Abstract
Although most psychological assessments are based on measures related to an individual's average level of performance, it has been proposed that measures of variability around one's average may provide unique individual difference information and have clinical significance. The current study investigated properties of within-person variability in measures of performance accuracy in a sample of more than 1,700 healthy adults. Contrary to what has been reported with measures of within-person variability in reaction time, measures of within-person variability in performance accuracy from different cognitive tests had weak correlations with one another, very low stability across time, and near-zero correlations with longitudinal change in cognitive abilities.
Keywords: aging, cognition, variability
In recent years, there has been a great deal of interest in within-person, or intraindividual, variability as a potentially important dimension of individual differences in cognitive functioning (see Hultsch, Strauss, Hunter, & MacDonald, 2008, for a review). Measures of within-person variability have been found to differ as a function of normal aging (e.g., Der & Deary, 2006; Hultsch, MacDonald, & Dixon, 2002; Nesselroade & Salthouse, 2004; Williams, Hultsch, Strauss, Hunter, & Tannock, 2005), clinical condition (e.g., Adams, Roberts, Milich, & Fillmore, 2011; Bleiberg. Garmoe, Halpern, Reeves, & Nadler, 1997; Burton, Strauss, Hultsch, Moll, & Hunter, 2006; Christensen et al., 2005; Dixon et al., 2007; Hultsch, MacDonald, Hunter, Levy-Bencheton, & Strauss, 2000; Strauss, Bielak, Bunce, Hunter, & Hultsch, 2007; Stuss, Murphy, Binns, & Alexander, 2003), subsequent cognitive decline (e.g., Bielak, Hultsch, Strauss, MacDonald, & Hunter, 2010; Lovden, Li, Shing, & Lindenberger, 2007; MacDonald, Hultsch, & Dixon, 2003), and time until death (e.g., Deary & Der, 2005; MacDonald, Hultsch, & Dixon, 2008; Shipley, Der, Taylor, & Deary, 2006). In addition, measures of within-person variability have been reported to be stable over short intervals (e.g., Hultsch et al., 2000; Nesselroade & Salthouse, 2004; Rabbitt, Osman, Moore, & Stollery, 2001; Saville et al., 2011) and to have a coherent structure in factor analyses (e.g., Hultsch et al., 2000, 2002; Li, Aggen, Nesselroade, & Baltes, 2001; Strauss et al., 2007). Taken together, these properties suggest that measures of within-person variability can provide valuable information about an individual's cognitive status. That is, measures of variability in cognitive functioning could be an early indicator of impending change and might serve as a unique marker of certain clinical conditions.
Several characteristics are common to much of the prior research investigating within-person variability. First, although there are exceptions (e.g., Hultsch et al., 2000; Li et al., 2001), most of the studies have investigated variability in reaction to time or other speeded tasks. Second, a large proportion of the studies have focused on short-term variability across trials within a single session rather than longer term variability across different sessions (but see Hultsch et al., 2000; Nesselroade & Salthouse, 2004; Rabbitt et al., 2001; Salthouse & Berish, 2005; Stuss et al., 2003). And third, the majority of the studies involved adults older than about 60 years of age (but see Der & Deary, 2006; Williams et al., 2005). These characteristics lead to questions as to whether within-person variability is primarily meaningful as an individual differences measure when it is based on speeded tasks, when it reflects momentary rather than day-to-day fluctuations, and when the research participants are older adults.
A different, and in some respects more surprising, form of variability is the variation in the accuracy of performance of the same cognitive task across sessions separated by days or weeks. Because cognitive abilities are generally considered to be relatively stable traits, this form of variability is often assumed to be very small. However, recent research has revealed that short-term variability in level of cognitive performance can be substantial (e.g., Salthouse, 2007; Salthouse, Nesselroade, & Berish, 2006). The goal of the current project was to investigate properties of this type of within-person variability to determine if it has some of the same characteristics as within-person variability in reaction time (RT) tasks and whether it may represent a meaningful dimension of individual differences. In particular, the magnitude, stability, and correlations of within-person variability in accuracy of cognitive performance were examined in 16 cognitive tests.
