between mental speed and limitations of the information-processing system is assumed to be the primary source of the correlation between measures of mental speed and test performance observed under untimed conditions. Limited capacity theories that account for this correlation were formulated by various researchers (e.g., Eysenck, 1986, 1987; Jensen, 1982, 1987a, 1992a, 1992b; Kyllonen & Cristal, 1989, 1990; Lehrl & Fischer, 1988; Necka, 1992; Vernon, 1983, 1987). According to all of these theories, limitations of the information-processing system are responsible for the transformation of speed or efficiency into the number of correct responses in a given test performance. The concept of a working memory system, proposed by Baddeley (1986), proved to be especially useful in explaining the transformation. Such a system includes an active part for performing cognitive operations and a passive part for storing information. This concept suggests a trade-off between the amount of information held and the amount processed simultaneously (Vernon, 1983). According to Jensen (1992a, 1992b) there is a race between the speed and efficiency of processing and the rate of decay of information in the working memory system. Individual differences in mental speed are thus transformed into individual differences in accuracy in information processing. Furthermore, individual differences in characteristic features of the information-processing system are assumed to contribute to those observed in reaction time as well as in intellectual ability. These are differences in working memory capacity, in breadth of declarative knowledge, and procedural knowledge (Kyllonen & Christal, 1989). Accordingly, empirical findings show that the efficiency of components of the working memory system correlates with ability test scores (e.g., Kyllonen & Cristal, 1990; Lehrl & Fischer, 1988; Necka, 1992; Vernon, 1983). Although the proposed transformation is not demonstrated by these results, the assumption of a trade-off is supported. This study was designed to provide such a demonstration by showing a gradual transition of speed into accuracy that is represented by the number of correct responses. Such a transition must include several partial transformations of increasing degrees of completeness to make the change obvious. According to the various limited capacity theories, such a demonstration requires one to apply tasks that are capacity demanding to the information-processing system. The speed-accuracy transition should become obvious in tasks that are capacity demanding to different degrees. The concept of complexity helps to differentiate between tasks that are capacity demanding to a greater or lesser degree (Crawford, 199 1). Complex tasks are usually regarded as being more capacity demanding than simple tasks. A transformation is more likely to occur in complex tasks than in simple tasks. Accordingly, Jenkinson (1983) observed that error was only correlated with cognitive ability at complex levels of processing. Furthermore, in experiments including complex tasks, the number of correct responses rather than processing time was used for representing efficiency (e.g., Roberts, Beh, Spilsbury, & Stankov, 1991; Roberts, Beh, & Stankov, 1988). Additionally, a
SPEED-ACCURACYTRANSITION
117
limited degree of specificity of a transformation can be expected due to individual task characteristics because investigations into the structural properties of reaction times indicated diversity (e.g., Kranzler & Jensen, 1991; Schweizer, 1993, 1994a). Consequently, a task including several experimental treatments corresponding to different degrees of complexity was designed for this study. These levels gave rise to several expectations. First, a decrease in the number of correct responses and an increase in reaction time were expected to occur when the degree of complexity was increased. Second, correct responses observed in complex tasks were expected to show higher correlations with cognitive ability than those observed in simple tasks. Additionally, mental speed, measured in elementary cognitive tasks (Carroll, 1981; Jensen, 1987b) was expected to show a negative relationship with the number of correct responses observed in complex tasks.
METHOD
Participants The sample included 100 university students (55 female and 45 male). The mean age of the sample was 23.4 years of age, with a standard deviation of 2.9. A mean Advanced Progressive Matrices (APM) score of 25.17 (SD = 4.90) was observed. The participants received a financial reward for their participation.
