aging, cohorts, and verbal ability - semantic scholar · ability, which depend on cultural...

Journal of Gerontology: SOCIAL SCIENCES2001, Vol. 56B, No. 3, S151-S161

Copyright 2001 by The Gerontological Society of America

Aging, Cohorts, and Verbal Ability

Duane F. Alwin and Ryan J. McCammon

Department of Sociology and Institute for Social Research, University of Michigan, Ann Arbor.

Objectives. Age-related differences in cognitive abilities observed in cross-sectional samples of individuals varyingin age may in part be spurious due to the effects of cohort differences in schooling and related factors. This study exam-ined the effects of aging on cognitive function controlling for any and all differences in cohort-based social experiencesof different age groups.

Methods. We examined age-related patterns in a measure of verbal ability using 14 repeated cross-sectional surveysfrom the General Social Survey (GSS) over a 24-year period.

Results. The raw GSS data show the expected age-related growth and decline in vocabulary knowledge, but theseage differences are reduced when adjusted for cohort differences. There is evidence of small age-related patterns in vo-cabulary knowledge within cohorts, but the curvilinear contributions of aging to variation in verbal scores account forless than one-third of 1 % of the variance in vocabulary knowledge, once cohort is controlled. Cohort differences inschooling contribute substantially to this effect.

Discussion. Within-age-group variation in vocabulary knowledge is vastly more important than age differences perse, and the complexities of the relationship of verbal skills to historical differences in the experience of schoolingpresent an interesting avenue for future research.

T is often hypothesized that age-related patterns on cog-nitive test scores may be due to differences in levels of

cognitive aging (Palmore, 1998; Park, 1998; Wilson & Gove,1999; Wolfle, 1980). A deeper examination of research onthe relationship between age and cognitive performance,however, suggests that the issue is more complex. The firstthing one needs to appreciate in this context is the factthat there may be little uniformity across domains of cogni-tive functioning, such that some, but not all, abilities showage-related declines (Hertzog & Schaie, 1988). There areseveral possible trajectories of the life-span stability of cog-nitive abilities, especially with regard to when the develop-ment of abilities seems to peak and level off, prior to anysignificant decline. Thus, it is important to be careful not togeneralize from one form of ability to another; naturally,one of the most important research questions in this area ofinvestigation involves the nature of the differences amongvarious ability domains in their trajectories of growth anddecline. Still, in general, longitudinal research on the life-span stability of intellective test scores indicates that theyare developed relatively early in adult life and are amongthe most stable components of human behavior (Bloom,1964; Brim & Kagan, 1980); however, because of the onsetof dementia of various forms in older adulthood, the aggre-gate scores of older adults on many cognitive tests showsome decline (Schaie, 1996).

At the same time, there is also evidence of declines in per-ceptual speed and memory in old age, and recent evidencesuggests that declines in measures of cognitive performance inthe older age ranges are probably linked to declines in pro-cessing and sensory abilities (Salthouse, 1996). Furthermore, aconvincing argument can be made that neurological functionis the more fundamental latent variable reflected in these kindsof data and is responsible for any observed age differences in

scores on cognitive measures; thus, net of differences in pro-cessing and sensory abilities, there may be few if any true agedifferences in test scores (Baltes & Lindenberger, 1997; Lin-denberger & Baltes, 1994, 1997). It is important, therefore, toattempt to understand age-related trajectories on cognitive testscores in terms of what they measure. In this regard, it is gen-erally thought that measures of processing abilities manifestthe earliest decline, whereas the more crystallized aspects ofability, which depend on cultural stimulation, decline muchlater (Cattell, 1971a, 1971b). Verbal skills, for example, whichare highly dependent upon the completion of formal school-ing, seem to reflect the kinds of abilities that grow through ad-olescence and by early adulthood stabilize throughout most ofthe life span until very old age. Given the relation of mostcrystallized forms of ability to the amount of schooling, it istherefore important to be able to separate aging processesfrom those that interact with schooling experiences.

Setting aside the question of what is measured by cogni-tive tests, and regardless of the type of cognitive measuresinvolved, there are several problems with drawing any con-clusions about the relationship between aging and cognitiveabilities based on much of the available research to thispoint. Age-related differences in cognitive abilities ob-served in samples of different-aged individuals may in partbe spurious because of the effects of cohort differences inschooling and related factors. Due to the confounding of ageand cohort in cross-sectional samples of individuals, any at-tempt to draw inferences regarding the effects of aging mustcontrol in the most advantageous manner for any differ-ences in cohort-based social experiences of different agegroups (Riley, 1973).

We investigated age differences in one aspect of thebroad spectrum of cognitive abilities, namely scores on atest of vocabulary knowledge, seeking to understand the na-

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S152 ALWINAND McCAMMON

ture and source of age differences in this dimension of ver-bal ability. Several earlier analyses, using data on nationallyrepresentative samples from the General Social Survey(GSS) have suggested that there are independent effects ofaging on vocabulary test-score data (Hauser & Huang, 1997;Huang & Hauser, 1998; Wilson & Gove, 1999). We arguethat some of these findings may result from not adequatelycontrolling for between-cohort variation in schooling andrelated experiences. In the following analysis we use the di-achronic data from the GSS to systematically examine pat-terns of age variation independent of cohort factors. Ouranalysis—an extension of the results presented in Alwinand McCammon (1999)—shows that in assessing age dif-ferences in cognitive scores, it is very important to controlvariation in cohort-linked factors, such as differences by co-hort in levels of formal schooling.