The analyses were conducted on data from the Virginia Cognitive Aging Project (VCAP), which is a mixed cross-sectional and longitudinal study involving a measurement burst design in which different versions of 16 cognitive tests were performed in each of three sessions. Participants in VCAP span a wide age range, and therefore separate analyses were reported for adults aged 60 to 95 years and 18 to 59 years. The former group is typical of most prior research, and the latter group allows the phenomenon to be examined at younger ages.
To summarize, the current study was designed to investigate the following properties of within-person across-session variability in accuracy of cognitive performance: magnitude (i.e., within-person variability relative to between-person variability), structure (i.e., interrelations of measures of within-person variability in different variables), longitudinal stability (i.e., correlations of within-person variability from Time 1 [T1] to Time 2 [T2]), and correlations of within-person variability with change in cognitive abilities from T1 to T2.
Method
Sample
The three-session measurement burst at T1 was completed by 1,725 adults, with 579 of them returning for a second measurement burst after an interval averaging about 2.3 years. Characteristics of the initial sample and of the sub-sample with longitudinal data are presented in Table 1. Note that the longitudinal participants had slightly higher scaled scores in word recall, but in other respects they were similar to the total sample.
Table 1.
18-59 years | 60-95 years | |
---|---|---|
Total sample | ||
N | 1,067 | 658 |
Age | 41.0 (13.5) | 71.7 (8.1) |
Proportion of females | 0.68 | 0.59 |
Health | 2.2 (0.9) | 2.4 (0.9) |
Years of education | 15.4 (2.5) | 16.1 (2.9) |
MMSE | 28.7 (1.6) | 28.1 (2.0) |
Scaled scores | ||
Vocabulary | 12.3 (3.2) | 13.0 (2.6) |
Digit symbol | 11.1 (2.8) | 11.4 (2.8) |
Logical memory | 11.5 (2.9) | 12.1 (2.8) |
Word recall | 11.8 (3.4) | 12.1 (3.5) |
Longitudinal sample at Time 1 | ||
N | 335 | 244 |
Age | 42.8 (13.4) | 71.7 (7.5) |
Proportion of females | 0.67 | 0.59 |
Health | 2.3 (0.9) | 2.4 (0.9) |
Years of education | 15.4 (2.5) | 16.1 (2.8) |
MMSE | 28.8 (1.5) | 28.3 (1.8) |
Scaled scores | ||
Vocabulary | 12.5 (2.8) | 13.5 (2.6) |
Digit symbol | 11.4 (2.8) | 11.8 (2.6) |
Logical memory | 11.6 (2.8) | 12.6 (2.7) |
Word recall | 12.2 (3.6) | 12.8 (3.3) |
Time 1 to Time 2 interval (years) | 2.3 (0.7) | 2.4 (0.6) |
Note. Health was a self-rating on a scale from 1 = excellent to 5 = poor. MMSE = Mini Mental Status Exam (Folstein, Folstein, & McHugn, 1975). Scaled scores are age-adjusted scores that have means of 10 and standard deviations of 3 in the normative standardization samples (Wechsler, 1997a, 1997b).
Participants were recruited from newspaper advertisements and referrals from other participants. Approximately 81% were Caucasian, about 10% African American, and the remaining distributed across other ethnicities or reporting more than one ethnicity. Most participants performed the sessions at the same time of day, but this was not always the case as the appointments were arranged to accommodate to the participants' schedules.
Cognitive Tests
Cognitive functioning was assessed with 16 tests selected to reflect 5 cognitive abilities (i.e., vocabulary, inductive reasoning, spatial visualization, episodic memory, and perceptual speed). The appendix contains a brief description of the tests and their sources. Most of the test versions had internal consistency and test–retest reliabilities of .7 or greater, and loadings of .7 or greater on their respective ability factors in confirmatory factor analyses of these 16 tests (i.e., Salthouse, 2007; Salthouse, Pink, & Tucker-Drob, 2008; Salthouse & Tucker-Drob, 2008).
