MEMORY, 2006, 14 (7), 804 813
The real relationship between short-term memory and working memory Roberto Colom and Pei Chun Shih Universidad Auto´noma de Madrid, Spain Carmen Flores-Mendoza Universidade Federal de Minas Gerais, Brazil Ma A´ngeles Quiroga Universidad Complutense de Madrid, Spain
Storage-oriented memory span tasks with no explicit concurrent processing are usually referred as shortterm memory (STM) tasks, whereas tasks involving storage plus concurrent processing requirements are designated as working memory (WM) tasks. The present study explores a question that remains unsolved: Do STM and WM tasks clearly tap distinguishable theoretical constructs? For that purpose, a large sample of 403 participants was tested through 12 diverse memory span tasks. Half of those tasks are widely accepted as measures of STM, whereas the other half measure WM. The results show that STM and WM share largely overlapping underlying capacity limitations, suggesting that all memory span tasks tap essentially the same construct. Some implications are discussed.
That working memory (WM) has a key role in cognition is beyond any reasonable doubt. However, it is also a matter of fact that there is no consensus in cognitive psychology regarding its nature (Shah & Miyake, 1999). First, WM cannot be easily distinguished from the construct of short-term memory (STM). Thus, for instance, Anderson (1990) suggested that STM and WM are quite similar constructs, Seamon and Kenrick (1994) postulated that WM is a subset of STM, and Cowan (1995) proposed that STM is a subset of WM. Second, some researchers emphasise the unitary nature of the WM system (Anderson, Reder, & Lebiere, 1996; Colom, Abad, Rebollo, & Shih, 2005; Colom, Rebollo, Abad, & Shih, in press; Colom, Rebollo, Palacios, Juan-Espinosa, & Kyllonen, 2004; Colom & Shih, 2004; Kyllonen
& Christal, 1990), while others support its nonunitary character (Mackintosh & Bennett, 2003; Martin, 1993; Shah & Miyake, 1996). Third, some authors claim that individual differences in WM capacity come from the variation in the total amount of mental capacity (Carpenter, Just, & Shell, 1990; Just & Carpenter, 1992), while others state that long-term memory accounts for those individual differences in WM (Ericsson & Kintsch, 1995). The present study focuses on an issue that remains unsolved, namely the relationship between storage-oriented and processing-plusstorage memory span measures (Engle, Tuholski, Laughlin, & Conway, 1999; Kane, Hambrick, Tuholski, Wilhelm, Payne, & Engle, 2004; Miyake, Friedman, Rettinger, Shah, & Hegarty, 2001).
Address correspondence to: Roberto Colom, Facultad de Psicologı´a, Universidad Auto´noma de Madrid, 28049 Madrid, Spain. E-mail:
[email protected] The research referred to in this article was supported by a grant funded by the Spanish Ministerio de Ciencia y Tecnologia (Grant No. BSO2002-01455.)
