Cumulative Deficit: A Testable Hypothesis? · intelligence in her textbook on human differences,...

Developmental Psychology1974, Vol. 10, No. 6, 996-1019

Cumulative Deficit:A Testable Hypothesis?1

ARTHUR R. JENSEN2

University of California, Berkeley

Cumulative deficit is an hypothesis concerning the cause of lower mental test scoresof groups considered environmentally deprived. It presupposes a progressive decre-ment in test scores, relative to population norms, as a function of age. Clarificationof the theoretical issues and the methodological problems involved in establishingthe progressive decrement phenomenon are discussed in relation to the relevantresearch on disadvantaged groups, especially American Negroes. In this group inparticular there is no methodologically adequate evidence in the literature for aprogressive decrement in IQ or other mental measurements. The present study,'usingdifferences between younger and older siblings, which satisfies more rigorousmethodological requirements for the detection of progressive decrement than haveexisted in previous studies, found a significant age decrement in verbal but not innonverbal IQ among a large sample of Negro elementary school children, althoughthe mean white-Negro difference is similar for nonverbal IQ and verbal IQ.

The term cumulative deficit refers to one ofthe most fundamental concepts in the nowvast literature of environmental deprivationand cultural disadvantage. It is also thekeystone of the rationale for compensatoryeducation.

The apparent phenomenon which thecumulative deficit hypothesis attempts to ex-plain has long been recognized. Gordon's(1923) striking finding of large decrementsin verbal IQ with increasing age ofeducationally deprived canal boat childrenin England is well known. But the termcumulative deficit itself is fairly recent. As faras can be determined, it is attributable toOtto Klineberg (1963), who, in attemptingto explain intellectual differences betweenraces, remarked that "it is as the children getolder that differences in test performance ap-pear. Surely this is to be expected on the basisof the cumulative effect of an inferior environ-

1 The data collection for this study was supported by agrant to the University of California by the BerkeleyUnified School District; the statistical analysis was aidedby a grant to the University of California from the Sterl-ing Morton Charitable Trust.

2 Requests for reprints should be sent to Arthur R.Jensen, Institute of Human Learning, University ofCalifornia, Berkeley, California 94720.

ment [p. 200]." As an example of thisphenomenon, Klineberg cited a study bySherman and Key (1932) of white childrenliving in the "hollows" of the Blue RidgeMountains, where the average IQ declinedfrom 84 at ages 6-8, to 70 at 8-10, to 53 at10-12! Following Klineberg's 1963 article,the concept of cumulative deficit rapidlyproliferated in the growing literature oncultural deprivation. The term is used exten-sively, for example, in a review of 99 researchreports on the disadvantaged publishedwithin four years after Klineberg's article(McCloskey, 1967). In this review, asgenerally elsewhere in the literature,cumulative deficit stands both for the pur-ported phenomenon of an increasing decre-ment in test scores with increasing age of dis-advantaged children relative to advantagedchildren, and for the hypothesis which ex-plains this phenomenon in terms of thecumulative effects of a deprived environ-ment. We read,

Both history and the modern science of aptitudemeasurement indicate that the relatively limitedcapabilities and achievements of disadvantaged pupilsare due mainly to restrictions of external environment,not to their internal potentials. Regardless of how "in-telligence," "aptitude" and "achievement" are denned,

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CUMULATIVE DEFICIT: A TESTABLE HYPOTHESIS? 997

research provides ample evidence that, at present, in-adequate and inappropriate schooling is largely respon-sible for stultification of many capacities [McCloskey,1967, p. 4].

Such deficits of development and learning arecumulative. They progressively reduce the emotionaland cognitive bases essential for normal rates of acquir-ing more complex concepts and capabilities. Conse-quently, as years pass, disadvantaged children tend tobecome progressively more retarded [McCloskey, 1967,p. 6].

More detailed explications of the cum-ulative deficit concept are presented in thewritings of Martin Deutsch on the cultur-ally disadvantaged and early childhoodcompensatory education. He refers tocumulative deficit as "the decline over timein their [i.e., experientially deprivedchildren's] scholastic achievements and inmeasures of 'intellectual abilities' [Deutsch,1967, p. 338]." More specifically,

it appears that, as Negro children get older, the dis-crepancy between their IQ scores and those of whitechildren increases, while the discrepancy between thetwo groups' scores on the language measures of thisresearch decreases. At the first-grade level, the disadvan-taged child's experiences seem to have been relativelysufficient to provide him with certain language skills. Bythe fifth grade, however, he does not seem to have hadthe background of experiences in the use of the morecomplex language necessary both for success on in-telligence tests and for expressing himself meaningfullyin complex sentence structure [Deutsch, 1967, p. 221]

In support of the cumulative deficit hy-pothesis, Whiteman and Deutsch note thatin their own study (based on compar-isons of different age groups) the magni-tude of the decrement in Lorge-ThorndikeIQ with increasing age is greater for thosechildren who score as most disadvantagedin the specific experiences assessed by a Dep-rivation Index, and the age decrement iseven greater for the Wechsler Intelli-gence Scale for Children (WISC) Vocab-ulary Test.