Description of the Exchange Task The experimental task required the participants to compare two lists composed of five figures each, and to determine the number of exchanges necessary for obtaining identical lists. Only pairwise exchanges of neighboring figures were allowed. In the beginning, a fixation point was shown in the middle of a screen. After 800 ms, this point was replaced by the first list. After another 1,000 ms, the second list appeared below the first one. An example of a pair of lists as they were presented on the screen is included in the upper part of Figure 1. In the example, the second, third, and fourth figures of the first and second lists differed. A participant might have mastered this task by mentally exchanging the second and third figures (the vertical line and the cross) of the second list in the first step. As a consequence, the vertical line would now be in the third position. In the next step, the new third and the fourth figures (the vertical line and the equal sign) would be exchanged to finally obtain a second list corresponding to the first list. This way the participant would have found out that two exchanges were necessary. The participants were instructed to determine the number of successive exchanges of neighboring figures as fast as possible, and to press the response key after completing this task. Afterward, the figures were masked by stars and the participants were requested to input the number of exchanges using the keyboard. No feedback on the appropriateness of the trial was provided in order to
SCHWEIZER
118
First Second
x+= Ixl+=-
List List
Treatment (Incomplete 1
+-+
Level Lists)
2
3
4
5
6
X-+ +X-
X-+ +-X
-Xl+ l-+X
x-I+ +X/-
X-I+ +-IX
Figure 1. Complete pair of lists (upper part) and incomplete lists according to the six treatment levels (lower part) (examples).
avoid frustration about erroneous responses in the more demanding treatment levels. There were six treatment levels, each differing in the number of figures that needed to be exchanged and the number of exchanges. Examples of these treatment levels are included in the lower part of Figure 1. These lists are incomplete in order to make the difference between the first and the second lists more obvious. 1.
2.
3.
4.
In the first treatment level, one exchange including two figures was required. This level did not challenge a participant’s information-processing capacity, because there was no alternative but to exchange the two figures. It represented the lowest degree of complexity. The reaction time obtained for this treatment level was selected to represent mental speed. In the second treatment level, two exchanges including three figures were required. However, because there was another level also involving three figures, the participants really had to perform the mental exchanges. This level was regarded as being the second degree of complexity. The third treatment level also required the participant to exchange three figures. However, three exchanges were now needed. It represented the third degree of complexity. The reordering of four figures was necessary in the fourth treatment level. Corresponding lists could be achieved by exchanging three figures. This treatment level was regarded as being the fourth degree of complexity because of the increase in the number of figures required to be reordered.
SPEED-ACCURACY
5. 6.
TRANSITION
In this treatment level, four figures needed four exchanges. It served as the fifth degree Five exchanges involving four figures were ment level, which posed the highest degree
119
to be reordered by performing of complexity. necessary in the highest treatof complexity.
In summary, only one solution was to be considered in the case where two figures needed to be exchanged, whereas at least two alternatives existed in all the other cases. The number of the treatment level was proportional to either the number of exchanges or the number of figures involved. There were 12 trials per treatment level. The trials were arranged in a quasirandom order. The experimental trials were preceded by 10 practice trials. Each participant received detailed instructions. The experimenter made sure that a proper understanding of the task existed before beginning the experimental trials. Individual measurements of the processing time as well as information on the correctness of the participants’ responses were stored on hard disk. Ability Scales Raven’s (1962) APM and a reasoning were administered to the participants. letters and numbers that were arranged (e.g., 6 8 10 11 14 16 18 20 22). The letter or number.
scale selected from Horn’s (1962) LPS The reasoning scale included series of in a regular manner with one exception participants had to identify the irregular
Procedure The exchange task was presented first. Afterward, the ability scales were applied in the following order: first the reasoning scale and then the APM. The APM was administered for 40 min and the reasoning scale for 8 min (according to the manuals). In order to also have a measure of untimed performance, the reasoning scale was applied a second time. After the end of the first application, the participants were given a colored pencil and instructed go on with this test until no further improvement could be expected. Usually, a participant worked for another 10 minutes on this task. Data Treatment and Statistical Investigation The median of the individual measurements was determined for representing a participant’s reaction time. Because the distributions of most reaction times and the numbers of correct responses were strongly skewed, Spearman-Rank correlations were computed in investigating relationships. Partial correlations were computed by means of the regression analysis of SPSS (Norusis, 1988). However, its application was restricted to the reaction time of the first treatment level
120
SCHWEIZER
and the numbers of correct responses of the fifth and sixth treatment because these variables showed the least degree of skewness.