The tests were administered in the same order in each session, but different versions of the tests were performed in each of the three sessions. Because the test versions could differ in mean performance, which would preclude direct comparisons across versions, the three versions were administered in a counterbalanced order to a separate sample of 90 adults between 20 and 79 years of age to determine average performance in each version without confounding version with sequence (Salthouse, 2007). Regression equations in this sample were used to predict performance in the original test version from scores on the second or third versions, and the intercepts and slopes of these equations were then used to adjust the scores on the second and third versions of every participant in the current study to remove any sequence-independent version differences in means. Detailed information on this calibration sample, including means and standard deviations (SDs) in each session, is reported in Salthouse (2007).
Analyses reported in Salthouse and Nesselroade (2010) revealed that the average accuracy of performance increased across the three sessions within each measurement occasion. Because any systematic linear trends could inflate the estimates of within-person variability, and confound them with short-term learning, they were removed with regression equations applied to the data of individual participants, and then SDs of the residuals were used as the index of within-burst variability for each variable.
Results1
As noted above, regression equations were used to adjust the scores on the second and third test versions to have the same expected means as the scores on the first version. All adjusted scores for each variable were then converted into z-score units based on the distribution of scores on the first session of the first occasion (T11) for that variable to express scores on different test versions in the same units. Regression analyses were also conducted on each participant's data relating test score to session number, with the SDs of the regression residuals used as the measure of within-person variability in each test for each participant. Note that two separate sets of regression equations were applied to the data, one set (which was the same for all participants) to equate the difficulty of the different test versions and a second set (consisting of different equations for each participant) to remove individual-specific across-session practice effects.
Magnitude of Standard Deviation
The averages of the within-person SDs for each cognitive variable in the two age-groups after the adjustments described above are reported in Table 2. Across the 16 tests, the median SD at the first (T1) occasion was .23. Because the T11 scores were in z-score units, the between-person SDs were very close to 1. The average within-person variability can therefore be inferred to be about 23% of the variation across people on the first assessment.
Table 2.
Total sample | Within-person variability (SD) | d | ||||
---|---|---|---|---|---|---|
| ||||||
18-59 years | 60-95 years | |||||
Variable | ||||||
Vocabulary | .22 (.19) | .22 (.22) | 0 | |||
Picture vocabulary | .21 (.16) | .21 (.16) | 0 | |||
Synonym vocabulary | .28 (.24) | .26 (.22) | −.09 | |||
Antonym vocabulary | .27 (.22) | .29 (.24) | .09 | |||
Matrix reasoning | .25 (.20) | .27 (.22) | .10 | |||
Shipley abstraction | .33 (.28) | .34 (.25) | .04 | |||
Letter sets | .27 (.23) | .30 (.26) | .12 | |||
Spatial relations | .27 (.20) | .28 (.21) | .05 | |||
Paper folding | .23 (.18) | .24 (.19) | .05 | |||
Form boards | .25 (.21) | .21 (.19) | −.20 | |||
Word recall | .22 (.17) | .24 (.19) | .11 | |||
Paired associates | .52 (.25) | .50 (.23) | −.08 | |||
Logical memory | .23 (.18) | .24 (.21) | .05 | |||
Digit symbol | .18 (.18) | .16 (.16) | −.12 | |||
Pattern comparison | .22 (.20) | .22 (.20) | 0 | |||
Letter comparison | .22 (.22) | .22 (.22) | 0 | |||
Longitudinal sample | Time 1 | Time 2 | ||||
|
|
|||||
Within-person variability (SD) | d | Within-person variability (SD) | d | |||
|
|
|||||
18-59 years | 60-95 years | 18-59 years | 60-95 years | |||
| ||||||
Variable | ||||||
Vocabulary | .20 (.16) | .20 (.18) | 0 | .19 (.19) | .22 (.22) | .15 |
Picture vocabulary | .20 (.16) | .22 (.16) | .13 | .18 (.15) | .20 (.17) | .13 |
Synonym vocabulary | .27 (.22) | .25 (.21) | −.09 | .29 (.23) | .28 (.20) | −.05 |
Antonym vocabulary | .28 (.22) | .27 (.20) | −.05 | .26 (.19) | .28 (.22) | .10 |
Matrix reasoning | .25 (.20) | .29 (.20) | .20 | .26 (.22) | .26 (.23) | 0 |
Shipley abstraction | .34 (.28) | .33 (.23) | −.04 | .21 (.17) | .25 (.17) | .24 |
Letter sets | .27 (.28) | .30 (.23) | .12 | .22 (.18) | .30 (.25) | .38 |
Spatial relations | .27 (.22) | .26 (.19) | −.05 | .25 (.20) | .27 (.21) | .10 |
Paper folding | .21 (.20) | .24 (.17) | .16 | .23 (.20) | .23 (.17) | 0 |
Form boards | .23 (.17) | .19 (.16) | −.24 | .24 (.17) | .22 (.18) | −.11 |
Word recall | .22 (.17) | .22 (.17) | 0 | .20 (.17) | .24 (.19) | .22 |
Paired associates | .53 (.26) | .50 (.22) | −.12 | .53 (.26) | .50 (.22) | −.12 |
Logical memory | .24 (.19) | .24 (.19) | 0 | .22 (.19) | .22 (.18) | 0 |
Digit symbol | .17 (.16) | .16 (.17) | −.06 | .21 (.23) | .20 (.22) | −.04 |
Pattern comparison | .21 (.19) | .22 (.19) | .05 | .23 (.23) | .18 (.15) | −.25 |
Letter comparison | .20 (.19) | .23 (.22) | .15 | .29 (.32) | .24 (.22) | −.18 |
p < .01.