The general tenor of these results points to the greatersensitivity of the language test to different patterns ofdisadvantage, whether these disadvantages are related togeneral socioeconomic level or to Negro status, or to thespecific background factors implied in the DeprivationIndex [Deutsch, 1967, p. 345].

That the cumulative deficit is the basis of the

rationale for compensatory education issuggested by statements such as

in order to arrest the cumulative-deficit process and togo beyond that by actually reversing deprivation effectsand carrying performance levels up to national-norm ex-pectations, more potent interventions along the linesdiscussed will be necessary [Deutsch, 1967, p. 27].

it would seem reasonable to conclude that if learningsets or the level of underlying abilities are influential in adecline in performance, an improvement of these skillsthrough an enrichment program at the preschool andkindergarten levels may be helpful in arresting or revers-ing the cumulative deficit [Deutsch, 1967, p. 338].

The cumulative deficit hypothesis has beenput forth in what is perhaps the most ex-plicitly testable form by a sociologist, wholikened the cumulative effects of the environ-ment on cognitive development to a com-pound interest table (Stinchcombe, 1969, p.518). For example, if two groups differ, onaverage, by x percent per year in rate of men-tal development because of differences in en-vironmental inputs, the cumulative (i.e.,"compound interest") effect would decreasethe ratio of the disadvantaged/advantagedgroup mental age means by more and moreeach year. This model clearly implies notonly an increasing mental age difference butalso an increasing IQ difference between thegroups, from early childhood to maturity,with its corollary of a negative correlationbetween IQ and chronological age in the en-vironmentally disadvantaged group.

Empirical Evidence

Though the earliest mentions of thephenomenon involved IQ decrements in chil-dren on English canal boats and inTennessee mountain "hollows," the greatestuse of the cumulative deficit concept in re-cent years has been in connection with thelower performance of Negro childrenrelative to white children on tests of in*telligence and scholastic achievement. Yet,surprisingly, it is difficult to find consistentor satisfactory empirical evidence of abilitydecrements increasing with age in Negroesrelative to whites. There is even a questionwhether the phenomenon which the cumula-tive deficit hypothesis is intended to explainactually exists, at least in the Negro popula-

998 ARTHUR R. JENSEN

tion, where cumulative deficit has been soprominent a part of the explanation ofNegroes' generally lower IQ and poorerscholastic achievements.

Leona Tyler, in the section on Negrointelligence in her textbook on humandifferences, mentions cumulative deficit,noting that "the higher the school grade inwhich the [IQ] tests have been given, thegreater the difference between Negro andwhite averages has turned out to be [Tyler,1965, p. 306]." She cites the Negro norms forthe Stanford-Binet Intelligence Scale ob-tained on some 1,800 Negro children in fiveSoutheastern states by Kennedy, Van DeRiet, and White (1963). Based on groups ofNegro school children from 5 to 16 years ofage, the results of this study are indeed strik-ing. From the age group of 5 years to the agegroup of 16 years, the mean Stanford-BinetIQ declines steadily from 86 to 51 (with anoverall mean of 80.71). Such a finding wouldbe impressive if it were not for highly likelyartifacts that could account for these results.The data are a cross-sectional sampling ofIQs at various age levels and not alongitudinal picture of IQ changes in thesame group of subjects as they advance inage. Such cross-sectional studies of IQ decre-ment can introduce selective sampling biaseswhich give the appearance of IQ decrementeven when no such decrement exists as a psy-chological phenomenon in individuals. Forexample, all 1,800 children in the study byKennedy,et al., although ranging in age from5 to 16 years, were selected from Grades 1through 6. Consequently, the youngestchildren (under age 6) are underage for firstgrade and are more likely to be intellectuallyadvanced for their years; they are thus an un-representative sample of 5-year-olds. At theother extreme, children in Grades 5 and 6who are beyond 11 or 12 years of age are alsoatypical, in the opposite direction; theoverage children in the later grades are morelikely to be retarded to some degree in theirintellectual development. This relationshipbetween "overageness" and decline in meanIQ of cross-sectional age samples was clearlydemonstrated in an early study by Wheeler(1942). These biasing artifacts due to themethod of sampling could well account forthe apparent increasing IQ deficit in the

study by Kennedy et al. Kennedy himselfsuspected this artifact. To check thispossibility, he carried out a longitudinalstudy of a representative sample of one sixthof the subjects in the original study(Kennedy, 1965). The longitudinal sample(N = 316) was retested on the sameStanford-Binet five years later and showedno decrement whatsoever in mean IQ (78.9versus 79.2). The cross-sectional data had in-deed been misleading in respect to thecumulative deficit hypothesis.