levels,
RESULTS The reaction times were expected to increase when the degree of complexity was increased, whereas numbers of correct responses were expected to decrease, because every increase in complexity should challenge the limitations of the processing system more severely than the previous one. Findings supporting these expectations are included in Table 1. The means showed the expected increase with respect to complexity. Whereas a mean reaction time of 1,695 ms was observed for the first treatment level, a time of 14,3 19 ms for the sixth level was observed. There was an almost linear increase in reaction time. The mean reaction time in the first treatment level was rather slow. This slowness was due to the number of individual figures to be encoded. According to research in preattentive processing, reaction time depends on the amount of material, even if it is presented outside the focus of attention (Schweizer, 1994b, 1995). The mean values of correct responses showed a monotonic decrease with respect to the treatment levels. The mean of the first treatment level, 11.72 correct responses, was quite large because errors were observed for only a few participants. In contrast, in the sixth treatment level, a mean of 7.62 correct responses indicated that a considerable number of participants were unable to identify the correct number of exchanges in several trials. The minimum number of correct responses even indicated that in the third, fifth, or sixth treatment level, at least one participant
Means, Standard
Treatment
Level
TABLE 1 Deviations, Skewnesses, Minimums, and Maximums and Numbers of Correct Responses (n = 100)
M
of Reaction Times,
SD
Skewness
Minimum
Maximum
449 I.526 2,822 4.020 5,861 8,720
I .75 1.06 1.27 2.15 1.15 2.10
I .060 I.855 2.255 2,325 3,260 2,010
3,990 10,400 16,660 30,015 32,170 5 1,455
I .04 1.88 2.88 2.42 3.12 3.42
5.26 2.63 I.87 1.10 .95 .83
4.00 1.00 .oo 2.00 .oo .oo
12.00 12.00 12.00 12.00 12.00 12.00
Reaction Time
I
1,695 4,661 6,502 8,61 I 5 12,014 6 14,319 Number of Correct Responses I I I .72 2 10.72 3 9.84 4 9.71 5 8.33 6 7.62
2 3 4
SPEED-ACCURACY
121
TRANSITION
was incorrect in all of the trials. The third column shows that all distributions were skewed. The lowest degrees of skewness were found for the numbers of correct responses of the fifth and sixth treatment levels (.95 and .83). Adjustments of Reaction Times A short reaction time as well as a maximum number of incorrect responses were observed for a few participants with respect to the sixth treatment level. Obviously, these participants did not really try to identify the correct number of exchanges of figures. They probably felt unable to meet the demands in this treatment level and, consequently, limited their effort. The reaction times of these participants did not represent the processing time that would have been observed in true attempts to solve the task. Therefore, it was decided to eliminate the reaction times of the participants yielding only incorrect responses from further investigations. However, this provision was restricted to the treatment levels for which the maximum number of incorrect responses were observed. Correlations of the Ability Scales The Spearman-Rank correlations of the ability scales and the reaction times, as well as the numbers of correct responses, are included in Table 2. Large correlations of cognitive ability and numbers of correct responses were expected for those conditions of greater complexity. The observed correlations widely corresponded to these expectations, as can be seen in the upper part of Table 2. Marginal correlations were found for the first treatment level and substantial correlations for almost all of the other levels. The low correlations in the first treatment level may reflect little variance due to a small number of errors. The
Spearman-Rank
TABLE 2 of Ability Scales and Reaction Times as Well as Numbers of Correct Responses (n = 100)
Correlations
Number of Exchanges Ability Scale _
1
2
Numbers of Correct Responses APMa - ,003 ,282” Reasoninga -.120 .158 Reasoningb - ,027 .192 Reaction Times APMa - .458** - .408** Reasoninga - ,230’ - ,233’ Reasonineb -.267” -.258** aTimed performance. -p < .05. **p < .Ol.
bWith additional
3
4
.331** ,147 .313** - ,224’ -.191 -.213* unlimited time.