# 2006 Psychology Press, an imprint of the Taylor & Francis Group, an informa business http://www.psypress.com/memory DOI:10.1080/09658210600680020
SHORT-TERM MEMORY AND WORKING MEMORY
Classical span measures such as digit or letter span are considered STM tasks, whereas measures such as reading or operation spans are considered WM tasks. WM tasks implicate the engagement in coordination of processing and storage requirements. It is assumed that concurrent processing interferes with storage (Engle et al., 1999). STM and WM tasks share their requirement of temporary storage of the information of interest, but the latter requires some extra component. The straight theoretical implication is that WM tasks cannot be satisfactorily carried out relying only on the same components required to successfully perform STM tasks. STM and WM must not be restricted by the same underlying capacity limitations if they are different psychological constructs. Several studies have analysed the relationship between STM and WM at a latent variable level. Engle et al. (1999) analysed three measures of verbal STM and three measures of verbal WM, finding a correlation of .68 between the corresponding latent factors. Conway, Cowan, Bunting, Therriault, and Minkoff (2002) studied four measures of verbal STM and three measures of verbal WM, finding a correlation of .82. Miyake et al. (2001) considered two measures of spatial STM and two measures of spatial WM, finding a correlation of .86 between the latent factors. Unfortunately, those studies considered verbal or spatial measures only, which preclude testing general models. There are three studies that analysed verbal and spatial memory span tasks. These were performed by Kane et al. (2004), Colom et al. (2005), and Colom, Abad, and Shih (2006). Kane et al. (2004) did not report the correlation between STM and WM, whereas Colom et al. (2005) found a correlation of .89 between these constructs. The latter researchers analysed the Kane et al. (2004) dataset, finding a correlation of .99 between their STM and WM latent factors. Further, Colom et al. (2006) found a correlation of .87 between STM and WM. Therefore, when STM and WM are appropriately represented across content domains by several memory span tasks, the relationship is so high that the statement that STM and WM are distinguishable constructs should be regarded with serious reservations. It is important to notice that if STM measures can be informatively and clearly distinguished from WM measures, then it is quite reasonable to test theoretical models suggesting that STM is a subset of the WM system or vice-versa. However,
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if STM is not clearly distinguishable from WM, then these theoretical models can be considered uncertain. Although the latent-variable approach has several advantages (Jo¨reskog, 1993), the findings largely depart from the observed raw data. Thus, for instance, the correlation at the latent variable level between STM and WM on the Kane et al. (2004) dataset is .99. From this almost perfect correlation (98% of shared variance) the conclusion that STM and WM reflect exactly the same underlying construct is almost inescapable. However, inspection of their correlation matrix reveals that the raw correlations among their memory span measures range from .31 to .73 (the mean raw correlation is .52). Apparently the raw correlations are not consistent with the statement that STM and WM are largely overlapping constructs and reflect the same basic underlying capacity limitations. Nevertheless, it should be noted that relatively low raw correlations between specific measures and one almost perfect correlation between latent constructs derived from these measures are consistent facts. This is because latent constructs represent only the shared variance between their measures. Anyway, we think it is interesting to consider both raw correlations and relationships from latent variable analyses (Beier & Ackerman, 2004). Therefore, the present study takes both an exploratory and a confirmatory analytic strategy in order to test the consistency of results across methods of analyses. Several diverse measures of STM and WM are selected to tap the constructs of interest as widely as possible. Then these measures are administered to a large sample in order to reliably estimate these constructs. All the obtained span scores are first subjected to an exploratory hierarchical factor analysis, and then several SEM analyses are undertaken to test a number of theoretical models. If STM and WM reflect clearly distinguishable cognitive limitations, then the analyses will reveal separate factors reflecting the corresponding constructs. However, if STM and WM share the same basic underlying capacity limitations, then the analyses will fail to separate factors by constructs.
METHOD A total of 403 psychology undergraduates took part in the study. The students participated to
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fulfil a course requirement. Their mean age was 21.20 and the standard deviation was 3.0. Verbal STM was measured by the forward and backward letter span tasks, whereas quantitative STM was measured by the forward and backward digit span tasks. Single letters and single digits were used as stimuli. It is quite important to note that backward span tasks fit with other tasks of STM, because a simple transposition of order is insufficient to move them from this domain to that of WM (Cantor, Engle, & Hamilton, 1991; Rosen & Engle, 1997). Spatial STM was measured by the corsi block and the dot memory tasks, both requiring the simple maintenance of spatial information (location sequences and dot configurations, respectively). The administered spatial STM tasks modelled those employed by Miyake et al. (2001). Verbal WM was measured by the ABCD and the alphabet tasks. Those verbal tasks were modelled after the CAM Battery (Kyllonen & Christal, 1990). The ABCD was employed by Ackerman, Beier, and Boyle (2002) as well as by Engle et al. (1999) as a measure of verbal WM. Quantitative WM was measured by the mental counters and computation span tasks. The mental counters task was modelled after Larson and Saccuzzo (1989) and it was employed by Mackintosh and Bennett (2003) as a measure of quantitative WM. The computation span task was modelled after Ackerman et al. (2002). Finally, spatial WM was measured by the dot matrix and the letter rotation tasks. Both tasks were modelled after Miyake et al.’s (2001) study and they involve visuospatial storage (dot locations and spatial orientations, respectively) with a concurrent visuospatial processing (verification of spatial matrix equations or mental rotation). A more detailed description can be seen in the Appendix.