Not all cross-sectional studies have foundan increasing difference between Negro andwhite IQs. In samples from rural Virginia,for example, Bruce (1940) found no greaterdecline in Negro than in white IQs in the agerange 6 through 12, though both groupsshowed a cross-sectional decline of about 10points over this period and both groupsoverall had below-average Binet IQs (white= 90, Negro = 76).

Shuey (1966, pp. 206-207) has examinedall the relevant studies on this point up to1965. She compared all the mean IQs ofNorthern and Southern Negro elementaryschool children of ages 6 to 9 with the IQs ofother Negro children in the same regions,ages 10 to 12. There were 19 studies in all,totaling some 9,350 children. The mean IQof the younger group was 84.03; of the oldergroup, 82.98. Since in many schools educa-tion was not compulsory until 7 years of age,Shuey suspected that the presence of 6-year-olds in the younger age group might havebiased the mean IQ upwards, since these 6-year-olds would tend to be more intellec-tually advanced than their age-mates. Whenthe 710 six-year-olds were excluded from theyounger group, its mean IQ was reduced to83.33, or just .35 above the mean of the10-12 year group. Shuey also compared IQsof Negro children in Grades 1 to 3 with thosein Grades 4 to 7, reported in a total of 43studies comprising some 19,000 Negro chil-dren. The mean IQs of the earlier and latergrades were 83.11 and 84.54, respectively.Shuey also examined the IQ results forNorthern and Southern Negroes separatelyand found no interaction with age. She con-cluded, "It seems, therefore, that betweenthe ages of 7 and 12 and between grades oneand seven there is a marked stability in the


IQ of colored children enrolled in the publicschools [Shuey, 1966, p. 207]." A limitationof Shuey's conclusion is that no account istaken of the probably different schooldropout rates with advancing grade levelin the white and Negro populations, Ifdropouts increase at a faster rate in theNegro group, and if dropouts come largelyfrom the lower half of the IQ distribution,the effect of such differential selection wouldbe to diminish or prevent the appearance of aNegro age decrement in IQ.

The most massive collection of relevantcross-sectional data is to be found in thewell-known Coleman report (Coleman et al.,1966), in which 450,000 children in Grades 1,3, 6, 9, and 12 in 6,000 schools across the na-tion were given tests of verbal and nonverbalability and of scholastic achievement. Exceptin the southern regions of the United States,the Coleman data indicate a fairly constantdifference of approximately 1 standarddeviation (based on whites in themetropolitan northeast) between whites andNegroes in verbal ability, reading com-prehension, and math achievement fromGrades 6 to 12. In the nonmetropolitanSouth, on the other hand, the meanwhite-Negro differences in Verbal Abilityare 1.5, 1.7, and 1.9 standard deviations inGrades 6, 9, and 12, respectively (Coleman,et al., 1966, p. 274). An increasing deficit inthe Southern Negroes is suggested but can-not be proved, since the cross-sectional datacould reflect selective migration of familiesof abler students out of the rural South, thuscausing an increasing accumulation ofpoorer students in the higher grades.

Moreover, the populations of the ruralSouth and of the metropolitan North differin average family size, and family size isnegatively correlated with IQ. The apparentage decrement in IQ among SouthernNegroes could therefore reflect merelyregional differences in family size. This ar-tifact in cross sectional studies is discussedmore fully in the next section, which dealswith methodology.

Probably the most carefully selected andrepresentative cross-sectional age data onmental tests in U.S. white and Negro chil-dren between ages 6 and 12 are those ob-tained by the National Center for Health

Statistics from 19.63 to 1965, as part of theNational Health Survey (Roberts, 1971). Atotal probability sample of 7,417 children,with approximately 1,000 in each year's agegroup between ages 6 to 12, was selected soas to be "closely representative of theroughly 24 million noninstitutionalized chil-dren 6-11 years of age in the United States[Roberts, 1971, p. 2]." Two subtests(Vocabulary and Block Designs) of theWISC were individually administered to 96%of the sample. From the raw score meansand standard deviations for Negroes andwhites in each of six age groups (presented inRoberts, 1971, Table 4, p. 31), it is possibleto determine the mean white-Negrodifference in sigma units at each age andseparately for boys and girls. (The sigma inthis case is the average of standarddeviations within each racial group.) Asystematic increase in the white-Negrodifference with increasing age is best deter-mined from the regression of the mean differ-ences on age. If the slope of the regression bis significantly greater than zero, it meansthere is a significant increase in thewhite-Negro mean difference (in sigmaunits) with increasing age (on the WISCVocabulary, for both sexes combined, b = +.035, t = 2.49, p < .05; for boys, b = .017, t =.78, ns.; for girls, b = .060, t = 3.43,/> < .05;in all cases df = 5). These regressions arevery small; the largest (.060) means that thewhite-Negro IQ difference increases only6/100ths of a standard deviation each yearfrom age 6 to 11. Yet for these data the effectis significant—for girls but not for boys.However, the sex difference between bs is notsignificant. The same trend is true of theWISC Block Designs (for both sexes com-bined, b = .051,? = 5.94, p< .01; for boys, b= .053, t = 1.51 ns.; for girls, b = .068, t =5.55, p < .01). Though the b is significant forgirls but not for boys, the difference betweenthe bs of boys and girls is nonsignificant. Theoverall mean white-Negro difference is .78 afor Vocabulary and .76 a for Block Designs.For boys the corresponding differences are.81 a and .78 CT, and for girls, .75 a and .75 a.So despite considerable mean differences, theevidence of Negro age decrement is slight.But little stock can be put in this evidencesince it is cross-sectional data, and although