5
,434”’ ,190 ,290” - .206* -.191 -.I33
6
.473** ,366’” ,444” -.I39 -.181 -.I56
.488** .369** ,467” -.016 -.I75 -.059
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SCHWEIZER
corresponding increases in magnitude were almost monotonic with only two exceptions. The highest correlation with APM and with the reasoning scale were obtained for the sixth treatment level (r = .488, ,367 and r = .467). These correlations did not differ very much in magnitude from the correlation between APM and the reasoning scale (r = .466 and .467), each of which was expected to represent general ability. The correlations of the reaction times and the ability scales showed trends that opposed the trends observed for the other correlations. Only marginal correlations were obtained for the fifth and sixth treatment levels, whereas substantial correlations were obtained for the first and second levels. The correlations with APM monotonically decreased from the first to the sixth treatment levels. The correlations with the reasoning scale applied under timed as well as untimed conditions showed corresponding trends although deviations existed. The correlations of the first and second treatment levels were rather low, although significant. This finding was probably due to participants applying either a safety or a risky strategy because winsorization (see Winer, 1971) led to increases in absolute magnitude over 0.30 for the first and second treatment levels. In order to test the hypothesis that there is a reciprocal relationship between the correlation of ability and reaction time and the correlation of ability and the number of correct responses as a function of the complexity of the task (Jensen, 1992a), correlations between the coefficients of the first and fourth, the second and fifth, as well as the third and sixth rows of Table 2 were computed. The correlation between the APM rows is - .90 (Rank-order correlation = - 1.O, p < .05), between the upper reasoning rows - .79 (Rank-order correlation = - .78, ns), and between the lower reasoning rows - .82 (Rank-order correlation = -.83, p < .05). Correlations of Reaction Times and Numbers of Correct Responses The transition of speed into accuracy was expected to modify the relationship between reaction time and number of correct responses. The respective correlations are included in Table 3. In the first treatment level, the reaction time was expected to represent mental speed because the capacity limit of the informationprocessing system should not be challenged by the task demands. Therefore, errors were not assumed to occur as a result of the speed-accuracy transformation in this level. The results supported these expectations. The reaction time and the number of correct responses did not correlate in the first treatment level Y = - .107).Also, the correct responses did not correlate with any of the other reaction times. In contrast, the reaction time substantially correlated with all of the other numbers of correct responses. This finding indicated that every other level leads to a transformation of speed into accuracy. The results of the second treatment level showed some degree of transformation. In this level, a moderate correlation of the reaction time and the number of correct responses was observed (1. = - .387). Additionally, the reaction time
SPEED-ACCURACY
Spearman-Rank
Treatment Level of Correct Responses
I
-.I07 - ,370 p.202 -.317 - ,229 - .339
2 3 4 5 6 .05.
p i
TABLE 3 Correlations of Reaction Times and Numbers of Correct Responses (n = 100) Treatment Level of Reaction Times
I
,’ i
123
TRANSITION
2 ,051 -.387 -.201 - .350 -.26l -.263
3
4
5
6
~ ,003 -.I23 ,090 .034 - ,092
,106 -.I64 .043 -.I67 -.065
,008 - ,059 ,078 ,033 .019
-.053 - ,020 ,213 .I21 ,075
-.I18
-.I09
- .043
-.008
.Ol
with the numbers of correct responses of higher levels, whereas the number of correct responses of this level only correlated with the reaction time of the first treatment level. The reaction times of the remaining treatment levels showed only one correlation that reached the level of significance. Because only 1 correlation in 20 was considered significant, this result was probably due to chance. In summary, these findings indicate that the main transition occurs between the first and the third treatment levels.
