Working memory and intelligence are highly related constructs, but why?

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1 Available online at Intelligence 36 (2008) Working memory and intelligence are highly related constructs, but why? Roberto Colom a,, Francisco J. Abad a, Mª Ángeles Quiroga b, Pei Chun Shih a, Carmen Flores-Mendoza c a Universidad Autónoma de Madrid, Spain b Universidad Complutense de Madrid, Spain c Universidade Federal de Minas Gerais, Belo Horizonte, Brazil Received 18 May 2007; received in revised form 5 January 2008; accepted 8 January 2008 Available online 12 February 2008 Abstract Working memory and the general factor of intelligence (g) are highly related constructs. However, we still don't know why. Some models support the central role of simple short-term storage, whereas others appeal to executive functions like the control of attention. Nevertheless, the available empirical evidence does not suffice to get an answer, presumably because relevant measures are frequently considered in isolation. To overcome this problem, here we consider concurrently simple short-term storage, mental speed, updating, and the control of attention along with working memory and intelligence measures, across three separate studies. Several diverse measures are administered to a total of 661 participants. The findings are consistent with the view that simple shortterm storage largely accounts for the relationship between working memory and intelligence. Mental speed, updating, and the control of attention are not consistently related to working memory, and they are not genuinely associated with intelligence once the short-term storage component is removed Elsevier Inc. All rights reserved. Keywords: Working memory; Intelligence; Short-term storage; Mental speed; Executive functioning; Updating; Controlled attention There are several studies reporting strong relationships, at the latent variable level, between working memory and intelligence (Ackerman, Beier, & Boyle, 2002, 2005; Colom, Rebollo, Palacios, Juan-Espinosa, & Kyllonen, 2004; Colom, Abad, Rebollo, & Shih, 2005; Colom & Shih, 2004; Conway, Cowan, Bunting, Therriault, & Minkoff, 2002; Kane, Hambrick, Tuholski, Wilhelm, Payne, & Engle, 2004; Kyllonen & Christal, Corresponding author. Facultad de Psicología, Universidad Autónoma de Madrid, Madrid, Spain. Tel.: (Voice). address: roberto.colom@uam.es (R. Colom). 1990; Miyake, Friedman, Rettinger, Shah, & Hegarty, 2001; Stauffer, Ree, & Carreta, 1996; Engle, Tuholski, Laughlin, & Conway, 1999). However, the components underlying their strong relationship remain mysterious, despite the research efforts made to date. We think this is because published reports do not comprise a comprehensive and concurrent assessment of the constructs of interest. There are some studies considering verbal and quantitative tasks only (Conway et al., 2002; Engle, Tuholski, et al., 1999), whereas others analyze spatial tasks only (Miyake et al., 2001). There are some studies measuring working memory and short-term memory (Colom, Abad, et al., 2005; Colom, Flores /$ - see front matter 2008 Elsevier Inc. All rights reserved. doi: /j.intell

2 R. Colom et al. / Intelligence 36 (2008) Mendoza, Quiroga, & Privado, 2005; Engle, Tuholski, et al., 1999; Kane et al., 2004), whereas others measure working memory and mental speed (Fry & Hale, 1996). Therefore, researchers undertake hard inferences about the components presumably underlying the relationship between working memory and intelligence. Is mental speed a key component? Is short-term storage capacity? Is the control of attention? Is executive functioning? Still we don't know. 1. Overview of the present studies Working memory tasks comprise short-term storage plus some sort of processing requirements (Conway, Kane, Bunting, Hambrick, Wilhelm, & Engle, 2005; Engle, Kane, & Tuholski, 1999; Miyake & Shah, 1999) so their correlation with intelligence could be attributed to storage, processing, or both. The present studies address the contribution of these storage and processing components. It must be emphasized from the outset that the tasks modelled for measuring the constructs of interest follow the mainstream. This underscoring implicates that here we are not concerned with the question of whether or not executive tasks, for instance, measure what they intend to. The tasks are modelled in ways routinely employed in the literature to tap the considered constructs. Their relationships regarding the working memory intelligence network are explored concurrently. Therefore, short-term storage is operationalized by simple memory span tasks, whereas working memory is defined by complex memory span tasks (Colom, Rebollo, Abad, & Shih, 2006). Engle, Tuholski et al. (1999) declare that tasks thought to be good short-term memory tasks ( ) can be performed with relative removal of attention from the representation of the list items, whereas working memory tasks are characterized as dual tasks in that attention must be shifted back and forth between the representation of the list items and the so-called processing component of the task (p. 314). Miyake et al. (2001) state: for simplicity (and to follow the convention in the field) we hereinafter refer to simple storage-oriented span tasks with no explicit concurrent processing as short-term memory span tasks and to complex span tasks that involve not only a storage requirement but also an explicit concurrent processing requirement as working memory span tasks. According to this classification, traditional verbal span measures such digit and word spans are considered short-term span tasks, whereas more complex span measures such as reading or operation spans are considered working memory span tasks (p. 622). Here we measure short-term memory by tasks requiring the temporary maintenance of verbal, quantitative, or spatial simple items for latter recall, whereas working memory is measured by tasks requiring processing + storage verbal, quantitative, or spatial information. Conway et al. (2005) discuss the problem of scoring procedures