it is a most carefully drawn probability sam-ple, such sampling confounds age, IQ, andfamily size, so that some degree of age decre-ment in Negro mean scores relative to thewhite would be expected as a demographicartifact. It may not reflect a psychological ordevelopmental phenomenon. This is ex-plained in the next section on methodology.

One of the most thorough comparativestudies of Negro and white children in therural South (North Carolina) is by Baugh-man and Dahlstrom (1968). They examinedtheir test data with respect to cumulativedeficit by cross-sectionally comparing Ne-gro and white samples at 1-year age-intervalsfrom 7 to 14 years of age on Stanford-BinetIQ. The Negro IQs were almost constantlyone standard deviation below the white IQsfrom age 7 to 14, although the gap narrowsslightly after age 11 due to a lowering of thewhite IQ by some 3 to 4 points. (The whitesin this study are below the average whitenorms, with a mean in the 95 to 100 range.)An analysis of variance of the Baughmanand Dahlstrom (1968, p, 45) data show asignificant decline in IQ with increasing agefor white boys and girls, and for Negro boys,but not for Negro girls. In all groups theeffect is small in any case. Other ability testsused in this study illustrate the high degree ofspecificity of the age deficit. For example, thevarious subtests of the Primary MentalAbilities: Some tests do, others do not showa decrement, and still others show the reverseof the hypothesized age decrement (Baugh-man & Dahlstrom, 1968, pp. 48-57). Thereseems to be no consistent trend according tothe type of mental ability measured by thePrimary Mental Abilities tests, although theauthors (p. 46-47) entertain the notion thatthe decrement sets in as language proficiencybecomes an increasingly important factor inthe test. This opinion has also beenemphasized by Deutsch (1967, p. 331). Yetthe vocabulary raw scores of both the Negroand white samples show an almost perfectlylinear increase with age over the range from7 to 14 years, thus revealing no decrement.The fact that the verbal requirements of mostmental tests increase at higher age levels isconfounded with the increasing degree ofabstractness of the item content and thecomplexity of the mental operations called

upon. The increasing deficit, if indeed it ac-tually exists, could be more a lag in concep-tual development than in verbal proficiencyper se. Also, as in other cross-sectionalstudies, family size was not controlled. Olderchildren, on the average, have more siblings,and larger families have slightly lower IQs,so that a cross-sectional study based on thecomparison of IQs of younger and older agegroups confounds the possible effects of agedecrement in IQ with the statistical effect offamily size.

Some of the Baughman and Dahlstrom(1968, p. 112) data lent itself to longitudinalanalysis. The overall Stanford-Binet IQchange over a 3-year period was —1.1 pointsfor Negroes and +.6 points for whites. Therewas some interaction of this race differencewith sex; girls, especially in the Negro group,showed little or no decrement.

Another longitudinal study in the ruralSouth (Georgia) showed no overall decline inmean IQ from Grade 6 to 10 for either Negroor white students, who differed by a constantamount of approximately 20 IQ points(Osborne, 1960).

A longitudinal study in the North, byHarris and Lovinger (1968), obtained in-telligence and achievement test scores on thesame group of disadvantaged Negro andPuerto Rican (in the ratio of 10 to 1) pupilsin Grades 1,3,6, 7, 8, and 9. (The junior highschool attended by these children had thelowest average achievement of any in theborough of Queens, New York.) There wasno evidence of a declining IQ in this group,that is, the eighth- and ninth-grade IQs wereapproximately equal to the first-grade IQs.