RESULTS The descriptive statistics are shown in Table 1. Task correlations and reliability estimates (Cronbach’s alpha) are also presented in Table 1. First, the correlation matrix was subjected to an exploratory factor analysis called Schmid-Leiman hierarchical factor analysis (Carroll, 1993; Loehlin, 2004). The Schmid-Leiman hierarchical factor analysis (SLHFA) departs from other exploratory factor analyses. Researchers within the field of working memory and related areas usually apply straight exploratory factor analyses
instead of the proposed hierarchical analysis (see, for instance, Bayliss, Jarrold, Gunn, & Baddeley, 2003, or Engle et al., 1999). In the SLHFA the higher-order factors are allowed to account for as much of the correlation among the observed variables as they can, while the lower-order factors are reduced to residual factors uncorrelated with each other and with the higher-order factors. The implication is that each obtained factor represents the independent contribution of the factor in question (Schmid & Leiman, 1957). It must be emphasised that a higher-order factor emerges from a hierarchical factor analysis if, and only if, a general factor is truly latent in the analysed correlation matrix. Thus, for instance, personality traits have been subjected to several factor analysis techniques, but a general personality factor has never been found. In sharp contrast, in the abilities domain a general factor always emerges, provided the number and variety of measures is sufficient (Jensen, 1998). The SLHFA was applied to the present dataset. Following Salthouse, Atkinson, and Berish (2003) factors with eigenvalues greater than 1 were retained. At the end of the computational process, each measure presents a value both in the higher-order and first-order factors, which can be used to compute the percentage of variance explained by these factors. The interpretation is quite straightforward: the higher the percentage of variance explained, the greater will be the relevance of the factor to account for the observed variance. The SLHFA is much more appropriate than non-hierarchical exploratory factor analyses, because the obtained factors after a non-hierarchical factor analysis confound the shared variance among all the measures and variance specific to groups of measures. The advantage of the SLHFA is that those distinguishable sources of variance are clearly separated (Colom et al., in press). Further, and especially important for the main goal of the present study, the higher-order factor will represent the shared variance among all the memory span measures, whereas the first-order factors will reflect the specific nature of these measures. As previously noted, if STM and WM are clearly distinguishable constructs, then firstorder factors should be loaded by STM measures, on the one hand, and by WM measures on the other hand. However, if STM and WM share both their common and specific variance, then (a) both tasks will load on the general factor with roughly
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TABLE 1 Descriptive statistics (Means and SD) for the dependent measures; correlation matrix and reliability indices also shown Measures 1. FLSPAN 2. BLSPAN 3. FDSPAN 4. BDSPAN 5. Corsi block 6. Dot memory 7. ABCD 8. Alphabet 9. Mental counters 10. Computation span 11. Dot matrix 12. Letter rotation Mean SD Reliability
1
9.3 2.4 .75
2
3
4
5
6
7
8
9
.58
.56 .51
.50 .65 .60
.33 .31 .25 .35
.21 .26 .19 .25 .46
.20 .23 .24 .20 .22 .17
.45 .44 .35 .47 .21 .15 .17
.20 .24 .23 .24 .33 .36 .24 .16
.35 .46 .43 .48 .28 .27 .22 .38 .31
.22 .24 .21 .35 .32 .34 .20 .29 .32 .34
.18 .30 .21 .28 .27 .30 .26 .19 .31 .26 .31
9.4 3.4 .85
13.5 2.7 .77
12.2 3.6 .83
10.2 2.4 .78
12.2 2.8 .71
8.9 4.2 .62
6.9 3.2 .76
9.7 3.6 .80
17.5 5.3 .92
76.8 7.9 .78
47.4 8.8 .76
equivalent values, and (b) both tasks will be intermixed on the specific factors, irrespective of the construct they are intended to tap. The results shown in Table 2 indicate that the higher-order factor accounts for 37% of the variance, whereas the first-order factors account for 7.3 and 5.5% of the remaining common variance, respectively. Beyond this general and largely informative estimate, there are several implications derived from the values shown in Table 2. First, the array of memory span measures considered in the present study share most of their common variance. Second, the average loading of the STM and WM measures on the higher-order factor is very similar (.65 and .56, respectively). Third, STM and WM tasks are not separated in distinguishable first-order factors. Instead, the first lower-order factor (F1) is mainly loaded by the verbal and quantitative measures, whereas the second lower-order factor (F2) is mainly loaded by the spatial measures. Note that ABCD and mental counters are intended to tap verbal and quantitative WM respectively, but they are loading on the first-order spatial factor. We think that this result is reasonable, given that those tasks comprise a significant spatial component, namely the relative position of several names and the concurrent computation after the appearance of a signal above or below a given counter, respectively (see Appendix). Therefore, it can be suggested that the obtained first-order factors are defined by the content domain of the memory span measures, irrespective of the presumed construct (STM or WM) they are tapping.