for working memory tasks, suggesting that they should exhaust the information collected with a task. Therefore, participants' scores were obtained as the number of correct answers in both the processing and storage sub-tasks. Because the processing component is multi-faceted, we measure mental speed (study 1), mental speed and executive functioning (study 2), and mental speed, executive functioning, and controlled attention (study 3) along with measures of short-term storage, working memory, and intelligence. Mental speed is measured by simple verbal, quantitative, and spatial verification tasks. Participants are requested to verify, as quickly and accurately as possible, if a given test stimulus is presented within a small sized memory set. Note we are tapping the construct of mental speed as a property of the working memory system (i.e. short-term recognition speed). The design expressly avoids tapping constructs such as perceptual speed. We can make this latter argument fully clear by comparing our approach with the study reported by Conway et al. (2002). According to our view, these researchers measured speed by tasks that do not tap directly the construct of interest. Firstly, they used psychometric speed tests (pattern comparison, letter comparison, and digit copying) widely known as measures of perceptual speed (Carroll, 1993). Mental speed may or may not correlate to perceptual speed, but mental speed, as a component of the working memory construct, should implicate at least minimal temporary storage requirements. Secondly, Conway et al.'s (2002) dependent measure was not speed per se, but the total number of correct responses. Thirdly, it is difficult to understand the high correlation between shortterm memory and perceptual speed (.40), but the very low correlation between perceptual speed and working memory (.06) in their study. Finally, the correlation between the perceptual speed factor and intelligence was surprisingly low (.07). For these reasons, we are inclined to suggest that, although interesting, Conway et al.'s (2002) operationalization of the speed component of the working memory construct should be seen with reservations. Executive functioning is usually defined by the control and regulation of mental processes. Miyake, Friedman, Emerson, Witzki, and Howerter (2000) as well as Friedman et al. (2006) analyzed factors representing three executive functions: inhibition, shifting, and updating. Inhibition

3 586 R. Colom et al. / Intelligence 36 (2008) implicates the suppression of automatic responses, shifting requires switching between tasks, and updating is based on the on-line addition or subtraction of information from the working memory system. Given that Friedman et al. (2006) found that only updating was genuinely related to intelligence, we focus here on tasks measuring this executive function (except in study 2, where shifting is also measured). Regarding the control of attention, we follow Baddeley's (2002) advice: the capacity to focus available attentional capacity is clearly an important feature of the central executive. It is however important to acknowledge that not all tasks, or indeed all complex tasks, are heavily dependent on this capacity (p. 90). Therefore, it is interesting to have specific measures of controlled attention. The control of attention can be defined as the ability to maintain mental representations in a highly active state in the presence of interference (Engle, Kane, et al., 1999). Kane and Engle's (2002) review nominates as measures of controlled attention the flanker task, the antisaccade task, or the stroop task, among others (see also Heitz & Engle, 2007). Thus, we measure this construct by means of a quantitative version of the flanker task (Eriksen & Eriksen, 1974) and a version of the Simon task (Simon, 1969). Finally, intelligence is measured by several standardized tests. These tests generally tap the constructs of fluid intelligence (Gf), crystallized intelligence (Gc), and spatial intelligence (Gv). Further, these constructs are collapsed into a single higher-order factor thought to represent general intelligence (g). We acknowledge that other classifications are possible, like perceptual vs. verbal tests (see Johnson & Bouchard, 2005) but we focus on g, so this is not especially relevant here. In summary, here we consider a broad spectrum of verbal, quantitative, and spatial cognitive tasks and tests in order to define factors for working memory, short-term memory, mental speed, executive functioning, controlled attention, and general intelligence as representative as possible (Ackerman et al., 2005). We are looking for the short-term storage and discrete processing components that predict the relationship between working memory and intelligence. 2. Study Method Participants One hundred and eleven participants (70% females) took part in the study to fulfil course requirements. They were recruited at high school (35%) and college institutions (65%). Their mean age was 18.0 (SD = 2.7) Measures Short-term memory was measured by three tasks requiring the temporary maintenance of verbal, quantitative, or spatial simple items for latter recall: forward letter span, forward digit span, and Corsi Block. Forward letter span (FLSPAN) and forward digit span (FDSPAN). Single letters or digits (from 1 to 9) were presented on the computer screen at the rate of one letter or digit per second. Unlimited time was allowed to type in direct order the letters or digits presented. Set size of the experimental trials ranged from three to nine items (7 levels 3 trials each=21 trials total). Letters or digits were randomly grouped to form trials. The score was the number of accurately reproduced trials. Corsi Block. Nine boxes were shown on the computer screen. Three different configurations of boxes changing on each trial were used. One box at a time turned orange for 650 ms each and the order in which they were sequentially highlighted must be remembered. There was unlimited time to respond. The sequences of the experimental trials increased from 3 to 9 (7 levels 3 trials each=21 trials total). The score was the number of boxes reproduced appropriately. Working memory was measured by three tasks requiring processing + storage verbal, quantitative, or spatial requirements: alphabet (Kyllonen & Christal, 1990), computation span (Ackerman et al., 2002), and letter rotation (Miyake et al., 2001). Alphabet. Successor and predecessor operations must be applied to a string with a given number of letters. If the first screen presented the letters B, L, A and the second screen displayed the operation + 1, then the correct response was C, M, B. The string of letters was presented for 3 s, the operation to apply was presented for 1.5 s, and there were unlimited time to enter a response. The trials increased the number of letters from three to seven (5 levels 4 trials each=20 trials total). For two trials within a given block 1 or 2 positions must be added, while for the other two trials 1 or 2 positions must be subtracted. The type of addition and subtraction was randomized within a given block of trials. The score was the number of correct trials. Computation span. This task included a verification task and a recall task. 6 s was allowed to see a math equation (but no time limit was set to verify its accuracy) like (10/2)+ 4=8, and the displayed

4 R. Colom et al. / Intelligence 36 (2008) solution, irrespective of its accuracy, must be remembered. After the final equation of the trial was displayed, the solutions from the equations must be reproduced in their correct serial order. Each math equation included two operations using digits from 1 to 10. The solutions were single-digit numbers. The experimental trials ranged from three to seven equation/solutions (5 levels 3 trials each = 15 trials total). The score was the number of correct answers in the verification and recalling tasks. Letter rotation. Several capital letters were presented sequentially and they can be displayed normal or mirror imaged. Further, the letters can be rotated in one of seven orientations (multiples of 45 ). There was a verification task (is the letter normal or mirror imaged?) and a recall task (the orientation of the displayed letters where was the top of each letter pointing?). The letters were presented for a maximum of 3 s, but no time limit was set to deliver the normal or mirror imaged response. After each set, a grid was depicted to mark the places corresponding to the positions of the tops of the presented letters in their correct serial order. The experimental trials increased progressively in size from two to five letters (4 levels 3 trials, 12 trials total). The score was the number of correct answers in the verification and recalling tasks. Verbal, quantitative, and spatial mental speeds were measured by verification tasks (short-term recognition speed). Participants were requested to verify, as quickly and accurately as possible, if a given test stimulus was presented within a small sized memory set (set sizes always ranged from two to four or five single items). The participants pressed the computer key 1 for a yes answer and the computer key 0 for a no answer. Two main dependent speed measures were used: the standard score, based on mean reaction time to all the trials from correct answers only, and the elementary score, based on the simplest trials (set size =3 for verbal speed and set size=2 for quantitative and spatial speeds) from correct answers only. This distinction was thought to ensure that we were treating this speed component of the working memory system with minimal (although not zero) short-term memory loadings. Verbal speed. Several letters were sequentially displayed for 650 ms each. Those letters defined a memory set comprised by three, four, or five uppercase and lowercase letters. After the last displayed letter, a fixation point appeared for 500 ms. Finally, the probe letter appeared in order to decide, as quickly and accurately as possible, if it had the same meaning as one of the letters presented within the memory set. Therefore, its physical appearance (uppercase or lowercase) must be ignored. Half of the trials requested a positive answer. The experimental trials ranged from three to five letters (3 levels 10 trials each = 30 trials total). The score was the mean RT for the correct answers. Quantitative speed. Several single digits were sequentially displayed for 650 ms each. Those digits defined a memory set comprised by two, three, or four digits. After the last displayed digit, a fixation point appeared for 500 ms. Finally, the probe digit appeared in order to decide, as quickly and accurately as possible, if it can be divided by one of the digits presented within the memory set. Half of the trials requested a positive answer. The experimental trials ranged from two to four digits (3 levels 10 trials each=30 trials total). The score was the mean RT for the correct answers. Spatial speed. Several arrows were sequentially displayed for 800 ms each. Those arrows defined a memory set comprised by two, three, or four arrows. The arrows can be displayed in one of seven orientations (multiples of 45 ). After the last displayed arrow, a fixation point appeared for 500 ms. Finally, the probe arrow appeared in order to decide, as quickly and accurately as possible, if it had the same orientation as one of the arrows presented within the memory set. The arrows have distinguishable shapes in order to guarantee that their orientation is both memorized and evaluated. Half of the trials requested apositiveanswer.theexperimentaltrialsrangedfrom two to four arrows (3 levels 10 trials each=30 trials total). The score was the mean RT for the correct answers. Note that in all these computerized tasks, participants completed a set of three practice trials as many times as desired to ensure they understood the instructions. Finally, intelligence was measured by the inductive reasoning (R) and vocabulary (V) subtests from the Primary Mental Abilities (PMA) Battery (Thurstone, 1938) and by the rotation of solid figures test (Yela, 1969). PMA-R. This test comprises 30 letters' series items. The rule (or rules) underlying a given sequence of letters [a-c-a-c-a-c-a-c] must be extracted in order to select a given letter from a set of six possible alternatives [a-b-c-d-e-f]. Only one alternative is