Still another longitudinal study (Rosenfeld& Hilton, 1971) compared groups of Negroand white pupils at 2-year intervals fromGrades 5 to 11 on a battery of scholasticachievement tests (Sequential Tests ofEducational Progress [STEP] and Schooland College Ability Tests [SCAT]). Whenthe means of later tests were adjusted bycovariance on scores obtained 2 yearspreviously, the Negro-white gap remainedconstant across age on some tests but still in-creased on others. Tests that showed in-creasing Negro decrements relative towhites, even after covariance adjustment oninitial status, were SCAT Verbal and Quan-


titative and STEP Math as well as STEPWriting (at ninth grade only). BetweenGrades 9 to 11, Negroes and whites grew atabout the same rates (after covariance ad-justment on previous scores) on Reading,Writing, Social Studies, and Listening. Theauthors suggest that differences in thecurricula of their Negro and white samplesare most likely to account for the observedincrease in the Negro-white gap from Grade5 to Grade 11. The majority of whites were inthe academic program while the majority ofNegroes were in the nonacademic program.Rosenfeld and Hilton rightly comment:

The content areas which these tests assess may be onesto which academic and nonacademic students aredifferentially exposed, thus accounting for the differencesobserved. In addition, curriculum membership in itselfis a complex interaction of self-selection, counselorjudgment, and school policy. The observed differencesare, therefore, as confounded as school differences andthe researcher is left with results to be explained ratherthan tested hypotheses [p. 281].

In addition to cross-sectional and longi-tudinal studies, there is one other method forinvestigating cumulative deficit: comparisonof younger and older siblings. This method,which has certain distinct advantages(detailed in the following section), has beenused, but not optimally, in only two studiesof cumulative deficit. The logic of themethod is clear: younger and older full sib-lings within a given family do not differ,when averaged over many families, in geneticpotential for mental development. Eachchild in a family receives a random allotmentof one half of each of his parents' genes, andthe ordinal position of his birth in no wayaffects this fact. Any systematic differencebetween younger and older siblings, there-fore, must be attributable to nongenetic, pre-sumably environmental, influences or togenetically conditioned differences indevelopmental rates. Significantly lower IQs(or other age-standardized scores) of theolder than of the younger sibs, on theaverage, should therefore constitute strongevidence of a genuine deficit (assuming con-trol of certain other conditions to be men-tioned later), whether genetic or en-vironmental or both, rather than merely aresult of sampling artifact such as we haveseen in cross-sectional studies and as can oc-

cur in longitudinal studies that have nonran-dom attrition of subjects throughout thecourse of the study, which is nearly alwaysthe case.

Gordon (1923), in England, was the first touse sibs to show that Stanford-Binet IQ fellwith age in educationally deprived canalboat children, who led a nomadic existencewith little or no schooling, The mean IQ ofthe youngest child in these families was 90, ofthe second youngest 77, of the third young-est 73, and of the oldest 60.3 This particularuse of sib data, however, is far from ideal,since, when we compare average IQs of thefirst, second, third, etc., child in a family anddo not explicitly control for family size, weconfound two variables—younger versusolder and family size; the first is the variablein question as regards the cumulative deficithypothesis; the second variable is alreadywell known to be negatively correlated(about -.30) with IQ (Anastasi, 1956;Baughman & Dahlstrom, 1968, pp.100-101). Thus, Gordon's finding maysimply reflect in part the fact that four-childfamilies have a lower mean IQ than three-child families, and three-child families have alower mean IQ than two-child families. Inthe entire group of Gordon's canal boat sub-jects, there was a correlation of -.76between IQ and chronological age. Theexistence of intrafamily sib differencesassociated with children's ordinal position inGordon's data, however, indicates that notall of the difference between the means offirst, second, third, etc., children can be at-tributable to the negative correlation be-tween IQ and family size. But the analysisdoes not sufficiently unconfound these twovariables to permit any strong quantitative

3 When the canal boat children were tested on nonver-bal performance tests, there was much less decline inscores and the average IQ of the children was 82, whichis a typical value for unskilled workers, as the canal boatpeople were. Fewer than 1 in 10 obtained performanceIQs below 70, and in fact there was a slight positive cor-relation between performance IQ and age (Gaw, 1925,p. 390). This dissimilarity of the English canal boat chil-dren's test scores from the scores of American Negroes,who generally obtain slightly lower scores on nonverbalperformance tests than on verbal tests (Shuey, 1965, p.504), brings into question the relevance of the canal boatfindings for understanding the Negro IQ deficit.


conclusions about the magnitude of the IQage decrement per se.

Baughman and Dahlstrom (1968, pp.102-103) found a relationship between sibs'ordinal position and Stanford-Binet IQ, butit involved a complex interaction with race,sex, and age; there was no consistent orstatistically significant tendency in either thewhite or Negro samples for the younger sibsto score higher than their older sibs, aswould be expected from the cumulativedeficit hypothesis. In fact, slightly the op-posite was the case, with the older sibs show-ing a slight superiority. As in Gordon'sstudy, Baughman and Dahlstrom presenttheir family data in terms of mean IQ forchildren in various ordinal positions (classi-fied into three categories: youngest, oldest,intermediate), and they arbitrarily assignedsingletons to the category of oldest children,thus again confounding IQ age decrementand family size. Such an analysis is of little orno value in determining the existence ormagnitude of the decremental effect whichthe cumulative deficit hypothesis aims to ex-plain.