Another method of evaluating the magnitude of within-person variability is to contrast it with the magnitude of cross-sectional age differences in the sample (Salthouse, 2007; Salthouse et al., 2006). Slopes of regression equations relating T11 scores to age for the variables with negative age relations (i.e., all variables except the vocabulary variables) ranged from −.015 to −.033 SD per year, with a median of −.026 SD per year. Dividing the median within-person variability (.23) by the median annual cross-sectional difference (−.026) indicated that the within-person variability for these variables was equivalent to about 8.8 years of cross-sectional age difference. The median within-person variability and the number of years of cross-sectional age difference were smaller than in prior studies (i.e., Salthouse, 2007; Salthouse et al., 2006), likely because the linear across-session trends were removed before computing within-person variability.
Inspection of the values in Table 2 reveals that the magnitude of within-person variability in each test was similar in the two age-groups and the effect sizes in d units for the group difference were all relatively small. Moreover, this was also true at both T1 and T2 for the longitudinal participants, whose data are presented in the bottom panel of Table 2. Correlations were also examined between age and within-person variability in the entire sample. All the correlations were relatively small, with a range from −.14 to .08 and a median of .01. Although within-person variability in cognitive performance was moderately large compared with both between-person variability and cross-sectional age differences, there was no evidence that these measures of within-person variability are related to the age of the participant.
Structure
An exploratory analysis was conducted to determine if there was structure in the measures of within-person variability. A principal components analysis on the T1 within-person SDs revealed that the first component was associated with 9.5% of the variance in the 18- to 59-year age-group and that the cumulative percentage of variance after two components was 17.3%. Corresponding values in the 60- to 95-year age-group were 9.1% and 16.9%, respectively.
For comparison purposes, similar analyses were conducted on the T11 scores representing average performance. In the 18 to 59 age-group, the first component was associated with 51.6% of the variance, and the cumulative percentage with two components was 63.7%. Corresponding values in the 60 to 95 age-group were 39.8% and 51.5%, respectively. The results with the T11 scores replicate the familiar pattern with cognitive test scores, but the weak interrelations with the measures of within-person variability in both age-groups suggest that they have little or no structure and weak relations with one another.
Stability
Correlations across the longitudinal interval were computed for the first session means (i.e., T11 and T21) and for the measures of within-subject variability at T1 and T2. It can be seen in Table 3 that these stability coefficients were moderately high for the Session 1 scores, with medians of .72 and .71, respectively, in the 18 to 59 and 60 to 95 age-groups. However, the correlations were very low for the within-person SDs, with medians of only .07 and .08 in the two groups.
Table 3.