5 588 R. Colom et al. / Intelligence 36 (2008) Table 1 Correlation matrix, descriptive statistics, and reliability indices (study 1) Tasks and tests Forward letter span Forward digit span Corsi Block Alphabet Computation span Letter rotation Standard verbal speed Standard quantitative speed 9. Standard spatial speed Elementary verbal speed Elementary quantitative speed 12. Elementary spatial speed 13. PMA-reasoning Rotation of solid figures PMA-vocabulary Mean Standard deviation Reliability (α) Note: Correlations of speed measures with the remaining measures are reflected for clarity of interpretation. correct. The score was the total number of correct responses. Rotation of solid figures. This test comprises 21 items. Each item includes a model figure and five alternatives must be evaluated against it. The participant must evaluate which alternative can be rotated within a 3D space to fit the model figure. Only one alternative is correct. The score was the total number of correct responses. PMA-V. This is a synonym test that comprises 50 items. The meaning of four alternative words must be evaluated against a given word that serves as model. For instance, STOUT: Sick Fat Short Rude. Only one alternative is correct. The score was the total number of correct responses Procedure Testing took place in three sessions. The cognitive tasks and intelligence tests were administered either individually or collectively (in groups of no more than 10 participants) for a total of 3 h/sessions approximately. The first and second sessions were dedicated to cognitive tasks, whereas the third session was dedicated to intelligence testing Results The descriptive statistics, raw correlations, and reliability indices are shown in Table 1. SEM analyses are conducted using AMOS 5.0 (Arbuckle, 2003). The models are assessed by the next fit indices. The CMIN/DF (Chi Square/Degrees of Freedom) ratio is first considered given that it is usually taken as a rule of thumb (Jöreskog, 1993). Values showing a good fit must be around 2.0 or lower. Second, the RMSEA index is sensitive to misspecification of the model. RMSEA values between 0 and.05 indicate very good fit, values between.05 and.08 indicate reasonable fit, and values greater than.10 indicate poor fit (Jöreskog, 1993; Byrne, 1998; Ackerman et al., 2002). Finally, CFI is also reported; acceptable values must be larger than.90 (Marsh, Balla, McDonald, 1988). First, we explore the relationships among short-term memory, working memory, and standard mental speed. The fit of this model is quite good: χ 2 (24) =28.95, CMIN/DF=1.2, RMSEA=.043, CFI=.98. Fig. 1 depicts the coefficients between these constructs. Fig. 1 shows a large relationship between short-term memory and working memory (.89). Further, there is a significant relation between working memory and mental speed (.31), whereas the relation between short-term memory and mental speed is non-significant (.12, p =.33). Thus, working memory shares a significant amount of variance with the short-term memory factor, as well as with the mental speed factor. The small (and non-significant) relationship between short-term memory and mental speed is consistent with the negligible storage requirement of the modelled

6 R. Colom et al. / Intelligence 36 (2008) Fig. 1. Confirmatory factor analysis (CFA) testing the relationships among short-term memory (STM), working memory (WM), and mental speed (Speed). Elementary speed results are shown in parenthesis. FLSPAN = forward letter span, FDSPAN = forward digit span. Dashed lines indicate no significant relations. measures of mental speed. This is worth noting, because it could be argued that the low demanding short-term storage requirement of these mental speed tasks reduces their quality as measures of speed mainly. The results tell that this is not the case. Nevertheless, to ensure that the current findings are solid, we test a new model using the elementary speed score, based on the simplest trials (set size =3 for verbal speed and set size=2 for quantitative and spatial speeds) from correct answers only. The fit of this model is very good: χ 2 (24) =31.5, CMIN/DF =1.3, RMSEA=.053, CFI=.98. Fig. 1 depicts the coefficients (in parenthesis) which are almost identical to those obtained from the standard speed scores. Second, the relation between short-term memory and intelligence, between working memory and intelligence, and between mental speed and intelligence is tested, but in separate analyses. The coefficients are.65,.82, and.42, respectively (for elementary mental speed the coefficient is.50). Therefore, short-term memory, working memory, and mental speed are significantly related to intelligence. Third, a model in which the short-term storage and mental speed factors predict working memory is tested (Fig. 2). The fit of this model is excellent: χ 2 (25) =29.9, CMIN/DF=1.2, RMSEA=.042, CFI=.98. Short-term storage predicts working memory with a value of.88, whereas mental speed shows a value of.23. When the elementary speed score is considered, the fit of the model is also appropriate: χ 2 (25) =35.1, CMIN/ DF=1.4, RMSEA=.061, CFI=.97. Further, the regression weights are pretty the same:.86 for short-term storage and.35 for mental speed. Finally, the general model is tested. Short-term storage and mental speed predict working memory. Short-term storage, mental speed, and the working memory residual (variance unpredicted by storage and speed) predict the intelligence factor. The working memory residual (WM-r) is obtained from the variance unexplained by the shortterm memory and mental speed factors. The fit for this model is reasonable: χ 2 (49)=73.79, CMIN/DF=1.5, RMSEA=.068, CFI=.94. Fig. 2. Structural equation model (SEM) testing the relationship of short-term memory and mental speed with working memory. Elementary speed results are shown in parenthesis.