correlated
Partial Correlations of Correct Responses and Ability Scales Partial correlations were computed in order to investigate the contribution of mental speed to the relationship between the number of correct responses and the ability scales. Therefore, the reaction time of the first treatment level was removed from the correlations of the number of correct responses and the APM, as well as from the reasoning scale administered under timed and untimed conditions. The computation was restricted to the fifth and sixth treatment levels, because the skewnesses of the correct responses were comparably low in these levels. Furthermore, the sample was reduced to 90 participants by winsorization (e.g., Winer, 1971) according to the overall number of errors in order to most accurately obtain correlations representing the true relationship. This way participants applying either a safety or a risky strategy were excluded from the sample. The results are included in Table 4. The second, third, and fourth columns include the correlations between intelligence and accuracy as well as reaction time, and between accuracy and reaction time. Some of the correlations reported in this table differ from corresponding correlations included in Tables 2 and 3, because the regression procedure of SPSS yields Pearson correlations and winsorization was also applied to the sample. The partial correlations are included in the fifth column. A comparison of the coefficients included in the second and the fifth
124
Correlations
SCHWEIZER
TABLE 4 and Partial Correlations of Selected Ability Scales (IQ), Number of Correct Responses (NR), and Reaction Times (RT) (n = 90) Correlation
Ability Scale APMa Reasoning= Reasoningb
Exchanges 5 6 5 6 5 6
=Timed performance.
of
NR-IQ
RT-IQ
RT-NR
,504 ,466 ,382 .361 ,461 ,417
- .490 -.490 - .351 -.351 -.330 - .330
-.30 -.32 -.30 - .32 -.30 -.32
bWith additional
Partial Correlation (NR-IQ.RT) .43 .37 .31 .28 .40 .35
Reduction in Common Variance (o/o) 21.2 35.6 34.6 40.5 23.8 30.0
unlimited time
columns indicates that in all cases, partialing out the reaction time led to a reduction in magnitude. The sixth column gives the percentage of the reduction in common variance observed due to this operation. From the numbers it is obvious that between 23% and 40% of the common variance is due to mental speed. In all cases, a stronger reduction in common variance was obtained for the sixth treatment level than the fifth treatment level. The reduction was especially high with respect to the reasoning scale administered under timed conditions. The consistency of the reductions in magnitude was most striking. Therefore, the combination of these results was submitted to a statistical test. At first, the z-differences between the zero order and the partial correlations were computed. The corresponding probabilities were 0.26 and 0.22 for APM, 0.29 and 0.27 for reasoning under timed condition and 0.3 1 and 0.30 for reasoning under untimed condition. Then the investigation was extended to those combinations of results that could be assumed to be independent of each other either due to the treatment levels or to the scales. Accordingly, the results of the APM and the reasoning scale under timed conditions were combined. Also the results of the APM and the reasoning scale under untimed conditions were combined. The probability of the first combination of results (0.26, 0.22, 0.29, 0.27) was smaller than the probability of a combination of events of which the probability was 0.29 (0.29, 0.29,0.29,0,29). According to the bionomial test, the probability of this combination was 0.007 (= 0.294). The respective probability of the results obtained for APM and the reasoning scale under untimed condition was 0.009 (= 0.314).