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Several SEM analyses were computed to test the likelihood of the view that there is a general latent dimension underlying all the memory span measures regardless of the construct they are intended to tap (e.g., short-term or working memory).1 The first model (Model 1) postulates two correlated latent factors for the STM and WM measures, respectively. Thus, the STM latent factor is defined by FLSPAN, BLSPAN, FDSPAN, BDSPAN, Corsi block, and dot memory, whereas the WM latent factor is defined by TABLE 2 Hierarchical factor matrix
Measures
Higher-order factor
Short-term memory FLSPAN BLSPAN FDSPAN BDSPAN Corsi block Dot memory Working memory ABCD Alphabet Mental counters Computation span Dot matrix Letter rotation % Variance
F1
F2
.639 .711 .640 .737 .620 .573
.414 .406 .413 .407 .041 .057
.035 .015 .033 .029 .326 .397
.439 .559 .559 .657
.052 .354 .035 .267
.207 .022 .367 .123
.581 .541
.030 .000
.315 .320
37
7.3
5.5
1 We thank an anonymous reviewer for suggesting these SEM analyses.
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alphabet, ABCD, computation span, mental counters, letter rotation, and dot matrix. Model 1 shows bad fit indices: x2(53) / 247.27, CMIN/ DF / 4.67, TLI / .83, RMSEA/ .095. Although this model shows bad fit indices, we report the correlation between the STM and WM latent factors for illustrative purposes only: r/ .86. Further, we tested if this correlation could be fixed to 1, finding a significant change of fit (^x2(1) / 24.98; p B/.01). Nevertheless, as fully explained elsewhere (Colom et al., 2005), memory span measures should be considered from a hierarchical view. According to this view, higher-order factors capture what is shared by all the measures, whereas first-order factors accumulate unique variance unpredicted by the higher-order factors. Therefore, hierarchical models assume that firstorder latent factors share most of their common variance, but they also have a given amount of uniqueness. Hierarchical models are less restrictive than those models presuming the unitary (or non-unitary) nature of the constructs of interest represented by the latent factors (Kane et al., 2004). Therefore, the second model (Model 2) postulates the same STM and WM latent factors defined in Model 1, but these first-order latent factors are predicted by one higher-order factor (Figure 1). Given that Model 1 and Model 2 are statistically equivalent, they show the same bad fit indices.2Anyway, it is interesting to note the very high structural coefficients from the higher-order latent factor to the STM and WM first-order latent factors (.99 and .87, respectively). Model 3 postulates three correlated latent factors: the verbal factor (defined by FLSPAN, BLSPAN, ABCD, Alphabet), the quantitative factor (defined by FDSPAN, BDSPAN, computation span, mental counters), and the spatial factor (defined by Corsi block, dot memory, dot matrix, letter rotation). Model 3 shows bad fit indices: x2(51) / 178.03, CMIN/DF / 3.49, TLI / .88, RMSEA / .079. Although this model shows bad fit indices, we report the correlation between the three latent factors for illustrative purposes only: verbal-quantitative / .94, verbal-spatial / .60, and quantitative-spatial / .67. Model 4 follows the findings derived from the exploratory hierarchical factor analysis. There2 Note that ‘‘statistical equivalence’’ does not implicate ‘‘psychological equivalence’’. Hierarchical models do not have the same theoretical meaning as non-hierarchical models.