Theory and Research on Cognitive AgingAt least since Cattell's publications, psychometricians

have distinguished two interrelated components of cognitiveabilities—-fluid and crystallized—both of which are sub-sumed under the general heading of cognitive abilities.Fluid intelligence is conceptualized as "the capacity for in-sight into complex relations ... independent of the sensory orcultural area in which the tests are expressed" (emphasis inthe original; Cattell, 1971a, p. 13). Crystallized intelligence,on the other hand, has it origins in experience but is not ex-pected to be independent of other capacities because it"arises as the result of the investment of fluid intelligence,over the years, in whatever higher-level cultural skills theindividual is exposed to" (p. 13). Similarly, Salthouse(1991, p. 34) distinguished between measures that are moreoriented toward "process" abilities and those that tap "prod-uct" abilities (see also Cattell, 1971b; Denny, 1982; Horn,1982a, 1982b; Horn & Cattell, 1967; Horn & Donaldson,1980). These two distinct aspects of cognitive functioningpotentially differ in their relationships to aging. Cattell(197la) argued that their development was collinearthrough adolescence (or age 15), whereupon fluid intelli-gence systematically declines with age, and crystallized in-telligence increases ever so slightly, or otherwise remainsrelatively stable with age (see Horn, 1982a).

Some of the best evidence for the life-span developmentof various cognitive abilities is Schaie's (1996) Seattle Lon-gitudinal Study (SLS; see Salthouse, 1991), which begantracking a cross-section of the adult population in 1956 at 7-year reinterview intervals. Schaie (1983) concluded, basedon 21 years of the SLS, that "reliably replicable age changesin psychometric abilities of more than a trivial magnitudecannot be demonstrated prior to age 60" (p. 127), and ifanything, a decrement is shown only in old age, noting thata "reliable decrement can be shown to have occurred for allabilities by age 74" (p. 127).

Schaie (1989,1990,1994,1996; see also Hertzog & Schaie,1986, 1988; Schaie & Hertzog, 1983), thus, has made astrong case for stability in measured abilities over most ofthe adult life span. During the 1970s, he, along with PaulBaltes, championed the argument for the life-long stabilityof mental abilities and challenged what they called the"myth of intellectual decline" (Baltes & Schaie, 1976),

against the arguments of Horn & Donaldson (1976, 1977,1980). Rather, Schaie and colleagues have argued that thereis relative stability of mean performance levels throughoutmost of the life span with some decline in old age, althoughthe "decline began later for the PMA [Primary Mental Abil-ities] subtest Verbal Meaning (a test of recognition vocabu-lary)," See Hertzog & Schaie, 1988, p. 122. Schaie's (1996)most recent evaluation of the age-related trajectories of cog-nitive abilities based on 35 years of the SLS reinforces hisprior conclusions.

While the SLS is one of the most important and influen-tial studies of cognitive aging, and its findings should not beignored in the investigation of life-span stability, even thosewho work closely with it realize some of its limitations. TheSLS is based on a nonprobability sample of unknown repre-sentativeness, and there are serious potential threats to inter-nal validity due to problems of attrition that Schaie (1996)himself acknowledges as a potential problem. However,even if one is willing to generalize from patterns of the Ver-bal Meaning score in the SLS, the longitudinal mean-leveldifferences reported by Schaie (1996) depict strong supportfor a story of stability from young adulthood to old age,with very little change with respect to age until at least age70 and beyond. Moreover, other evidence from the litera-ture on cognitive aging suggests that, whereas there areclear declines in old age in measures of processing abilities,there is little relationship of age to verbal skills (Park,1998). Using a small sample of 310 college-educated adultsaged 20-90, Park and colleagues (1996) found evidence forsystematic differences in performance across age groups onspeed of processing, working memory, and free and cuedrecall tasks; however, measures of vocabulary knowledgedid not show an age-related difference, suggesting that mea-sures of knowledge or more crystallized measures are rela-tively stable across the life span.

METHODSWe examined age-related patterns in a measure of verbal

ability using 14 repeated cross-sectional surveys from theGeneral Social Survey (GSS) over a 24-year period, con-trolling for relevant cohort and schooling experiences. TheGSS is a biennial survey of the American public that beganas an annual survey in 1972 (NORC, 1999). In surveys be-ginning in 1974 and extending through 1998 (1974, 1976,1978,1982, 1984,1987,1988,1989, 1990,1991,1993,1994,1996, and 1998), the GSS interview included a short 10-item vocabulary test developed for survey measurement(Miner, 1957; Thorndike, 1942; Thorndike & Gallup, 1944).Thorndike and Gallup described it as a "test of verbal intel-ligence ... [assessing] the nature of past learnings and notthe ability to make novel adaptations" (pp. 78-79). Mea-sures of vocabulary knowledge correlate highly with tests ofgeneral intelligence—usually 0.8 or higher (Miner, 1957)—and are good indicators of the verbal component of standardtests of general intelligence.

In the GSS, 10 vocabulary words were given to respon-dents; for each word, they were given 5 other word choicesand asked to select the one that was the "closest to themeaning." These data permit an assessment of age-relatedpatterns in verbal ability as well as variations among sub-

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AGING, COHORTS, AND VERBAL ABILITY S153

groups of the population. The GSS vocabulary measure isthe number of correct answers on these 10 vocabulary items, ascore that has an internal consistency reliability of 0.72. Weexpect the GSS vocabulary test score to behave much morelike a crystallized ability than a fluid or processing kind ofability, say compared to Schaie's (1996) measure of Thur-stone's PMA (Primary Mental Abilities) Verbal Meaningscore, which is a "highly speeded test with a significantloading on Perceptual Speed," and which therefore clearlytaps processing abilities to a much greater extent (p. 52).