Theoretical, Psychometric, andMethodological Considerations

First, a clear distinction must be madebetween cumulative deficit as a psychologicalhypothesis and the empirical phenomenonwhich the hypothesis purports to explain.This important distinction has not been at allclear or explicit in the literature. The distinc-tion is important because, scientifically, thehypothesis is, of course, needless unless thereis actually a phenomenon to be explained.The importance of the hypothesis alsodepends to some extent upon the magnitudeof the phenomenon in relation to otherrelated phenomena, such as the magnitude ofthe overall average Negro-white differencein IQ and scholastic achievement. Therefore,we should look first at the phenomenonitself, and at the methodological problemsinvolved in establishing its existence.

To distinguish the phenomenon from thehypothesis, the writer originally proposedthe term "progressive achievementdecrement" (Jensen, 1966), or "progressiveachievement gap" (Jensen, 1971). These

terms seemed to be merely descriptive of thephenomenon and, unlike the termcumulative deficit, are not laden with anytheoretical overtones as to its cause. But theword "achievement" in "progressiveachievement decrement" or "progressiveachievement gap" also seems insufficientlyneutral for a scientific descriptive term, andsimply the term progressive decrement nowseems preferable. It would be more completeand more accurate to say "progressive rankorder decrement" or "progressive standardscore decrement," since the phenomenondoes not consist of a loss or progressivedecrement with age in the absolute amountof anything (as may well be the case in oldage and senility), but consists of an in-dividual's or a subpopulation's progressiveloss in relative standing or rank (as reflectedin an age-standardized score) among age-mates with increasing age during the periodfrom' early childhood to maturity. Forbrevity, however, we will continue to use theterm progressive decrement.

The cumulative deficit hypothesis wasmade explicit as follows:

All learning beyond the first few weeks or months oflifedepends upon previous learning. Knowledge and abilitydevelop in a hierarchical fashion; the development ofeach new level is facilitated by transfer from earlier lear-ning. More complex forms of learning build on simplerforms of learning. When the habits, skills, or cognitivestructures that are prerequisite for some "new" learn-ing have not been fully acquired, the capacity for thenew learning will be impaired: learning will be retarded,inefficient, incomplete, or even impossible, dependingupon the degree of inadequacy of prerequisite skills.Since learning builds on previous learning, weakness atany stage creates still greater weakness at later stages.Because subsequent learning depends upon transferfrom prior learning, learning deficits are cumulative.Thus the term cumulative deficit [Jensen, 1966, pp.40-41].

It has been assumed that the cumulativedeficit in scholastic achievement occurs inmany environmentally disadvantaged andminority children because at the time ofschool entry they have acquired fewer of theprerequisite skills for school learning thanare possessed by the majority of theirmiddle-class age-mates.

The counterhypothesis holds that theprogressive decrement of low-socioeco-nomic-status children is not in the main a


matter of learning and transfer, but a matterof a different rate of development or adifferent growth function of the intrinsicmaturation of cognitive abilities and theirneurological underpinnings. The twohypotheses are, of course, not mutually ex-clusive. Both kinds of causes, extrinsic andintrinsic, could be operating simultan-eously. Then the task of investigation wouldbe to disentangle them and weigh theirrelative contributions to the progressivedecrement phenomenon. The present study,however, does not attempt anything so am-bitious as that but instead focuses on theprior question of whether a progressivedecrement can even be shown to exist in anyminority school-age population in theUnited States, for as we have seen, theevidence to date is not at all conclusive onthis point. Methodological shortcomingsand the likelihood of overriding artifactsmake the existing evidence for progressivedecrement in the U.S. Negro populationhighly dubious.

But now let us first be clear about what isnot meant by progressive decrement. It doesnot mean only the increasing spread with agebetween the raw test scores of individualswith initially average (or above-average)scores and of individuals with initiallybelow-average scores. This phenomenon isnearly always observed for raw scores ontests as well as for mental age (MA, which isobtained from the regression of raw scoreson chronological age) and for gradeequivalents (the regression of raw scores onschool grade in months or some other frac-tion of a year). Nearly all mental ability andachievement tests in the age range from 5 or6 to 14 or 15 years show a more or less linearincrease in raw scores with increasing age,and generally there is a constant propor-tionality between the standard deviation andage. This fact underlies the relative con-stancy over the years from 5 to 15 of ratioscores such as the IQ and the educational quo-tient. The regularly increasing standard devia-tion of raw scores from early to later agesis characteristic of virtually all growthcharacteristics, physical as well as mental.Thus, in the absolute units of physicalmeasurement (e.g., height and weight) or inthe raw score units of aptitude and achieve-