fore, Model 4 postulates two correlated latent factors: the verbal-quantitative factor (defined by FLSPAN, BLSPAN, FDSPAN, BDSPAN, alphabet, and computation span) and the spatial factor (defined by Corsi block, dot memory, ABCD, mental counters, letter rotation, and dot matrix). We must acknowledge that this is a sort of post hoc model, but the advantage is that it appropriately represents the obtained data. Further, it should be remembered that the ABCD and mental counters tasks comprise germane spatial components, so it can be argued that they actually tap spatial span mental processes. As expected, Model 4 shows a good fit: x2(53) / 118.96, CMIN/DF / 2.24, TLI / .94, RMSEA / .056. The correlation between the verbal-quantitative and spatial latent factors was .62. We tested if this correlation could be fixed to 1, finding a significant change of fit (^x2(1) / 153.29; p B/.01). Finally, Model 5 is the hierarchical version of Model 4 (Figure 2). Therefore, the verbal-quantitative and spatial latent factors are predicted by one higher-order factor. Given their statistical equivalence, Model 4 and Model 5 show the same good fit indices. This final model is consistent with the hierarchical view endorsed in the present article: there is a higher-order latent dimension underlying all the memory span measures regardless of the construct they are intended to tap. Further, this higher-order factor strongly predicts the content domain of the considered span measures.
DISCUSSION The present study administered several diverse STM and WM tasks to a large sample of participants. The main conclusion that can be extracted from the observed results is that storage-oriented memory span measures and storage/processing memory span measures share most of their germane variance, although specific sources of variance are identified. The hierarchical models derived from both the exploratory and SEM analyses are consistent with this general result. The findings nicely fit the hierarchical view of the WM system based on both domain-general and domain-specific components proposed by Engle et al. (1999) and explicitly tested by Colom et al. (in press). The hierarchical view indicates that a general factor can be equated with the
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FLSPAN .69 .02
.78 .70
BLSPAN FDSPAN
STM
.99
.80
BDSPAN
.47
CORSI BLOCK
.38
DOT MEMORY
.37
ABCD
G
.58
.87
.66
ALPHABET COUNTERS
WM
.24
.45
COMPUTATION
.45
L ROTATION
.51
DOT MATRIX
Figure 1. Hierarchical model in which first-order latent factors for STM and WM are predicted by one higher-order latent factor (Model 2).
domain-general component of the so-called WM system, whereas specific factors can be equated with its domain-specific components. Interestingly, the best-fitting SEM shows that specific latent factors should be separated by the content facet of the memory span tasks, but not by the theoretical construct they are intended to tap (STM and WM). Colom et al.’s (in press) re-analyses of the datasets of Engle et al. (1999), Miyake et al. (2001), Conway et al. (2002), Bayliss et al. (2003), and Kane et al. (2004) failed to find empirical evidence supporting the view that WM measures should be distinguished from STM measures. The five datasets converged in that WM and STM measures load with one equivalent magnitude on a higher-order factor. Further, those measures loaded on the same first-order factor, not in separate first-order factors, which suggested that they share the same basic components as well. Thus, they concluded that memory span measures must be considered from the hierarchical view of the WM system wisely suggested by Engle et al.
(1999). Colom et al.’s (in press) results demonstrated that between 20% and 30% of the variance is accounted for by a strong general component, whereas 7% of the variance is accounted for by specific components linked to both WM and STM measures, but irrespective of the construct they are intended to tap. Therefore, the general component was found to be about four times more important than the specific components. The theoretical implication was that individual differences in memory span tasks are strongly explained by some general component, while the contribution of specific components is much less germane. The results observed in the present study are entirely consistent with that hierarchical view: the higher-order factor representing the general component of the WM system accounted for 37% of the variance, whereas the first-order factors representing the specific components of the WM system accounted for 7.3% and 5.5% of the variance. Therefore, it seems reasonable to state that STM and WM are restricted by the same
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FLSPAN .70 .42
.76 .71
BLSPAN FDSPAN
VERBAL
.76
.81
BDSPAN
.58
ALPHABET
.60
COMPUTATION
.39
ABCD
G
.56
.82
.63
COUNTERS CORSI
SPATIAL
.33
.61
DOT MEMORY
.52
L ROTATION
.56
DOT MATRIX
Figure 2. Hierarchical model in which first-order latent factors for verbal-quantitative and spatial measures are predicted by one higher-order latent factor (Model 5).