Because of the limitations in sampling of minority immi-grant populations, we generalize only to the native-born En-glish-speaking population of persons aged 24 and older liv-ing in households in the United States. We focus only onnative-borns because of the association between nativityand cohort membership (x2 = 51.43, 19 degrees of freedom,(df), p = .00008) and the vast differences between nativesand nonnatives on the GSS vocabulary test (F ratio with 1and 14,510 df = 157.36, p = .0000). We focus on personsaged 24 and older for two reasons: (1) until about age 24 theamount of schooling attained is censored for vast numbersof the population aged 24 and under, and (2) because ofsampling and field procedures the GSS has a great deal ofdifficulty obtaining an unbiased sample of younger mem-bers of the population in any cross-sectional survey. Finally,in order to generalize to a population of people rather thanhouseholds, the analyses reported here weight the data bythe number of adults in the household. The way in which wedefine the population may account for some differences be-tween our findings and those of others. Hauser and Huang(1997) and Huang and Hauser (1998) include the youngestmembers of the GSS samples but exclude those respondents

over age 65. Wilson and Gove (1999) do not restrict thesample in any way. However, we suspect that the differ-ences in results among these studies and ours probably havemore to do with the treatment of the data than the definitionof the population.

RESULTSThe numeric data in Table 1 present patterns of the raw,

unadjusted GSS vocabulary test scores by age and cohortmembership. Figure 1 displays these scores by 1-year unitsof age, which is comparable to the patterns in the Total rowfor the grouped data of Table 1, which gives the averageGSS vocabulary test score by 4-year age categories. Herewe define cohort categories in terms of 4-year spans exceptfor the extreme categories, where different widths are used.Similarly, 4-year spans are used to define the age categoriesas well. In later analyses we employ 1-year spans to definecohort categories. The data in Table 1 illustrate a fundamen-tal problem with the nature and sources of data available todraw inferences about the effects of aging. In short, theproblem is linked to the classic under-identification prob-lem in separating age, period, and cohort influences in re-peated cross-sectional surveys (Mason & Fienberg, 1985).This is revealed in part by the fact that the data for theyoungest age groups, those under 30, come primarily frompeople born after World War II, and the data for the oldestage groups, those over 60, come principally from those bornduring the early quarter of this century. Age and cohortmembership are fundamentally confounded in data of thissort, and without being able to separate the effects of agingfrom cohort, the source of the patterns in the data is ambigu-

Table 1. Raw, Unadjusted GSS Vocabulary Test Score Means by Age and Cohort

Age

Cohort

1885-18981899-19021903-19061907-19101911-19141915-19181919-19221923-19261927-19301931-19341935-19381939-19421943-19461947-19501951-19541955-19581959-19621963-19661967-19701971-1974

Totaln

24-27

6.055.855.675.705.845.835.71

5.811664

28-31

6.036.286.206.166.025.935.85

6.071716

32-35

6.336.326.685.986.096.095.86

6.161698

36-39

6.236.236.436.706.486.386.37

6.421560

40-43

6.106.206.656.446.556.536.10

6.391385

44-47

6.186.486.025.926.266.686.49

6.311168

48-51

6.365.865.686.006.526.766.77

6.351065

52-55

5.876.276.346.046.106.176.46

6.17982

56-59

6.366.186.075.916.086.266.53

6.19887

60-63

6.276.026.135.725.965.966.05

6.01872

64-67

5.996.166.066.046.266.526.24

6.18769

68-71

5.335.375.565.946.046.255.76

5.80741

72-75

5.595.185.775.906.285.575.81

5.76639

76-79

5.405.875.465.235.836.105.33

5.69463

80-83

5.935.976.225.075.435.61

5.63277

84-89 Total

5.04 5.435.20 5.635.25 5.385.03 5.525.71 5.92

6.135.946.146.096.076.136.306.396.526.266.096.025.885.845.71

5.17 6.12254

F Ratio

1.770.890.941.731.420.671.431.701.741.400.372.46*2.52*3.85***5 51***

4.51**470**

0.180.01

—

14.65***

Eta2

0.0250.0140.0150.0230.0160.0060.0110.0110.0110.0100.0020.0130.0110.0140.0180.0140.0130.0010.000

—

0.013

n

178210286438575733833897847788928

109113331608150013851108786448168

16140

Note: GSS = General Social Survey.*p < .05; **p < .01; ***p < .001.

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S154 ALWIN AND McCAMMON

Figure 1. Raw and predicted General Social Survey vocabulary test scores by age. — raw vocabulary test scores; vocabulary test scorespredicted from Age and Age2.

ous. The entries in this table also illustrate the phenomenonof cohort replacement.

Several of the age differences across the rows of Table 1are statistically significant, and as shown in Figure 1, thereappears to be a tendency for growth in vocabulary knowl-edge through age 50, with substantial declines well after age60. As already noted, the problem with interpreting this interms of patterns of cognitive aging is that persons born intoearlier cohorts, as compared to later cohorts, have very dif-ferent experiences that could potentially affect their cogni-tive scores. For example, earlier cohorts have much less ed-ucation, and they are therefore less likely to perform as wellon verbal tests compared to cohorts born later. The earlierborn cohorts are disadvantaged due to their lower overalllevels of formal schooling. At the same time, while more re-cent cohorts may be expected to have higher verbal scoresdue to their greater amounts of schooling, their scores maybe depressed in part because of cohort-related experiencestied to declining complexity of learning materials used inschools (Alwin, 1991; Alwin & McCammon, 1999; Chall &Conard, 1991; Chall, 1983; Chall, Conard, & Harris, 1977;Hayes, Wolfer, & Wolfe, 1996; Stedman, 1996). Thus, eachcohort trajectory potentially begins at a different location onthe scale, which results from cohort-related differences inexperiences relevant to verbal skills. In addition, there couldbe period factors shaping the scores of all cohorts at varioustimes (Alwin, 1991).

