The information in the preceding sections indicates that most measures postulated to assess WM have been found to have significant age relations, and thus it is reasonable to conclude that there are age differences in WM as the construct is assessed by these tasks. However, because a large number of cognitive variables have been found to have significant age differences, it is possible that the measures may not represent anything special. Information relevant to this point is illustrated in Figure 14.2, which portrays age trends in measures of reasoning, memory, and speed in the same format as Figure 14.1. Note that the age trends with these measures were all quite linear and, if anything, were more strongly negative than those for theWM measures in Figure 14.1. A key question with respect to aging and WM, therefore, is not whether WM measures are related to age, because that certainly seems to be the case, but rather the nature of the relations of WM measures with measures of other types of cognition.
Internal relations can be conceptualized as relations among hypothesized components within the same task, or among measures from similar tasks. As
FIGURE 14.2 Means and standard errors of z-scores representing performance in tests of reasoning (Ravens Matrices), memory (Word Recall), and speed (Digit Symbol) as a function of decade
Source: Data from various Salthouse studies.
an example, Salthouse and Babcock (1991) proposed that processing efficiency, storage capacity, and coordination effectiveness are the primary components of complex span tasks, and they obtained measures of each hypothesized component from adults across a wide age range. Path analysis models suggested that a large proportion of the age differences in WM were mediated through components postulated to reflect processing efficiency and coordination effectiveness. Reanalyses of these data were conducted by Salthouse (1994) to identity' the proportional contributions of the different components to individual differences in WM. The results revealed that the combination of the three components accounted for 60% of the variance in complex span measures ofWM, with 50% accounted for by the processing efficiency component alone. Furthermore, the largest contribution to the age-related variance in complex span WM measures was variability in processing efficiency.
Motivated in part by this discovery of strong relations between processing efficiency and WM, a number of studies were conducted to investigate the reduction in cross-sectional age-related variance in WM after controlling the variance in various measures of speed (e.g. Salthouse, 1991,1992b, 1993; Salthouse & Babcock, 1991; Salthouse & Meinz, 1995). In every case the results revealed a moderate to large attenuation of the age-related variance in WM, and the following interpretation of these results was proposed:
One possible interpretation of the relation between speed and working memory is that working memory has a dynamic quality, perhaps somewhat analogous to someone trying to juggle several objects simultan- eouslv.That is, just as the number of items that can be successfully juggled depends on the rate at which they can be caught and tossed, so might the limits on the number of distinct ideas that can be kept active (or mentally juggled) in working memory be set by the rate at which information can be processed. From this perspective, therefore, working memory might be interpreted as the set of items currently active in consciousness, and age differences in working memory might be hypothesized to originate because increased age is associated with a reduction either in the ability to activate new information or in the ability to maintain the activation of old information.
(Salthouse, 1992b, p. 422)
A key aspect of this conceptualization ofWM is that aspects of processing efficiency or effectiveness are at least as important as aspects of information storage, particularly with respect to age differences in WM.
Although complex span tasks are distinguished from simple span tasks by a requirement for simultaneous processing in addition to storage of information, most studies in which complex span tasks have been used have only considered storage measures in their analyses, and have either ignored the processing component, or have treated it as an exclusionary criterion by discarding data from participants with low levels of processing accuracy. However, it may only be meaningful to neglect one component if there is little variation across people in the measures of that component, or if the measures of that component have a weak relation to the relevant construct. Research from my laboratory and from other laboratories suggests that neither of these conditions is likely to be true (e.g. Babcock & Salthouse, 1990; Duff & Logie, 2001; Salthouse & Babcock, 1991; Waters & Caplan, 1996). For example, Salthouse, Pink, and Tucker-Drob (2008) found substantial individual difference variance, and significant age differences, on measures of both storage and processing in complex span tasks. Moreover, an unpublished study (Salthouse & Tucker-Drob, 2008) found significant relations between the storage and processing measures. Three models of possible organizations among the storage and processing measures from different complex span tasks (i.e. operation span, symmetry span, and reading span) considered in that study are portrayed in Figure 14.3.The model in the top panel represents the possibility that all of the measures reflect a single modality- independent WM construct.The model in the bottom left panel postulates that the measures are best organized in terms of the modality-specific WM tasks from which they were derived, and the model in the bottom right panel postulates the existence of separate constructs corresponding to storage and processing components. The models were examined with data from the two studies in Salthouse, Pink, and Tucker-Drob (2008).