basic underlying capacity limitations. Both are characterised by the temporary storage of the information. People differ in their capacity to temporarily store that information, so apparently STM and WM are not fuelled by different cognitive limitations. Engle et al. (1999) suggest that performance in WM tasks is determined by STM capacity and a so-called controlled-attention ability. Controlled attention is conceived as a domain-general limited-attention ability for performing controlled processing. Presumably, this domain-general attention ability should be equated with the higherorder factor identified in the present study. However, one aspect is how many elements can be temporarily retained in a reliable state, and another aspect is the presumed control processes dedicated to keeping a representation active in the face of a different concurrent requirement. The general view we endorse relies on the concept of overall capacity for storage rather than on a problem of interference between two
concurrent activities (Colom et al., in press). From that perspective, the higher-order factor should not be equated with any domain-general limited-attention ability. STM measures are not characterised by dedicated cognitive components to select any relevant information, given that all the information is germane. Those measures simply require the temporary maintenance of any given information. Instead, WM measures require control processes, because they impose dual task demands *maintaining target items while performing concurrent cognitive processing. If the obtained higher-order factor reflects a domain-general limited-attention ability properly tapped by WM measures, then those measures should show higher loadings than STM measures on this factor. But the available results reveal that this is not the case. The WM system is clearly devoted to keeping memory representation active, accessible, and reliable. Cowan (2004) states that the main difference between STM and WM measures
SHORT-TERM MEMORY AND WORKING MEMORY
appears to be the benefit of rehearsal in STM tasks, so the necessary concurrent processing that takes place on WM measures precludes rehearsal. Therefore, there could be a general ability to maintain any given information in an active and reliable state. Engle and colleagues suggest that this general ability must be attributed to one presumed controlled-attention ability, whereas we propose that the available empirical evidence is more consistent with the view that this general ability derives from a unitary capacity for storage (Colom & Shih, 2004). The latter view is largely consistent with two key findings derived from the impressive study reported by Oberauer et al., (2003). This study considered 24 tasks thought to represent germane factors for the working memory construct, finding that (a) supervision (operationalised by tasks measuring the switching function of the central executive) was not central to working memory, and (b) the content factors were highly correlated. The authors concluded that ‘‘working memory should be characterised as a highly interrelated ensemble of cognitive functions’’ (p. 190). Nevertheless, we must acknowledge that this does not imply that the results observed in the present study demonstrate that controlled attention plays a null role. Obviously, to appropriately test the model endorsed by Engle and associates, controlled attention must be explicitly measured. However, although the evidence is far from conclusive, there are some studies raising serious doubts about the likelihood of such a model (see Colom et al., 2005; in press). Further, Oberauer et al. (2004) have recently reported a study failing to support theories identifying WM with the ability to resist interference or the ability to coordinate two concurrent tasks. Their results suggest that the difference between WM and STM cannot be interpreted as measuring the added contribution of a general executive device: ‘‘our data should at least motivate proponents of the interference account of WM (including ourselves) and proponents of the central executive account to specify more precisely under which conditions the amount of dual task interference should reflect WM (or the capacity of the central executive)’’ (Oberauer et al., 2004, p. 93). Manuscript received 7 March 2003 Manuscript accepted 9 March 2006 First published online 15 June 2006
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Appendix