To summarize, the diachronic data within cohorts con-found age and period, while the synchronous data within timeconfound age and cohort. In this situation it is difficult to

draw any inferences about the effects of aging, unless one iswilling to make some simplifying assumptions about the na-ture of the effects of these various factors. One approach tobegin separating the influences of aging from other factors isto examine the diachronic data more carefully while control-ling for cohort, making the assumption that period influencesare minimal. Most of the available evidence suggests that, al-though people may be reading less, the nature of the standardvocabulary of modern American English has not changedwithin the period covered by the GSS, 1974 to 1998, which isthe time interval within which such potential period effectswould have to be operating (see Glenn, 1994; Hauser &Huang, 1997; Huang & Hauser, 1998; Weakliem, McQuillan,& Schauer, 1995; see Wilson & Gove, 1999, for an alternateview.) Given the unlikelihood that serious errors will resultfrom assuming minimal period effects during this time on theaspects of vocabulary assessed by the GSS vocabulary test, itis then more readily possible to separate aging and cohort in-fluences (Alwin & McCammon, 1999).

Following this approach, we can control for cohort by plot-ting each cohort's age variation in the GSS vocabulary test ona common scale, thus achieving what might be viewed as asynthesis of the various age trends. The numeric results ob-tained in this case are given in Table 2. We obtained theseresults by deviating the GSS vocabulary test score for eachcase from its cohort mean and then recentering this resultabout the grand mean. In parallel to Table 1, these resultspresent the age trajectory for each cohort, but after having re-moved the case's cohort mean from its score. In the terminol-ogy of the analysis of variance (ANOVA), we have parti-

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Table 2. Adjusted GSS Vocabulary Test Score Means by Age and Cohort

Age

Cohort

1885-18981899-19021903-19061907-19101911-19141915-19181919-19221923-19261927-19301931-19341935-19381939-19421943-19461947-19501951-19541955-19581959-19621963-19661967-19701971-1974

Totaln

24-27

5.675.705.755.786.066.156.12

5.891664

28-31

5.745.866.086.196.136.206.07

6.061716

32-35

6.146.086.305.856.106.216.08

6.101698

36-39

6.206.076.146.306.346.436.44

6.301560

40-43

6.186.216.436.156.156.406.08

6.231385

44-47

6.226.466.005.736.016.286.35

6.131168

48-51

6.305.895.806.036.356.486.34

6.211065

52-55

6.066.306.396.146.095.986.24

6.16982

56-59

6.366.355.995.926.106.206.37

6.18887

60-63

6.465.996.305.735.995.996.09

6.07872

64-67

6.576.386.086.246.286.576.25

6.34769

68-71

6.156.085.755.926.226.195.80

6.04741

72-75

5.975.826.286.106.285.735.86

5.99639

76-79

5.536.566.225.736.036.115.52

6.00463

80-83

6.736.266.855.775.635.58

6.11277

84-89 Total

6.03 6.125.73 6.125.96 6.125.70 6.125.92 6.12

6.126.126.126.126.126.126.126.126.126.126.126.126.126.126.12

5.87 6.12254

F Ratio

3.07*1.250.911.501.420.721.451.581.860.990.242.49*2.52*3.77***^ 55***

4.17**4.73**0.480.17—

3.80

Eta2

0.0420.0200.0150.0200.0170.0060.0110.0100.0120.0070.0010.0130.0110.0140.0180.0120.0130.0010.000

—

0.004

n

178210286438575733833897847788928

109113331608150013851108786448168

16140

Note: GSS = General Social Survey.*p < .05; **p < .01; ***p < .001.

tioned the GSS vocabulary test score into two parts, a within-cohort part and a between-cohort part. In Table 2 we havedisplayed the within-cohort portion of the GSS vocabularyscore, centered around the grand mean (i.e., we have removed

the between-cohort part of the variation in the score). Notethat because of the way in which we have defined this score,all cohort categories have the same mean, namely the grandmean for the entire sample. Figure 2 presents the pattern of

20

Figure 2. Raw and adjusted General Social Survey vocabulary test scores predicted from Age and Age2. — raw scores; — adjusted scores.

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within-cohort adjusted GSS vocabulary test means plotted interms of age differences (see the dotted line for adjusted GSSvocabulary test scores). Each of the two curves plotted is adifferent age trajectory of GSS vocabulary test scores, given aparticular model. The solid line is the best-fitting model for anonlinear function of age based on the raw vocabulary scoredata, as in Figure 1. The second curve is the original score af-ter having been adjusted for cohort membership. These re-sults suggest that a substantial part of the differences poten-tially attributable to age in Table 1 are removed uponcontrolling for differences among cohorts in factors shapingvocabulary knowledge. The curvilinear relationship of vocab-ulary knowledge to age is still apparent in the adjusted vocab-ulary score data, although the dramatic nature of the age tra-jectory we observed in the raw GSS test-score means istempered considerably. Rather than a decrement from age 50to 80 of three quarters of a word on the ten-item scale, the co-hort-adjusted decline is in the neighborhood of one quarter ofa word. Between ages 40 and 70 the cohort-adjusted vocabu-lary scores are relatively flat, although a slight curvilinearpattern is still apparent. There is a noticeable decline in oldage, say after age 70, but the changes in the cohort-adjustedscores are gradual and slight, compared to the raw unadjustedfigures.