DISCUSSION The transition of speed into accuracy was investigated by exposing participants to task demands that were characteristic of working memory tasks. Preliminary results were to be produced and stored for further use in later steps both before
SPEED-ACCURACY
TRANSITION
12.5
and after pairs of items were reordered by the central processor. The efficiency of this system was probably challenged more by the storing and the retrieving of the preliminary results than by the individual exchanges. A trade-off between mental speed and limitations of the information-processing system was assumed to occur when several items were to be stored and retrieved. Different numbers of exchange operations were required by the various treatment levels except in the fourth level. The mean reaction times of the treatment levels showed corresponding increases. The working memory system provides various opportunities for errors to occur. Preliminary results may be lost or inaccurately remembered. Furthermore, inappropriate exchanges may occur. This type of error is probably rare, because these operations are quite efficient due to their frequent use. Loss or inappropriate retrieval are ordinarily due to decay, which happens when the system is too slow. Therefore, the occurrence of error can be assumed to depend on mental speed. These considerations are supported by the results. The reaction time obtained for the first treatment level negatively correlates with the numbers of correct responses of the higher treatment levels. Obviously, in the higher levels the task demands enforce the transformation of individual differences in mental speed into individual differences in the number of correct responses. The main part of the transformation of speed into accuracy occurs between the first and third treatment levels. Although the efficiency of the transformation increases up to the sixth level, the initial effect is more dramatic than the effects of higher levels. No transformation is observed in the first treatment level. In this case, the storing of preliminary results is not required. In contrast, storage operations are required due to the task demands of the other levels. Obviously, the additional operations greatly enhance the probability of errors. The correlations of the numbers of correct responses and the ability scales observed in the third, fourth, fifth, and sixth treatment levels support these expectations. The considerations concerning the working memory system suggest that there is no fundamental difference in processing due to ability testing under timed and in processing under untimed conditions. The individual tasks included in an ability scale are to be regarded as being rather independent challenges to the working memory system. In each case, mental speed as well as the limitations of the system substantially contribute to the likelihood of finding a correct solution as long as enough testing time is available. Otherwise, the difficulty of a task would be of no importance and a participant would always arrive at the correct solution within the limits of testing time. Furthermore, the difficulty of an individual task cannot be predicted from its position within a series of tasks in mental testing. Processing in a reaction time task seems to be more similar to processing under untimed conditions as compared to timed conditions because time is not restricted. Therefore, it is not surprising that slightly larger correlations between the reasoning scale and reaction time as well as accuracy were obtained for untimed than for timed conditions.
126
SCHWEIZER
Furthermore, a cautionary note concerning “timed” and “untimed” testing needs to be added. A definite testing time (e.g., 10 minutes) can be defined as timed testing for one participant but as untimed testing for another participant who is more capable. Additionally, motivation needs to be considered. When the testing time is very long, the motivation for an additional effort is usually quite low. Both these arguments are to be considered in planning a study. In this study, the APM as well as the reasoning scale were applied according to the guidelines of the manuals, thus guaranteeing comparability with the results of other studies. However, some participants did not require all of the provided time for completing APM. Furthermore, participants do not usually spend much more time on completing the APM when additional time is made available, probably because of lack of motivation. In contrast, in applying the reasoning scale for a second time, as done in this study, motivation is not a problem, because the testing time according to the manual is only 8 minutes. In this case, the subjects spent a lot more time on this test so the results of the second administration are really due to power testing. Therefore, the procedure selected for this study possesses the advantage that the results can be compared with the test norms and that in the untimed conditions the limits are really tested. Finally, the substantial reduction in the amount of common variance due to the elimination of mental speed needs to be emphasized. Through this observation, it is clear that speed is really transformed into accuracy. The degree of transformation shows an increase from the fifth to the sixth treatment level, the latter of which is more demanding to the working memory system. Although the reduction is considerable, it is incomplete. Obviously, individual differences in mental speed are not the only sources of individual differences in performance on ability tests. As already indicated in the introductory section, further contributions can be expected from individual differences in capacity limitation, in declarative knowledge and in procedural knowledge. Additionally, it needs to be indicated that the reduction in common variance due to mental speed is incomplete. In comparing the percentage in reduction with the percentage of the variance of ability test scores predicted by reaction time composites in independent studies (e.g., Kranzler & Jensen, 1991; Schweizer, 1994a; Vernon, 1983), it becomes obvious that the transformation of speed into accuracy is incomplete. Task demands requiring other mental operations can be considered to yield the additional transformation. REFERENCES Baddeley, A. (1986). Working memory. Oxford: Clarendon Press. Berger, M. (1982). The “scientific approach” to intelligence: An overview of its history with special reference to mental speed. In H.J. Eysenck (Ed.), A model for intelligence.New York: Springer. Canoll, J. B. (198 I). Ability and task difficulty in cognitive psychology. Educarional Researcher. IO. 11-21.