Forward letter span (FLSPAN), Backward letter span (BLSPAN), Forward digit span (FDSPAN), and Backward digit span (BDSPAN). Single letters or digits (from 1 to 9) were presented on the computer screen at the rate of one letter or digit per second. Letters or digits were randomly grouped to form trials, with the restriction that letters or digits did not repeat within a given trial. Unlimited time was allowed to type in direct or reverse order the letters or digits presented. Set size ranged from three to nine (7 levels / 3 trials each / 21 trials total). The number of accurately reproduced trials is obtained as the participant’s score. Corsi block. Nine boxes were shown on the computer screen and three different configurations of boxes that changed on each trial were used. One box at a time turned orange for 650 ms each and the order in which they were tapped had to be remembered. There was unlimited time to respond. The sequences increased from three to nine taps (7 levels / 3 trials each / 21 trials total). The number of trials reproduced appropriately was obtained as the participant score. Dot memory. One 5/ 5 grid was displayed for 750 ms on the computer screen. Each grid had between two and seven spaces comprising solid dots. Dot configurations forming regular patterns were avoided. After the grid presentation, the locations that contained dots had to be recalled. The trials increased progressively from two to seven dots (6 levels/ 3 trials each / 18 trials total). The number of trials correctly reproduced was obtained as the participant score. ABCD. Two categories and five words in each category were used. The categories were Trees and Food. Three study frames were displayed on the computer screen for 3 seconds each. The first
SHORT-TERM MEMORY AND WORKING MEMORY
frame indicated the order of two members from one category (Cedar before Oak), the second frame indicated the order of two members from the other category (Garlic not before Salt) and the third frame indicated the order of the categories (Trees not before Food). After the third study screen, an eight-choice answer screen was presented in order to select the correct order of the words obtained from the information given by the displayed sentences. A maximum of 10 seconds to select a response were allowed. The use and ordering of category members were balanced across items, as well as the variations of order (before, not before). There were 14 trials. The number of correct trials was obtained as the participant’s score. Alphabet. This task required successor and predecessor operations applied to a string with a given number of letters. If the first screen presents the letters D, A, P and the second screen displays the operation /1, then the correct response is E, B, Q. The string of letters is presented for 3 s, the operation to apply is presented for 1.5 s, and there is 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 one or two positions must be added, while for the other two trials one or two positions must be subtracted. The number of additions and subtractions are randomised within a given block of trials. The number of correct trials is obtained as the participant’s score. Mental counters. Three boxes representing counters appeared on the computer screen. At the beginning of each trial, the value of the three counters was set to 0, 0, 0. A yellow star appeared above or below one counter for 500 ms. If the star appeared above the box, one had to be added (/1) to that counter, but if the star appeared below the box, one had to be subtracted (/1) to that counter. The task required keeping a running track of the value of the three counters. At the end of each trial, the cumulative total of all three counters had to be reported. There was unlimited time to enter a response. There were 10 trials with five counter changes, and 10 trials with seven
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counter changes. The number of correct trials was obtained as the participant score. Computation span. This task included a verification task and a recall task: 6 s were allowed to verify the accuracy of a maths equation and the participant had to remember the displayed solution, irrespective of its accuracy. After the final equation of the trial was displayed, the solutions from the equations had to be remembered in their correct serial order. Each math equation included two operations using digits from 1 to 10. The solutions were single-digit numbers. The trials ranged from three to seven equation/solutions (5 levels / 3 trials each / 15 trials total). The participant’s score was obtained after the number of hits in the verification and remembering tasks. Dot matrix. The participant had to verify a matrix equation and then retain temporarily a dot location displayed in a 5/5 grid. The matrix equation required adding or subtracting simple line drawings and 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 had to be recalled. The trials increased progressively in size from two to five equations and dots (4 levels / 3 trials / 12 trials total). The number of hits in the verification and remembering tasks were obtained as the participant’s score. Letter rotation. Several capital letters were presented sequentially normal or mirror imaged, and could be rotated in one of seven orientations (multiples of 458.) There was a verification task (is the letter normal or mirror imaged?) and a recall task (the orientation of the displayed letters *where is 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 trials increased progressively in size from two to five letters (4 levels/ 3 trials, 12 trials total). The number of hits in the verification and remembering tasks were obtained as the participant’s score.