These results present an interesting tentative conclusion:namely, that after controlling for differences among cohortsin the GSS data, there are age-related patterns on the vocab-ulary test score, but they are substantially smaller than onewould expect based on the raw data. Before drawing theseconclusions, however, we need to examine the complex na-ture of the relationship between aging, cohorts, and school-ing. This is necessary because within-cohorts schooling isthe single most powerful predictor of vocabulary knowl-edge, and cohorts differ significantly in their average levelof schooling completed. The correlation between years of

schooling completed and GSS vocabulary test scores is 0.53and the unstandardized regression coefficient is approxi-mately 0.4. This means that an increment or decrement in 4years of schooling—roughly the difference between havinga high school education or not, or the difference betweenhaving a college degree or not—produces a difference inabout 1.5 words on the GSS vocabulary test score. More-over, as already mentioned, cohorts differ significantly inthe number of years of schooling completed, with earlier-born cohorts having the benefit of many fewer years ofschooling.

Age Patterns, Cohorts, and SchoolingIf aging and cohort effects on cognitive test performance

are confounded due to the relationship of education to testperformance, and if there are cohort differences in school-ing experiences, then some of the effects of controlling forcohort (see Figure 2) may be attributable to schooling. Tothe extent that cohort differences in schooling account forthese effects, it may be possible to correct for the problem incross-sectional data by controlling statistically for school-ing. In nonexperimental research, schooling can be con-trolled either through selection or through statistical con-trols (Kish, 1987). In the present case we rely on statisticaladjustments. In Table 3 we demonstrate the effects of con-trolling for level of education in our estimation of the pa-rameters in the regression of the GSS vocabulary test scoreson age variation. We use a set of polynomials to representthe effects of age, Age and Age2. Due to the definition ofour sample, we have defined Age as Age — 24. Schooling ismeasured as the number of years of schooling completed,centered at the grand mean.Although it may be advisable tospecify the nature of the functional form more precisely(e.g., Goldberger, 1964, pp. 214-215), we should point outthat this form of the model fits the general curve of the data

Table 3. Regression Models for GSS Vocabulary Score

Model (1)

Centered Schooling 0.3659***(SE) (0.0047)

Mean Cohort Schooling(SE)

Age(SE)

Age2

(SE)

Intercept 6.1212***(SE) (0.0142)

R2 0.2771**ModelsR2 Increment

(2)

0.0386***(0.0036)

-0.0008***(0.0001)

5.8712***(0.0401)

0.0112***

(3)

0.3844***(0.0048)

0.0419***(0.0030)

-0.0005***(0.0001)

5.5605***(0.0342)

0.2931***3 vs. 1

0.0161***

(4)

0.3948***(0.0049)

6.1718***(0.0836)

0.3036***4 vs. 1

0.0265***

(5)

0.3953***(0.0049)

0.0226***(0.0044)

-0.0006***(0.0001)

5.9946***(0.0965)

0.3063***5 vs. 4

0.0027***

(6)

0.3948***(0.0049)

-0.2346***(0.0140)

6.1212***(0.0141)

0.2894***6 vs. 1

0.0123***

(7)

0.3932***(0.0049)

-0.2141***(0.0273)

0.0368***(0.0031)

-0.0006***(0.0001)

5.7713***(0.0434)

0.2958***7 vs. 6

0.0064***

16140 16140 16140 16140 16140 16140 16140

Notes: The GSS (General Social Survey) is the dependent variable in all models. Models 4 and 5 include 89 dummy variables representing 90 cohorts (1947 is theomitted category).

***/?< .001.

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quite well (see Figure 1). Also, a model that includes a setof dummy variables representing 1-year age intervals pro-vides a marginally better fit to the data, as measured by theimprovement to the explained variance (data not presented).However, given the large sample sizes for most of the co-horts represented here, we suspect that these departuresfrom a more or less continuous nonlinear form for the agefunction do not represent substantive differences worthy ofretaining in the model. Thus, we rely solely on the Age andAge2 terms to describe the age function here.

In the first model we estimate the linear effect on GSSvocabulary test scores associated with years of schooling.Because of the selectivity of schooling on cognitive abili-ties, it is unclear whether this coefficient should be inter-preted as an "effect" of schooling or as a consequence ofprior cognitive abilities mediated by schooling (Alwin &McCammon, 1999). In either case, the magnitude of the re-lationships suggests that schooling should be controlled inthe assessment of effects of other variables, such as aging,on GSS test score data. In the second model we estimate thecoefficients for Age and Age2 without any controls. This isthe model that generated the raw means for the GSS vocab-ulary test scores in Figure 1. These results suggest that ag-ing has significant effects on vocabulary knowledge, suchthat vocabulary knowledge increases with age up to a pointwhere it levels off, and later begins to decline and deterio-rate in old age (Wilson & Gove, 1999). However, it shouldbe pointed out that aging contributes only a small propor-tion—about one percent—to the explained variance in vo-cabulary knowledge, although the results are statisticallysignificant. In model 3 we examine these same effects con-trolling for schooling. These results indicate that an adjust-ment for age differences in schooling does not modify theconclusions one would reach about the effects of aging onvocabulary knowledge, and if anything, the effects of agingare ever so slightly stronger. Although we have includedschooling in the equation, we have not explicitly includedcohort levels of schooling (i.e., to this point we have as-sessed only the reduced-form of the effects of schooling onvocabulary knowledge).

In order to assess the extent to which cohort factors areimportant in explaining variation in GSS test scores, inmodel 4 we include cohort differences as well as schoolingin the model. This indicates that cohort effects on vocabu-lary knowledge contribute significantly to the explainedvariance. By adding Age and Age2 to this equation (seemodel 5), we can assess within this framework the extent towhich aging contributes to vocabulary knowledge, net ofboth schooling and cohort. Note that in this regression, be-cause we have centered the schooling variable at the grandmean and define Age as Age — 24, the intercept is the ex-pected value of the GSS vocabulary score for persons 24years of age. Changing the zero point on an interval scalerearranges the information contained in this regression in-volving interaction terms involving that variable, but in thiscase it does not change the basic interpretation of the effectsof age or its contribution to the explained variance (see Alli-son, 1977).