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Crawford, J.D. (1991). Intelligence, task complexity and the distinction between automatic and effortful mental processing. In H.A.H. Rowe (Ed.), Inrelligence: Reconceprualizurion and measurement. Hillsdale. NJ: Erlbaum. Eysenck, H.J. (1986). The theory of intelligence and the psychophysiology of cognition. In R.J. Stemberg (Ed.), Advances in psychology of human intelligence (Vol. 3). Hillsdale, NJ: Erlbaum. Eysenck, H.J. (1987). Speed of information processing, reaction time, and the theory of intelligence. In P.A. Vernon (Ed.), Speed of information-processing and inrefligence. Norwood. NJ: Ablex
Horn. W. ( 1962). Leistun~spriif~~sfem [Efficiency-test-system). Giittingen: Hogrefe. Jenkinson, J.C. (1983). Is speed of information processing related to fluid or to crystallized intelligence’? Inrelligence. 7. 9 I - 106. Jensen, A.R. (1982). The chronometry of intelligence. In R.J. Stembeg (Ed.), Advances in research on inielligence (Vol. 1). Hillsdale, NJ: Erlbaum. Jensen, A.R. (1987a). Individual differences in the Hick paradigm. In P.A. Vernon (Ed.), Speed of i~formarion processing and inrelligence. Norwood, NJ: Ablex. Jensen, A.R. (1987b). Psychometric g as a focus of concerted research effort. Intelligence. II. 193198. Jensen, A.R. (1992a). Relation between information-processing time and right/wrong responses. American Journal on Mental Retardation, 97, 290-292. Jensen, A.R. (1992b). Understanding g in terms of information processing. Educational Review, 4, 271-308. Kranzler, J.H., & Jensen, A.R. (1991). The nature of psychometric g: Unitary process or a number of independent processes? Intelligence, 15. 397-422. Kyllonen, P.C., & Christal, R.E. (1989). Cognitive modeling of learning abilities: A status report of LAMP. In R. Dillon & J.W. Pellegrino (Eds.), Testing: Theorefical and applied issues. New York: Freeman. Kyllonen, P.C., & Christal, R.E. (1990). Reasoning ability is (little more than) working-memory capacity?! Intelligence, 14. 389-433. Lehrl, S., & Fischer, B. (1988). The basic parameters of human information processing: Their role in the determination of intelligence. Personality and Individual D#erences, 9. 883-896. Lord, F.M. (1956). A study of speed factors in tests and academic grades. fsyhometrika, 21, 3l50. McFarland, R.A. (1928). The role of speed in mental ability. Psvchological Bullerin, 25. 595-612. Necka, E. (1992). Cognitive analysis of intelligence: The significance of working memory processes. Personality and fndividual Di$erences. 13, 103 I- 1046. Norusis, M.J. (1988). SPSS/PC+ Advanced srarisfics TM V 2.0. Chicago: SPSS Inc. Peak. H., & Boring, E.G. (1926). The factor of speed in intelligence. Journal cf Experimental Psw-hology, 9, 7 I-94. Raven, J.C. (1962). Advanced progressive matrices. London: Lewis & Co., Ltd. Roberts, R.D., Beh, H.C., Spilsbury, G., & Stankov, L. (1991). Evidence for an attentional model of human intelligence using the competing task paradigm. Personality and Individual Diferences. 12, 445-455. Roberts, R.D., Beh, H.C.. & Stankov, L. (1988). Hick’s Law, competing tasks, and intelligence. Intelligence. 12, IOI- 120. Schweizer, K. (1993). Verbal ability and speed of information-processing. Personality and individual Differences. 14. 645-652. Schweizer, K. (1994a). Structural diversity of the speed-ability relationship due to informationprocessing skills. Personality and Individual D$erences. 17. 607-616. Schweizcr, K. (1994b). Focal-attentive and preattentive processes in letter- and figure-search tasks. Perceprrccrl und Motor Shills. 79. I347- 1354.
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