7 590 R. Colom et al. / Intelligence 36 (2008) Fig. 3 shows that the coefficient between short-term memory and intelligence is.63, whereas the coefficient between mental speed and intelligence is.41. Both coefficients are significant (p b.01). However, the coefficient between the working memory residual (WM-r) and intelligence (.38) is not statistically significant (p =.11). These results indicate that shortterm memory and mental speed predict intelligence, whereas the working memory factor (with short-term storage and speed partialed out) does not. Once again, to know if the current findings are solid, we test a new model using the elementary speed score (based on the simplest trials only). The fit of this model is reasonable: χ 2 (49)=84.79, CMIN/DF=1.7, RMSEA=.081, CFI =.92. Fig. 3 depicts the coefficients (in parenthesis) which are almost identical to those obtained from the standard speed scores. The coefficient between short-term memory and intelligence is.59, whereas the coefficient between mental speed and intelligence is.45. Both coefficients are significant (p b.01). However, the coefficient between the working memory residual (WM-r) and intelligence (.34) is not statistically significant (p =.22). This result reinforces the conclusion that short-term memory and mental speed predict intelligence, whereas the working memory factor (with short-term storage and speed partialed out) does not Discussion This study shows that short-term storage and mental speed account for the relationship between working memory and intelligence. Note that 88% of the working memory variance is explained by short-term storage and mental speed. Further, the residual working memory factor (with short-term storage and mental speed partialed out) does not predict individual differences in intelligence: the high coefficient linking working memory (comprising short-term storage and mental speed) and intelligence (.82) turn to be non-significant when short-term memory and short-term recognition speed are statistically removed. Beyond this general finding, the results have several further points of interest. First, short-term memory and working memory share 79% of their variance, whereas working memory and mental speed share 9% of their variance. This suggests that short-term storage is the main component explaining the relationship between working memory and intelligence. Fig. 3. General model testing the relationship of short-term memory, mental speed, and the working memory residual with the intelligence factor. Elementary speed results are shown in parenthesis. FLSPAN = forward letter span, FDSPAN = forward digit span, STM = short-term memory, WM = working memory, WM (r) = working memory residual, Intell = intelligence, PMA-R = reasoning subtest from the Primary Mental Abilities Battery, Solid Figure = rotation of solid figures, PMA-V = vocabulary subtest from the Primary Mental Abilities Battery. Dashed lines indicate no significant relations.

8 R. Colom et al. / Intelligence 36 (2008) To appropriately evaluate the high shared variance between short-term and working memory it is necessary to consider the accumulated empirical evidence: (a) analyzing verbal measures, Engle, Tuholski et al. (1999) and Conway et al. (2002) found that these constructs share 46% and 67% of their variance respectively; (b) considering spatial measures, Miyake et al. (2001) found that they share 74% of their variance; (c) measuring verbal and spatial measures, the re-analysis performed by Colom, Abad et al. (2005) from the Kane et al.'s (2004) dataset found that they share 98% of their variance; (d) like Kane et al. (2004), Colom, Abad et al. (2005) considered verbal and spatial short-term and working memory measures, finding that they share 79% of their variance. Therefore, the average shared variance can be roughly estimated at a value of 75%. Thus, the evidence suggests that short-term and working memory do not reflect sharply distinguishable cognitive limitations (r=.87). Second, mental speed is related to working memory, but not to short-term memory. This suggests that the shortterm storage and mental speed components of the working memory system are only weakly related. Therefore, their contribution to the prediction of intelligence might be considered separately. Further, the contribution of the short-term storage component of working memory must be seen as much more relevant than that of mental speed, which suggests, as stated before, that the temporary storage of the information is the main factor underlying the relationship between working memory and intelligence (Colom & Shih, 2004; Colom, Flores-Mendoza, et al., 2005; Colom, Rebollo, et al., 2006). Third, the relation between short-term memory and intelligence is almost the same as the relation between short-term memory and intelligence when the four-way relationship among short-term memory, working memory, mental speed, and intelligence is analyzed. This result is consistent with the finding reported by Colom, Abad et al. (2005) after the analysis of the three-way relationship among short-term memory, working memory, and intelligence. However, both findings are not consistent with the assumption held by Kane et al. (2004), namely, that the shared variance between working memory and short-term memory reflect executive functioning rather than common short-term storage. Indeed, Colom, Abad et al.'s (2005) findings are consistent with Engle, Tuholski et al. (1999) and Conway et al. (2002) given that the factor representing common storage does not change its nature when the storage component is statistically extracted from the working memory factor. Fourth, the relation between mental speed and intelligence is very close in magnitude to the relation between mental speed and intelligence when the fourway relationship among short-term memory, working memory, mental speed, and intelligence is analyzed (regardless of the consideration of standard or elementary mental speed scores). Thus, the factor representing common mental speed does not change its nature when this processing component is statistically extracted from the working memory factor. Finally, the results are not consistent with the theory proposed by Engle, Kane et