These results reinforce those presented earlier with re-spect to the consequences for the aging hypothesis of con-

trolling for cohort, namely that by controlling for cohort inthese regressions, the effects of aging are substantially re-duced—the increment to the R2 for model 5 compared tomodel 4 is .0027, which is less than one third of 1% of thevariance. Compared to the unadjusted R2 of .0112, this seemsquite small. As suggested earlier, there is support here forthe conclusion that aging contributes to vocabulary knowl-edge, but the cohort-adjusted differences are much smaller.By including cohort differences in the model, we have defacto removed any and all differences among cohorts fromthe slopes for Age and Age2, although it is not clear fromthis what aspects of cohort differences account for this ef-fect.

That the apparent effect of aging is significantly reducedby taking into account cohort differences is reflected in thecomparisons between the two age functions in Figure 2.This is also reflected in the magnitude of the Age and Age2

coefficients in model 5. For example, controlling for cohortreduces the linear age coefficient by 46%—compare model3 versus model 5 in Table 3. These results show rather con-vincingly that a substantial portion—roughly half—of theeffects of the linear increase in the GSS vocabulary scoreassociated with aging operates via the between-cohort com-ponent of the GSS test-score data. Although we draw thiscomparison here, we think it is risky to make absolute com-parisons across models involving quadratic terms, that is,models including product terms like Age2. The fact is thatthe magnitude of the linear age coefficient is dependent en-tirely upon where the age distribution is centered and istherefore somewhat arbitrary (see Allison, 1977, pp. 145-148). In a similar case, Allison recommends that, due to thislimitation of not being able to interpret the linear coefficientindependently of the intercept, the best strategy in assessingthe fit of the model is to evaluate the increment to R2 (Alli-son, 1977, p. 149).

Assuming there is some validity to these claims, the ques-tion arises as to whether it is cohort differences in level ofschooling that account for these findings. To address this, inmodels 6 and 7 we include a measure of between-cohort dif-ferences in schooling—the cohort-specific mean years ofschooling completed. This variable is included to assess theeffects of the composition of schooling on GSS test scoresin order to help us decide whether it is cohort differences inschooling that account for the effect of cohort differences inpatterns of age-related variation in vocabulary knowledge.As in model 5, the addition of the Age and Age2 variables tothe equation containing cohort differences in schooling (seemodel 7) results in very little improvement in variance ex-plained, namely .0064. By comparing the proportions ofvariance explained by Age and Age2 in GSS test scores inmodel 2 prior to any controls for cohort, and the incrementsto R2 linked to the addition of Age and Age2 (model 5 vsmodel 4, .0027, and model 7 vs model 6, .0064), we see thatcohort differences in schooling account for approximately43% of the effect of controlling cohort on estimates of agingparameters. It is relatively clear, then, that a substantial por-tion of the cohort differences responsible for the spuriousassociation of aging and test scores can be summarized byintercohort differences in average level of schooling at-tained.

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In order to investigate the robustness of the age effects inthese analyses, we also included controls for race, gender,and family background (results not reported here). Specifi-cally, the inclusion of controls for race, gender, parental ed-ucation, father's occupational prestige, maternal employ-ment, sibship size, rural upbringing, Southern upbringing,and family intactness as a child did not change any of theabove results. In these analyses there were significant maineffects of race (favoring Whites), gender (favoring women),parental education (favoring those with more educated par-ents), father's occupational prestige (favoring those withhigher prestige occupations), sibship size (favoring smallsibships), rural upbringing (favoring those from urban back-grounds), and Southern upbringing (favoring non-South ori-gins). The effects of these variables on verbal test scores arebeyond the scope of the present analysis (but see Alwin,1991). However, we examined the interaction effects ofgender and race with the age functions estimated in thesemodels and found no significant differences—both in thecase of gender [F (df = 2 and 16,044) = 2.268, p = .104]and race [F (df = 2 and 16,044) = .581, p = .560]. Thus,our conclusions about the consequences of aging for vocab-ulary knowledge seem to be quite general with respect tocategories of gender and race.

Cohort Differences in Effects of SchoolingIn these analyses we examined a within-cohort model for

the effects of Age and Age2 (see model 2 in Table 3), indi-cating that aging seems to have only minimal effects on ver-bal knowledge net of cohort. Although these effects are sta-tistically significant, they explain very little variance in GSSvocabulary test scores. Including schooling in this modeldid not change the results for the effects of aging, over andabove the effects of controlling for cohort. In that model wewere assuming that the effect of schooling was constantover cohorts. In fact this may not be the case, because theremay have been some form of decline in the value of school-ing with regard to verbal ability. Here we address this ques-tion by examining more closely the differential effects ofschooling on vocabulary knowledge cohort by cohort. Spe-cifically, we address the possibility that the effects of yearsof schooling on vocabulary knowledge differ significantlyacross cohorts. Within each birth-year category, we re-gressed the GSS vocabulary test score on the amount ofschooling. In order to provide all relevant information forthe examination of this hypothesis, Table 4 presents: eachcohort category (1), the mean age range covered (2), thesample size (3), the correlation between age and birth yearwithin the category (4), the mean GSS vocabulary score (5),

Table 4. Within-Cohort Regression of GSS Vocabulary Test Score on Schooling and Age

(1)

Cohort

1885-18981899-19021903-19061907-19101911-19141915-19181919-19221923-19261927-19301931-19341935-19381939-19421943-19461947-19501951-19541955-19581959-19621963-19661967-19701971-1974

(2)

Mean AgeRange

80-8973-8969-8966-8861-8558-8253-7750-7445-7042-6538-6133-5730-5426-5024-4526-4124-3824-3424-2925-26