ment tests (which are at best only an intervalscale and usually only a more or less nor-malized ordinal scale), there is an increasinggap from younger to older ages between thescores of the upper and lower halves of thedistribution. If this gap at each age is dividedby the standard deviation at the correspond-ing age, the gap (now in sigma units) may ormay not remain constant over the age range.It is only when there is an increasing gapbetween the means of two subpopulations asexpressed in sigma units that we have poten-tial evidence of a progressive decrement. Ifthe increasing gap exists only for the rawscores (or the derivative MA and gradeequivalent), while the gap in sigma units isconstant across age, it means that themembers of the subpopulation with thelower overall mean do not show any moreprogressive decrement than do thosemembers of the higher subpopulation whohave the same initial scores as the membersof the lower subpopulation. As was noted inthe Coleman report,

the lag of Negro scores (in Verbal ability) in terms ofyears behind grade level is progressively greater. Atgrade 6, the average Negro is approximately l'/i yearsbehind the average white. At grade 9, he is ap-proximately 2'/4 years behind the average white. Atgrade 12, he is approximately 3'/4 years behind theaverage white [Coleman, 1966, p. 273].

The report then notes that the difference (inmetropolitan Northeast) is constant innumber of standard deviations: "Thus in onesense it is meaningful to say the Negroes inthe metropolitan Northeast are the same dis-tance below the whites at these threegrades—that is, relative to the dispersion ofthe whites themselves [p. 273]." The reportillustrates this by pointing out that at Grade6 about 15% of whites are one standarddeviation, or l'/2 years, behind the whiteaverage; at Grade 12, 15% of the whites areone standard deviation, or 314 years, behindthe white average.

Though the absolute or raw-score gap isnot the main point of theoretical interest interms of the cumulative deficit hypothesis, itis the absolute gap which is so readilyperceived by teachers and parents, and itbecomes increasingly obvious at each highergrade level. Children who are one standard

1004 ARTHUR R . J E N S E N

deviation below the average are hardly dis-tinguishable in kindergarten or first grade,while an achievement lag of one standarddeviation at high school age is uncomfort-ably conspicuous to everyone, often beingequivalent to three or four grade levels belowthe average for the student's age.

One point in the statement from theColeman report quoted above is apt to bemisleading, that is, saying that Negroes arethe "same distance" below the whites atGrades 6, 9, and 12. "Distance" implies anamount of something, that is, measurementon an absolute scale, like height and weight.This we surely do not have in the psy-chological tests used in the Coleman studyor, for that matter, in the tests used in anystudy that is at all relevant to the progressivedecrement phenomenon. All that our testscores (either raw scores or standardizedscores) at any given age really represent is anindividual's relative standing in the nor-mative group. At best, we can make apretense of having an interval scale (but notan absolute scale which is distinguished by atrue zero point on the trait) by assuming thatindividual differences in the trait in questionare the result of a number of small, indepen-dent, additive effects. Genetically, therefore,they should be normally distributed in thepopulation, and by "normalizing" our stan-dardized scores, a procedure which mathe-matically forces them into the so-calledGaussian or bell-shaped curve, we can claiman interval scale, given the theoreticalassumptions. (IQs in most modern in-telligence tests are such a scale.) Nothingreally is lost by doing this, and probablynothing much of any psychological signifi-cance is gained from this procedure of con-verting standardized scores (i.e., deviationsof raw scores from the mean, expressed insigma units) into ranks, which are in turnconverted (via percentile ranks) to nor-malized standardized scores. But somestatistical conveniences may be gainedthereby; if, perchance, our assumption ofnormality of the population distribution ofthe trait is correct, we have the added advan-tage of a true interval scale of measurement,so that a difference in one part of the scale isequivalent to the same numerical differencein another part of the scale in terms of

whatever trait the scale happens to measure.If we look at standardized scores, in which

the mean and standard deviation are madeexactly the same at every age level, we noticechanges across ages in individuals' stan-dardized scores. That is to say, there arechanges with age in individuals' position inrelation to the position of others in thegroup, unless, of course, there is perfect cor-relation of the scores at each age with thescores at every other age. But this never per-tains in actual longitudinal data. The uni-versal finding of a decreasing correlationbetween scores as the age interval betweentests increases, from early childhood tomaturity, means that individuals are shiftingin position across age (Bloom, 1964, pp.52-94). If we should select out a subsampleof older children or young adults all withbelow-average scores at their present age andwere able to trace back their scores on thesame (or similar) tests at each previous year,we would find that these individuals for themost part had steadily declined in theirrelative position. Some would have hadaverage or above-average scores to beginwith. We could say that this group of low-scoring adults had shown a progressivedecrement throughout their development,whatever the cause. And if we picked a groupof high-scoring adults, we would find thesame thing, but in the opposite direction;their scores at each age from childhood tomaturity by and large would have steadily in-creased. Conversely, if we pick a group oflow-scoring subjects in early childhood, theirscores on the average gradually rise over theyears. By the same token, high-scoring pre-schoolers show a gradual decline over theyears. This is all familiar as "regressiontoward the mean."