al. (1999). This theory assumes that short-term storage has little to do to predict the relationship between working memory and intelligence, as noted above. Further, mental speed should not contribute to the relation between working memory and intelligence. The theory predicts that the central executive (controlled attention) component of the working memory system is responsible for the relationship between working memory and intelligence. Crucially, their theory postulates that controlled attention must be distinguished from shortterm storage and mental speed. The implication is that the residual working memory component obtained after partialing out short-term storage and mental speed must predict individual differences in intelligence. However, the results of this first study indicate that this is not likely. In conclusion, this first study shows that the ability of working memory to predict individual differences in intelligence is no longer statistically significant once its short-term storage and short-term recognition speed components are partialed out. This finding is not consistent with theoretical accounts appealing to other working memory components like executive functioning or controlled attention. Nevertheless, we acknowledge that direct measures of executive functioning and controlled attention must be explicitly considered to strengthen this main conclusion. Factors representing these cognitive functions are required, in addition to short-term storage and mental speed. With this purpose in mind, the second study focuses on the same constructs considered in the first study, but the role of executive functioning is also explicitly addressed. 3. Study Method Participants 261 university undergraduates (80% females) took part in the study. They participated to fulfil a course requirement. Their mean age was 20.2 (SD=3.4) Measures Short-term memory was measured by forward letter span (FLSPAN), forward digit span (FDSPAN), and dot

9 592 R. Colom et al. / Intelligence 36 (2008) memory. FLSPAN and FDSPAN were the same as in study 1. The dot memory task was modelled after Miyake et al. (2001). One five five grid was displayed for 750 ms at the computer screen. Each grid had between two and seven spaces comprising solid dots. After the grid presentation, the locations that contained dots must be recalled, clicking with the mouse on an empty grid. The experimental trials increased from two to seven dots (6 levels 3 trials each=18 trials total). The score was the number of dots correctly reproduced. Working memory was measured by reading span, computation span, and dot matrix. Computation span was the same task administered in study 1. The reading span task was modelled after Kane et al. (2004). Participants verified which discrete sentences, presented in a sequence, did or did not make sense. Sentences were adapted from the Spanish standardization of the Daneman and Carpenter's (1980) reading span test (Elosúa, Gutiérrez, García-Madruga, Luque, & Gárate, 1996). Each display included a sentence and a to-be remembered capital letter. Sentences were words long. As soon as the sentence letter pair appeared, the participant verified whether it did or did not make sense (it did half the time) reading the capital letter for latter recall. Once the sentence was verified by pressing the answer buttons (yes/1 no/2) the next sentence letter pair was presented. At the end of a given set, participants recalled, in their correct serial order, each letter from the set. Set sizes of the experimental trials ranged from 3 to 6 sentence/letter pairs per trial, for a total of 12 trials (4 levels 3 trial =12 trials total). The score was the number of correct answers in the verification and recalling tasks. The dot matrix task was modelled after Miyake et al. (2001). A matrix equation must be verified and then a dot location displayed in a five five grid must be retained. The matrix equation required adding or subtracting simple line drawings and it was presented for a maximum of 4.5 s. Once the response was delivered, the computer displayed the grid for 1.5 s. After a given sequence of equation grid pairs, the grid spaces that contained dots must be recalled clicking with the mouse on an empty grid. The experimental trials increased in size from two to five equations and dots (4 levels 3 trials = 12 trials total). The score was the number of correct answers in the verification and recalling tasks. 1 1 Fig. 1 in Colom, Escorial, Shih, and Privado (2007) shows an example for the dot matrix task. Mental speed was measured by the same short-term recognition speed tasks administered in study 1. However, given that we did not find any effect for the distinction between standard and elementary scores, only standard scores were considered in study 2. Executive functioning (updating and shifting) was measured by 2-back, keep track, and number letter. The 2-back task was modelled after Hockey and Geffen (2004). Upper and lower case letters (B, b, D, d, F, f, N, n) were presented in one of eight equidistant spatial locations around the center of a computer monitor. These positions were 30, 60, 120, 150, 210, 240, 300, and 330 from the vertical axis. No stimuli were presented on the X-axis (90 and 270 ) or the Y-axis (0 and 180 ). Stimuli were presented for 200 ms, and participants had 1300 ms to respond. There were 66 experimental stimuli of which 21 were target stimuli. Participants pressed the space bar of the keyboard to make a target response (a letter presented in the same spatial location 2 positions back in the sequence). The score was the number of correct answers. Keep track was modelled after Miyake et al. (2000). In each trial, participants saw several target categories at the bottom of the computer screen. Fifteen items, including two or three exemplars from each of the six possible categories (Odd, even, vowel, consonant, lowercase pairs of letters, and uppercase pairs of letters) were then presented serially and in random order for 1500 ms each, with the target categories remaining at the bottom of the screen. The task was to remember the last item presented in each target category and then write down the items at the end of the trial. For example, if the target