Total (1)

Total (2)

(3)

n

178210286438575733833897847788928109113331608150013851108786448168

16140

16140

(4)

'"cohort.age

-0.698***-0.194**-0.166**-0.060-0.192***-0.077*-0.112**-0.111***-0.171***-0.096**-0.098**-0.077**_Q 134***

-0.162***-0.064*-0.206***-0.171***-0.077*-0.352***-0.473***

-0.131***

0.000

(5)Mean

VocabularyScore

5.435.635.385.525.926.135.946.146.096.076.136.306.396.526.266.096.025.885.845.71

6.12

6.12

(6)

MeanSchooling

9.369.979.98

10.6111.0811.3011.6411.9211.9312.4012.5613.0113.1013.7913.5113.5213.5513.5813.7813.66

12.71

12.71

(7)

Intercept

6.546.586.326.326.526.646.376.426.396.206.196.186.226.075.925.745.715.555.515.38

—

(8)

Slope forSchooling

0.3330.3460.3440.3790.3650.3660.3980.3520.3860.4130.4050.4140.4250.4250.4320.4360.3740.3820.3090.348

0.395

0.395

(9)SchoolingIncrement

to/?2

0.3060.3500.2510.2380.2880.2500.3220.2530.3320.3300.3000.3230.3340.3020.2970.3020.2170.2440.1640.234

0.286Age2

0.283Age2

(10)

Slope forAge

-0.053-0.035-0.019-0.053***-0.041***-0.019-0.016-0.016*-0.008-0.012-0.015*-0.015*

0.0040.0080.020**0.0110.030*0.0080.065

-0.330**

0.024***-0.001***

0.023***-0.001***

(11)Age

Incrementto/?2

0.0080.0070.0020.022***0.016***0.0030.0030.003*0.0010.0020.003*0.003*0.0000.0010.004**0.0010.004*0.0000.0050.035**

0.003***

0.003***

Notes: The reported sample size is unweighted and is based on a population of U.S. natives (see text) age 24 or older having non-missing data for the vocabularytest score and schooling. All other information presented in this table is based on weighted data. The "mean age range" refers to the mean age of the cohort group in thefirst and last GSS (General Social Survey) years in which the vocabulary test score was obtained. For most cohorts this is the mean age in 1974 and 1998. Results inthe Total (1) row use a baseline model containing 18 dummy variables for the cohort categories. Results in the Total (2) row use a baseline model containing 89 single-year cohort dummy variables. Age has been centered at 24 years. All values reported in columns 7, 8, and 9 are statistically significant (p <.001).

*p < .05; **p < .01; ***p < .001.

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mean years of schooling (6), the intercept (7) and slope forschooling in the prediction of the GSS vocabulary score (8),the R2 for schooling in the prediction of the GSS vocabularyscore within cohorts (9), the slope for Age when added tothe previous model (note that in the total sample we includeboth Age and Age2) (10), and the increment to the R2 forAge (and Age2 in the total sample) over and above that con-tributed by schooling (11). Note that in these within-cohortregressions we center the schooling variable at the grandmean of the population.

In this set of models what one normally considers to becohort effects are reflected in the intercepts (see Alwin, 1991;Alwin & McCammon, 1999). These are unconstrained bythe imposition of the "common slope" as in the analysis ofcovariance. By contrast, the effect of the covariance adjust-ment on these intercepts (i.e., the adjusted means [not pre-sented in Table 4]) does impose a common slope; these twovalues are virtually identical (r = .99 over cohort catego-ries), indicating that the within-cohort slopes for schoolingdo not vary a great deal around the common slope. In eithercase, the observed difference among these intercepts proba-bly reflects differences in cohort experiences. Here we seethat, net of schooling, there are systematic declines in GSSvocabulary test performance from earlier born to more re-cently born cohorts. The differences seem particularly pro-nounced for cohorts born after 1946, although these patternsare also consistent with the possibility that vocabularyknowledge increases with age.

It is also possible to consider differences in the slopes inthe regression of the GSS vocabulary test score on school-ing as cohort effects as well, and we investigate this here.The question of whether there is a common slope forschooling amounts to whether units of education havechanged their meaning over time with respect to vocabularyknowledge. Does it take more or less schooling now than itused to in order to bring about the same amount of learning?Did a year of schooling obtained in the 1920s produce thesame amount of learning, for example, in students' knowl-edge of vocabulary, as it did in the 1960s? In other words, inaddition to differentials in exposure to amount of school, isit possible to argue that there were differences in school ex-periences as well? This hypothesis is actually about a sec-ond-order cohort effect, that is, an effect on the relationshipamong variables rather than their mean levels. We can ex-amine this question by inspecting the numbers in column 8of Table 4, which suggest some systematic variation inthese slopes across cohorts. It appears that the within-cohortslopes are smaller for earlier born cohorts (those born be-fore 1939), suggesting that schooling produced less learningper year. Also, it appears that the effect of schooling on vo-cabulary knowledge is also systematically smaller in the co-horts born after 1958. However, despite the curvilinear pat-terns to these slopes, the differences in these slopes are notall that large. Regardless of cohort, a 4-year schooling ad-vantage results in a gain of about 1.5 words on the GSS vo-cabulary score scale. The standard F test for the differencesamong these slopes results in a significant value (F = 2.173with 19 and 16,100 df; p = .0022). However, despite thishigh degree of statistical significance, the model includingdifferent cohort-specific slopes increases the R2 by .0018—

less than two tenths of 1% of the variance. On this basis, itis probably reasonable to assume homogeneity of slopes forpurposes of estimating aging effects and cohort differences,as we have here, although we recognize there may be a sub-stantive interpretation of the differences in these slopes.

