Decomposing adult age differences in symbol arithmetic

Abstract

A componential analysis was conducted to determine the locus of adult age differences in symbol arithmetic. Measures of the duration of two proposed components, substitution of digits for symbols and the addition or subtraction of the digits resulting from these substitutions, were obtained from 52 young adults and 52 older adults. Tests of working memory, perceptual speed, motor speed, and associative learning were also administered to all subjects. The results were most consistent with an interpretation postulating that the speed of many different cognitive processes decreases with increased age. Considerable age-related variance remained in the measures of symbol arithmetic performance after statistical control of working memory and associative learning performance, casting doubt on alternative hypotheses of the source of age-related differences in this task.

The processing-speed theory of adult age differences in cognition.

“…Although this concern is valid, exceptions to the general pattern were detected in both the Madden et al (1992) and the Salthouse and Kersten (1993) studies. For example, in the Salthouse and Kersten (1993) study, the time taken by older adults to perform the Digit Symbol reaction time task after an opportunity to learn the associations between digit-symbol pairs was greater than that expected from the systematic relation.…”

“…A similar method was applied in a recent study by Salthouse and Kersten (1993), and it resulted in the elimination of most of the age-related differences across a variety of speed measures. Furthermore, very similar results were obtained even when the adjustment was based on different types of speed tasks (i.e., those derived from paper-and-pencil procedures rather than from reaction time tasks).…”

“…It should also be noted that, in several studies, the proportional attenuation of the age-related variance was greater with speed measures from tasks involving perceptual or cognitive operations, such as substitution, transformation, or comparison, than with tasks merely requiring copying or line drawing responses (Salthouse, 1992b(Salthouse, , 1993d(Salthouse, , 1994a(Salthouse, , 1994dSalthouse & Kersten, 1993;Salthouse etal., 1995). As suggested by the path analysis results illustrated in Figure 5, the speed most relevant to the mediation of adult age differences in cognition therefore appears to reflect the duration of cognitive operations rather than simply the speed of sensory and motor processes.…”

“…If the complete function is available, then parameters of the mathematical function can be examined and compared across experimental conditions or age groups (e.g., Kliegl et al, 1994;Mayr & KJiegl, 1993;Salthouse & Coon, 1993). Figure 8, based on results of an unpublished study by Kersten and Salthouse (1993), illustrates a typical pattern from manipulations of stimulus presentation time in adults of different ages. 5 The task in this study, which was performed by 39 young adults (Mage = 20.5 years) and 39 older adults (Mage = 67.9 years), was a continuous associative memory task involving letter-digit pairs.…”

Age-Related Preservation of Top-Down Attentional Guidance During Visual Search.

“…The assumption of this analysis is that Age Group ϫ Task Condition interactions that remain significant in analyses of variance of mean RT, following this transformation, can be interpreted as being independent of the generalized slowing represented in the Brinley function (see Faust, Balota, Spieler, &Ferraro, 1999, andKersten, 1993, for related approaches). The Brinley function for the eight task condition means in this experiment yielded Equation 1 (r 2 ϭ .98).…”