categories were odd, consonant, and even, then, at the end of the trial, participants recalled the last odd number, the last consonant, and the last even number in the list. Therefore, participants had to monitor the items presented and update their memory representations for the appropriate categories when the presented item was a member of one of the target categories. Before the task begins, participants see all categories and the exemplars in each to ensure that they know to which category each item belong and then practice with three target categories. After the practice trials, they performed three trials with four target categories, and three trials with five target categories, recalling a total of 27 items. The number of items recalled correctly was the dependent measure. The number letter task was modelled after Miyake et al. (2000). A number letter pair (4B) was presented in one of four quadrants on the computer screen. Participants were instructed to indicate whether the number is odd (by pressing the computer key 1) or even (by pressing the computer key 0) (2, 4, 6, and 8 for even;

10 R. Colom et al. / Intelligence 36 (2008) , 5, 7, and 9 for odd) when the number letter pair was presented in either of the top two quadrants and to indicate whether the letter was a consonant (by pressing the computer key 1) or a vowel (by pressing the computer key 0) (G, K, M, and R for consonant; A, E, I, and U for vowel) when the number letter pair was presented in either of the bottom two quadrants. The number letter pair was presented only in the top two quadrants for the first block of 32 trials, only in the bottom two quadrants for the second block of 32 trials, and in a clockwise rotation around all four quadrants for the third block of 128 trials. The trials within the first two blocks required no task switching, whereas half of the trials in the third block required participants shifting between these two types of categorization operations. In all trials participants responded by button press (1 for even or vowel and 0 for odd or consonant) and the next stimulus was presented 150 ms after the response. The shift cost was the difference between the average RTs of the trials in the third block that required a mental shift (trials from the upper left and lower right quadrants) and the average RTs of the trials from the first two blocks in which no shifting was necessary. Note that for all these computerized tasks, participants completed a set of three practice trials as many times as desired to ensure they understood the instructions. Finally, fluid intelligence was measured by the abstract reasoning (AR) subtest from the Differential Aptitude Test (DAT) Battery (Bennett, Seashore, & Wesman, 1990) and the inductive reasoning (R) subtests from the Primary Mental Abilities (PMA) Battery (Thurstone, 1938). Crystallized intelligence was measured by the verbal reasoning (VR) subtest from the DAT and the vocabulary (V) subtest from the PMA. Spatial intelligence was measured by the mental rotation (S) subtest from the PMA and the rotation of solid figures test (Yela, 1969). PMA-R, PMA-V, and rotation of solid figures were the same tests administered in study 1. Table 2 Correlation matrix, descriptive statistics, and reliability indices (study 2) Tests and tasks DAT-AR PMA-R PMA E Solid figures 5. DAT-VR PMA-V FLSPAN FDSPAN Dot memory 10. Reading span 11. Computation span 12. Dot matrix Verbal speed 14. Quant Speed 15. Spatial speed Back Keep.23 track 18. Number letter Mean , SD Reliability (α) NA.79 NA Note: Correlations of speed measures with the remaining measures are reflected for clarity of interpretation. NA = not available.

11 594 R. Colom et al. / Intelligence 36 (2008) DAT-AR is a series test based on abstract figures. Forty items are comprised in this test. Each item includes four figures following a given rule, and the participant must choose one of five possible alternatives. The score was the total number of correct responses. DAT-VR is a reasoning test comprising 40 items. A given sentence stated like an analogy must be completed. The first and last words from the sentence are missing, so a pair of words must be selected to complete the sentence from five possible alternative pairs of words. For instance: is to water like eating is to (A) Travelling Driving, (B) Foot Enemy, (C) Drinking Bread, (D) Girl Industry, (E) Drinking Enemy. Only one alternative is correct. The score was the total number of correct responses. PMA-S comprises 20 items. Each item includes a model figure and six alternatives must be evaluated against it. Some alternatives are simply rotated versions of the model figure, whereas the remaining figures are mirror imaged. Only the rotated figures must be selected. Several alternatives could be correct for each item. The score was the total number of correct responses (appropriately selected figures simply rotated) minus the total number of incorrect responses (inappropriately selected figures mirror imaged) Procedure Testing took place in four sessions 1 h each. Intelligence tests and cognitive tasks were collectively administered in groups of no more than 20 participants for a total of 4 h approximately. The first and second sessions were dedicated to intelligence testing, whereas the third and fourth sessions were dedicated to cognitive tasks Results The descriptive statistics, raw correlations, and reliability indices are shown in Table 2. SEM analyses are conducted using AMOS 5.0. The models are assessed by the same fit indices described in study 1. First, we explore the relationships among short-term memory, working memory, mental speed, and executive functioning. The fit of this model is very good: χ 2 (48)= 82.16, CMIN/DF=1.7, RMSEA=.052, CFI=.94. Fig. 4 depicts the resulting coefficients between these constructs. Fig. 4 shows a large relationship between short-term memory and working memory (.83). Working memory correlates.38 with mental speed, whereas the relation between short-term memory and mental speed is.26. Fig. 4. Confirmatory factor analysis (CFA) testing the relationships among short-term memory, working memory, mental speed, and executive functioning. FLSPAN = forward letter span, FDSPAN = forward digit span.