Variable | Session 1 score | Within-person variability (SD) | ||
---|---|---|---|---|
|
|
|||
18-59 Years | 60-95 Years | 18-59 Years | 60-95 Years | |
Vocabulary | .86* | .74* | .14* | .12 |
Picture vocabulary | .89* | .83* | .22* | .14 |
Synonym vocabulary | .85* | .72* | .20* | .18* |
Antonym vocabulary | .76* | .57* | .11 | .10 |
Matrix reasoning | .74* | .66* | .04 | .08 |
Shipley abstraction | .87* | .83* | −.02 | −.05 |
Letter sets | .70* | .61* | .07 | .04 |
Spatial relations | .86* | .79* | .04 | .17* |
Paper folding | .72* | .65* | .07 | −.03 |
Form boards | .72* | .69* | .02 | .19* |
Word recall | .69* | .66* | .11 | .24* |
Paired associates | .67* | .65* | .42* | .18* |
Logical memory | .65* | .65* | .05 | .08 |
Digit symbol | .77* | .74* | .08 | −.06 |
Pattern comparison | .66* | .71* | .02 | −.02 |
Letter comparison | .70* | .71* | .07 | −.06 |
p < .01.
Correlations
A final set of analyses examined whether within-person variability at the first occasion (T1) predicted cognitive change from T1 to T2. A latent change model (Ferrer & McArdle, 2010) as portrayed in Figure 1 was used in these analyses. The variables reflecting cognitive ability (e.g., word recall, paired associates, and logical memory for memory ability) are represented by squares, and the latent level (L) and latent change (C) constructs are represented by circles. Of primary interest in the current context are the relations between the measures of within-person variability for a given cognitive test variable (represented in the box at the top of the figure) and the latent change construct (the circle labeled C). Advantages of latent change models for the analysis of change are that change is evaluated in terms of latent constructs that theoretically have no measurement error and that all available data can be used in the analyses with the full-information maximum likelihood algorithm.
A total of 65 (out of 160, consisting of 16 tests related to each of five cognitive abilities in the two age-groups) relations were significant in the prediction of the level parameter in these latent change analyses. Most of the relations were negative, indicating that greater within-person variability was associated with lower levels of cognitive ability. However, only 6 of 160 relations were significant (p < .01) in the prediction of the latent change parameter, and they were distributed across different combinations of within-person variability measures and cognitive abilities. These results therefore provide little evidence of a systematic relation of the measures of within-person variability with longitudinal change in cognitive ability.
Discussion
The results reported above indicate that across-session within-person variability in accuracy of cognitive performance is moderately large, as it is almost one fourth the magnitude of the between-person variability in average performance in a given session and is equivalent to nearly 9 years of cross-sectional age difference. However, this type of variability appears to be unsystematic because the correlations with measures of within-person variability in other cognitive tests were very small, with little evidence of structure among the measures; the measures had almost no across-time stability; and the correlations with longitudinal change in cognitive abilities were all very small. Moreover, in each of these respects the pattern was very similar in independent samples of adults between 60 and 95 years of age and between 18 and 59 years of age.
Why is the pattern of within-person variability in accuracy of performance different from that reported with measures of within-person variability in RT, in which the measures of variability have been reported to have moderate stability and significant relations to one another and to other types of variables? Both methodological and substantive factors may be involved. For example, RT variability is sensitive to a few very slow RTs, and in some studies the elimination of extreme scores may have been incomplete because outliers were identified on the basis of group means rather than means of individual participants. It is also possible that in some studies the measure of variability might not have been independent of the mean, and therefore relations with measures of within-person variability may have indirectly reflected relations with the mean. To illustrate, Hultsch et al. (2000) attempted to remove the effects of mean RT by partialing the effects associated with group membership (and occasion and trial effects) before computing SDs of the residuals, but these “purified residuals” still had substantial correlations (ranging from .54 to .94) with mean RT. There is currently no consensus on the ideal method of controlling influences of the mean, and complicated methods may be needed because Schmiedek, Lovden, and Lindenberger. (2009) recently reported that the relations between mean and variance can differ across individuals. Whatever method is used, however, before interpreting relations involving within-person variability, it is important to verify independence of mean and variability empirically because within-person variability may not be a unique dimension of individual differences if it is not independent of the mean.
Among the possible substantive reasons for the differences across studies are the time frame over which variability was assessed and the nature of the dependent variable. That is, variability across trials within a single session may reflect the ability to maintain attention over a brief period of time, whereas variability across days may reflect fluctuations in mood or in one's general state. Another possibility is that RT and other measures of speeded processing are simply more sensitive than measures of accuracy of performance, such that subtle aspects of variability are more detectable with RT measures than with accuracy measures. For example, measures of within-person variability with RT can be computed across a few trials, whereas many trials must be aggregated to obtain a sensitive measure of accuracy, and even more are needed to allow within-person variability to be computed.