FIGURE 14.3 Three alternative models of the organization of storage and processing measures in complex span WM tasks
Key: OS = operation span storage, OP = operation span processing, SS = symmetry span storage, SP = symmetry span processing, RS = reading span storage,
RP = reading span processing
The best-fitting model in both studies had separate, but moderately correlated (r = .73 and .47 in the two studies),storage and processing constructs. Similar results were reported by Unsworth et al. (2009) in a study involving 138 young adults. That is, in the Unsworth et al. study a model based on separate task constructs did not fit the data very well, but a model with separate processing and storage constructs had a good fit, with an estimated correlation of .61 between the processing accuracy and storage constructs. These results have at least two important implications. First, they suggest that it can be misleading to ignore the processing measures in analyses of complex span performance because people differ in their levels of processing accuracy, and individual differences in processing accuracy are related to individual differences in the storage measures. And second, at least with these types of complex span WM tasks, it appears that the individual differences are more consistent with a general, modality-independent WM factor rather than with several separate modality-specific factors.
Another issue relevant to internal WM relations concerns the magnitude of correlations ofWM measures with each other because moderate correlations would be expected if the various measures represent a single coherent construct. Initial information relevant to this question based on small samples of 20 young and 20 old adults who each performed several WM tasks was reported in Salthouse (1988). The WM tasks consisted of: repeating a digit sequence in reverse order (backwards digit span), repeating digits after subtracting two from each digit (subtract 2 span), identifying the missing digit when the sequence was repeated in random order (missing digit span), and remembering digits while simultaneously performing arithmetic operations (computation span). Large age differences favoring young adults were found in all except the missing digit span task. Most importantly in the current context was the finding that the measures were moderately correlated with one another, and to a similar extent in the two age groups. Similar results with a somewhat different combination ofWM tasks were reported by Waters and Caplan (2003).
Subsequent studies in my lab have revealed correlations between measures from computation span and listening or reading span tasks ranging from .40 to .79 (e.g. Salthouse, 1991, 1992c, 1993; Salthouse & Babcock. 1991; Salthouse, Babcock, & Shaw, 1991; Salthouse & Kersten, 1993; Salthouse & Meinz, 1995), and similar values have been reported in studies by other researchers (e.g. de Frias, Dixon, & Strauss, 2009; McCabe et al., 2010). Correlations between measures from other complex span tasks ranging from .52 between operation span and symmetry span to .71 between operation span and reading span were reported by Salthouse and Pink (2008).
One issue relevant to age differences in WM measures is whether the structure is similar at different ages. Studies by Park et al. (2002) and Hale et al. (2011) found similar patterns of interrelations ofWM measures at different ages. Johnson, Logie, and Brockmole (2010) also found a strong common WM factor at all ages, although there was also evidence of age differences in the residual variances in some measures. No formal comparisons were conducted on the data from Study 2 in Salthouse, Pink, and Tucker-Drob (2008), but inspection of the standardized coefficients among the WM measures in Table 14.1 reveals that the pattern was similar in three different age groups, with very strong relations of the WM construct with a Gf construct in each group, suggesting qualitatively similar WM constructs at each age.
It is clear from the results summarized in Table 14.1 that there are moderate correlations among different measures postulated to assess WM. Although these results are consistent with the assumption that the measures represent a common construct or dimension of individual differences, that information is only relevant to the convergent validity of a construct, and information about discriminant validity is also needed to establish that the construct is distinct. That is, in addition to determining that the measures presumed to represent the same construct are moderately correlated with one another, it is also important to determine if they have weaker correlations with measures assumed to represent different constructs because otherwise the constructs may not be truly distinct, and they could reflect the same underlying dimension of individual differences.