12 R. Colom et al. / Intelligence 36 (2008) Note the high correlation (.90) between working memory and the executive factor. This latter correlation deserves some comment, because Table 2 shows that keep track and number letter are much higher correlated with computation span and dot matrix than between themselves and with 2- back. Further, keep track shows higher correlations with the three measures of short-term memory than with the other executive measures. The implication is that the executive factor is not particularly well defined, and that their measures reflect a great storage component. Note that this is a usual finding and cannot be attributed to the particular measures modelled in the present study. Thus, for instance, Miyake et al. (2001) noticed that although the correlation among executive tasks are frequently lower than with other withinconstruct correlations zero-order correlations of this magnitude (often.30 or less) are common among executive tasks, partly because they involve a good deal of variance related to non-executive processes as well as measurement error (p. 630). The correlations among the executive tasks and the remaining measures discussed above suggest that the non-executive processes of the former are strongly related to temporary storage. Second, the relation between short-term memory and intelligence, between working memory and intelligence, between mental speed and intelligence, and between executive functioning and intelligence is tested, but in separate analyses. The resulting coefficients are.56,.69,.51, and.86 respectively. Therefore, all the cognitive factors are significantly related to intelligence. Third, short-term storage, mental speed, and executive functioning predict working memory. This model reveals which factors are significant predictors of working memory. However, this model must take into account the correlation between the predictors. To overcome this multicollinearity problem, the shortterm storage factor is defined by all the measures (Conway et al., 2002), whereas the speed and executive factors are defined by variance orthogonal to the storage factor (Fig. 5). Importantly, Fig. 5 shows that the nature of the short-term memory factor remains the same when the other six measures contribute to its variance (note the weights for FLSPAN, FDSPAN, and dot memory in Figs. 4 and 5). The fit of this model is good: χ 2 (45) = 95.3, CMIN/DF=2.1, RMSEA=.066, CFI =.92. Fig. 5 shows that short-term storage predicts working memory to a high degree (.85). Interestingly, removing the simple storage variance from the executive factor Fig. 5. Structural equation model (SEM) testing the relationship of executive functioning, short-term memory and mental speed with working memory. Dashed lines indicate no significant relations.

13 596 R. Colom et al. / Intelligence 36 (2008) Fig. 6. General model testing the relationship of short-term memory and the working memory residual with the general factor of intelligence. Specific measures for fluid intelligence, crystallized intelligence, and spatial intelligence are omitted for simplicity. has dramatic effects on their measures; all the regression weights turn to be non-significant. This is largely consistent with the argument made above concerning the storage component of the executive measures. Mental speed does not predict working memory either, even when the short-term memory factor predicts spatial speed only. 2 Finally, the general model is tested: given that shortterm memory is the single predictor of working memory, short-term memory (STM) and the working memory variance unpredicted by STM (WM-r) are allowed to predict the intelligence factor (Fig. 6). The fit of this 2 One anonymous reviewer tested an alternative model to that shown in Fig. 5: STM, executive (Exec), and speed factors are correlated, and these three factors predict WM. The reviewer's conclusion was: there is a strong correlation between the STM and Exec factors, and comparatively speaking, none of the partial regression weights relating the more elemental factors to WM appears to be very substantial in impact. For example, the Exec to WM partial regression weight, although apparently large in magnitude (.84) comes with a large standard error, with a parameter-to-s.e. t ratio less than 2.0. The chi-square change of 7 is significant at pb0.01, but only marginally. The factorial correlations between Exec and WM, between STM and WM, and between Speed and WM in the model are 0.89, 0.83, and 0.39, respectively. These results seem to suggest that it is the common variability shared between the more elemental factors, particularly between the STM and Exec factors, that is the most predictive of WM. Given that the Exec factor in the present study was defined using variables also involving the STM mechanisms but the STM factor was indicated by variables involving minimum executive functions, the common variability shared between the two factors is plausibly more of the STM rather than the Exec mechanisms. Therefore, the implication is pretty the same to that derived from Fig. 5, which reinforces our theoretical interpretation. model is very good: χ 2 (48) =81.6, CMIN/DF =1.7, RMSEA=.052, CFI =.97. Fig. 6 shows that short-term storage and the working memory residual predict the intelligence factor. Therefore, short-term storage does not fully account for the relationship between working memory and intelligence. The obtained working memory residual contains variance, not tapped by short-term memory, accounting for the relationship with intelligence Discussion The results comprise several points of interest. First, short-term storage predicts working memory to a high degree (72% of explained variance). This is consistent with study one. Second, mental speed does not predict working memory variance. This result is not consistent with study one and cannot be explained by the fact that shortterm memory is allowed to predict speed measures. Note that the storage factor actually predicts one single speed measure. Third, the executive factor is not a significant predictor of working memory once its storage component is removed. As Table 2 shows, executive measures are more related to short-term and working memory measures than among themselves. Leaving executive components alone has the effect of erasing their relationship to the working memory factor. Fourth, the general model shows that both short-term storage and working memory variance unpredicted by the former significantly predict the intelligence factor. Given that the executive and speed factors are not related to working memory, these factors were not