It should be noted that although not measured in units of time, three of the cognitive tests in this project were designed to assess perceptual speed (i.e., digit symbol, letter comparison, and pattern comparison). However, the results in Tables 2 and 3 indicate that the patterns for these measures were very similar to the others, and therefore the most relevant distinction regarding differential properties of within-person variability may be between RT and other measures of cognitive performance, not between speed and accuracy of performance.
Regardless of the reasons for the differences between RT and other measures of performance, it is important to recognize that other studies have reported results similar to those in this study. For example, Hultsch et al. (2000) noted that their measures of within-person variability of memory accuracy were less sensitive to clinical group membership than RT measures of within-person variability, and Li et al. (2001) reported very low values of stability and reliability of within-person variability for measures of memory accuracy. Furthermore, with data from a subset of the current sample, Salthouse (2007) reported reliabilities of within-person variability based on correlations of within-person SDs from odd-numbered and even-numbered items. The median reliabilities across the cognitive variables in the two studies, respectively, were .26 and .26, compared with median reliabilities of .94 and .92 for the mean scores in the same individuals. Although reliabilities and other psychometric properties of within-person variability of accuracy measures might be stronger with different cognitive variables, or with additional sessions of measurement, the assessment of cognition in this project was fairly broad, and in most testing situations it may not be practical to administer more than three separate versions of each test.
In conclusion, the results of this study suggest that it is important to distinguish different types of within-person variability, as variability in accuracy across three sessions appears to have different properties from variability in RT across multiple trials within a single session. In light of its weak psychometric properties, within-person across-session variability in accuracy of cognitive performance does not appear to provide unique information about an individual's cognitive (and possibly clinical) status, and thus it may not be a useful individual difference characteristic.
Acknowledgments
Funding: The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The project was supported by Award Number R37AG024270 from the National Institute on Aging.
Appendix
Description of Reference Variables and Sources of Tasks.
Variable | Description | Source |
---|---|---|
Wechsler Adult | Provide definitions of words | Wechsler (1997a) |
Intelligence Scale | ||
vocabulary | ||
Picture vocabulary | Name the pictured object | Woodcock and Johnson (1990) |
Antonym vocabulary | Select the best antonym of the target word | Salthouse (1993b) |
Synonym vocabulary | Select the best synonym of the target word | Salthouse (1993b) |
Matrix reasoning | Determine which pattern best completes the missing cell in a matrix | Raven (1962) |
Shipley abstraction | Determine the words or numbers that are the best continuation of a sequence | Zachary (1986) |
Letter sets | Identify which of five groups of letters is different from the others | Ekstrom French, Harman, and Dermen (1976) |
Spatial relations | Determine the correspondence between a three-dimensional figure and alternative two-dimensional figures | Bennett, Seashore, and Wesman (1997) |
Paper folding | Determine the pattern of holes that would result from a sequence of folds and a punch through folded paper | Ekstrom et al. (1976) |
Form boards | Determine which combinations of shapes are needed to fill a larger shape | Ekstrom et al. (1976) |
Logical memory Free recall | Number of idea units recalled across three stories Number of words recalled across Trials 1 to 4 of a word list | Wechsler (1997b),Wechsler (1997b) |
Paired associates | Number of response terms recalled when presented with a stimulus term | Salthouse, Fristoe, and Rhee (1996) |
Digit symbol | Use a code table to write the correct symbol below each digit | Wechsler (1997a) |
Letter comparison | Same/different comparison of pairs of letter strings | Salthouse & Babcock (1991) |
Pattern comparison | Same/different comparison of pairs of line patterns | Salthouse & Babcock (1991) |
Footnotes
Author's Note: The content is solely the responsibility of the author and does not necessarily represent the official views of the National Institute on Aging or the National Institutes of Health.
Declaration of Conflicting Interests: The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Because of the large number of statistical tests and the moderately large sample size, a significance level of .01 was used in all the analyses.
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