Returning explicitly to the examination of the aging hy-pothesis, the results in Table 4 also present the estimation ofthe parameters of a within-cohort regression model includ-ing, in addition to schooling, coefficients for Age (and Age2

in the total sample) as defined earlier. These results (shownin column 11 of Table 4) indicate fairly clearly that there isonly marginal support for effects of aging. Note that in thetotal sample there are systematic patterns to the age varia-tion, as we reported earlier, but the age differences, thoughstatistically significant, simply do not explain a substantialamount of variance. We realize that, given the nature of thedata, there may be problems of redundancy between age andcohort that could bias their assessed effects; however, notethat using 4-year spans of birth years to define cohorts (as inTable 1) in the typical case within cohorts, age and cohortare correlated about -.13 in the total 1974-1998 GSS data,so the potential bias is probably minimal. Indeed, the resultspresented in Table 4 are not affected by this level of correla-tion, because in the extreme case of setting this correlationto zero (see the Total (2) line of Table 4), the results are un-changed. This further reinforces the tentative conclusiondrawn from Figure 2 that when cohort differences are re-moved from the comparisons, there are only very small"pure" age differences in vocabulary knowledge. In only afew cases are the cohort-specific Age coefficients signifi-cant; however, the signs of these coefficients are generallyconsistent with the patterns predicted by Cattell, namelypositive slopes, or growth in verbal ability in young adult-hood coupled with declines in test performance with age inthe older age ranges. It is worth noting, however, that whilethese coefficients are significant in the total sample, wherethe sample size is quite large, the effects are of very smallmagnitudes—together they explain only three-tenths of 1%of the variance. Given the small magnitude of these effectsof aging, examined here within cohorts, we seriously doubtthat differences in aging can explain the cohort effects in-ferred from the differences among intercepts in column 7 ofTable 4.

DISCUSSIONWe began this article by arguing that, in order to assess

the effects of aging on cognitive skills in repeated cross-sec-tional surveys, it was essential that the effects of aging beseparated from the effects of cohort. Using GSS data on ameasure of vocabulary knowledge obtained for several setsof cohorts over a period of 24 years, there appears to be atendency for growth in vocabulary knowledge through toage 50, with a gradual decline after age 60. Despite thesefindings, we argued, an important problem with interpretingthese patterns in terms of cognitive aging is that personsborn into earlier cohorts or to later cohorts have very differ-ent experiences, which could potentially affect their cogni-tive scores. Our results indicate that most of the age differ-ences in the GSS vocabulary measure are removed uponcontrolling for differences among cohorts in factors shaping

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vocabulary knowledge. Because cohorts differ significantlyin the number of years of schooling completed, we arguedthat the observed decline in vocabulary scores at older ageranges is attributable largely to the growth in schooling overthe post-World War II period. Moreover, there is little evi-dence that the relationship between vocabulary knowledgeand educational attainment has changed significantly acrosscohorts. Returning to Figure 2, we should again note thatthe main comparison reveals that some of the raw age-pat-terning of the GSS vocabulary test scores is spuriously dueto the lack of independence of age and cohort as measuredin repeated cross-sectional surveys. It is necessary, there-fore, to examine age trajectories of GSS test scores net ofcohort; as already noted, the results of these calculations asshown in the line predicted by Age and Age2 reveal a muchflatter age trajectory. Still, there is evidence of small age-re-lated patterns in vocabulary knowledge, with slight incre-ments through roughly age 60 and increasing rates of de-cline thereafter.

Because of the complex nature of the relationship be-tween aging, cohorts, and schooling, we engaged in a de-tailed analysis of the effects of aging and school attendanceon verbal skills using diachronic GSS data within cohorts.These analyses further reinforce the conclusion that whencohort differences are removed from the comparisons, thereare only very small "pure" age differences in vocabularyknowledge. Greater attention should be paid to an investiga-tion of the ways in which access to schooling and its bene-fits vary across cohorts. Too little is known about these pro-cesses. Such results should be examined across a widervariety of measures of cognitive ability. At the same time,while it is interesting to pursue further the question of howintercohort sources of variation may inform differencesamong age groups in verbal scores, it remains the case thatwithin-age-group variation in vocabulary knowledge isvastly more important than age differences per se.

We would also conclude that it is important to better un-derstand the ways in which schooling develops resourcesthat can be translated into successful cognitive test perfor-mance and how these processes may change historically.And finally, given the prevailing wisdom that aging islinked to declines in cognitive skills and job performance,further research is necessary, not only to investigate thelinks between aging and test performance, but more impor-tantly, on the relationship between cognitively linked de-clines in work performance and decisions to disengage orretire from work. As already mentioned, available cognitivetests cover a broad range of function, and it is difficult toobtain pure measures of theoretically interesting aspects ofability. Schooling and other cohort-related experiences maybe differentially linked to different types of cognitive scores,and therefore one must be careful in generalizing too widelyregarding the relationship of aging and cognitive abilities onthe basis of measures of a restricted range of function.

ACKNOWLEDGMENTS

Support for this research was provided by grants to the senior authorfrom the National Institute on Aging: "Stability of Individual DifferencesAcross the Life-Span" (AG-04743-08) and "Socioeconomic Factors, Agingand Cognitive Functioning" (AG-015437-02). We are indebted to David

Featherman, Robert Hauser, Linda Wray, and Yu Xie for helpful commentson previous drafts of this material. This is a revised version of a paper pre-sented at the August 1999 annual meetings of the American SociologicalAssociation, Chicago.

Address correspondence to Dr. Duane F. Alwin, Institute for Social Re-search, University of Michigan, 426 Thompson Street, Ann Arbor, MI48106-1248. E-mail: [email protected]

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Received July 17,2000Accepted November 10, 2000

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