But some of the observations involvinggroups may seem rather puzzling at firstglance. For example, if one selects fromamong upper-middle-class white childrenentering kindergarten a group of low scorers,all of whom test below IQ 100 with a meanof, say, 90, and follows these childrenlongitudinally with yearly tests all the way upto high school, one finds a marked steadyrise in the average IQ of the group. By age 16or 17 they probably average close to 110. If,on the other hand, one takes a group of low-


socioeconomic-status Negro kindergartnerswith the same mean IQ of 90 and followsthem to high school, their IQs, on theaverage show an opposite trend; they declineto about 85. In the one case there is aprogressive increment; in the other, aprogressive decrement. The cause of thisphenomenon is another question altogether,which this article does not attempt toanswer. The empirical fact, however, is thateach of the two groups just described, evenwhen selected in the same manner and fromthe same school, show regression toward thefinal (i.e., high school age) means of the sub-populations from which they were selected.This was demonstrated by Osborne (1960) ina longitudinal study of IQ and scholasticachievement scores, in which the means ofextreme groups (lower third and upper third)of Negro and white children tested at Grades6, 8, and 10 each showed convergencetoward the means of their respective pop-ulations rather than toward a commontenth-grade mean.

The same thing would happen if one com-pared groups of upper and lower socioeco-nomic-status white children. The mean IQ ofkindergarten children averaging IQ 100 in alow-socioeconomic-status white neighbor-hood shows some decline over the years; themean IQ of kindergarten children averaging100 in a high-socioeconomic-status whiteneighborhood shows some rise over theyears. At least in theory, the total regressionmay be analyzed into regression toward anumber of different values, the algebraic sumof which is the value toward which theregression effect converges. The individual'sobtained score converges toward his own"true score" (i.e., regression due to measure-ment error), toward his own genetic value(i.e., h*[X - X] + X, where /i2 is theheritability of the trait, X is the individual'sscore, and X is the population mean), towardhis own "environmental value" (i.e., [1 —h*][X - X] + X), toward his own family'smean, toward his social class mean, andtoward the mean of the population. (Studiesby Lawrence, 1931 and by Honzik, 1957,show that the IQs of orphanage children andof adopted children regress to some degreetoward the IQs of their own biologicalparents, whom they have never known,) The

net effect, in some cases, is progressive in-crements in scores from early childhood tomaturity; and in the other cases, progressivedecrements. But regardless of their socialclass and environmental circumstances,school children who become diagnosed asbackward or retarded are known to haveshown progressive decrements in theirrelative standing in mental growth andscholastic achievement (Burt, 1961, p. 636).

Cross-sectional studies. Cross-sectional agedata are quite unsatisfactory for studyingprogressive decrement because of selectivemigration, student turnover related to adultemployment trends in the community,overageness in later school grades, and otherfactors correlated with age in the particularschool population. Because family size is notorthogonal to age, it is one of the possible ar-tifacts entering into cross-sectional data onage decrement, even when sampling in termsof various demographic factors perfectlymatches the population statistics on thesefactors. For example, a perfectly randomsample of, say, 5-year-olds represents abiased estimate of "true" family size, withsmaller size families over represented, ascompared with a random sample of, say, 15-year-olds, since more of the families of the15-year-olds are already complete. And ifthere is a negative relationship betweenfamily size and intelligence test performance,an artifactual age decrement in IQ appears inthe comparison of 5-year-olds and 15-year-olds (or any two groups of differing age). Ifthe age groups are matched for family size,more children in the older groups will befirstborn and more children in the youngergroups will be later-born, so that age is con-founded with the effects of birth order on IQ.If the average family size differential acrossage groups is greater for Negroes than forwhites (as is the case), these cross-sectionaldata would show a larger artifactual agedecrement in IQ for Negroes than for whites.To the extent that family size is a causal en-vironmental factor in the negative correla-tion between family size and IQ, the evidencesuggests that this possible artifact isprobably not a large one. If birth order andfamily size were major causal factors in IQvariance, then, within families, later-born


children should have lower IQs than earlierborn and IQ should decline as a function ofthe number of previous siblings. McKeownand Record (1971) in a properly designedstudy, have found this not to be the case.They state, "There are very large variationsin a general population of births in relationto maternal age and birth order; but theseare due to differences between rather thanwithin families, for there is little variation ac-cording to birth rank between sibs [p. 52]."The between-families differences reflectdemographic factors (such as socio-economic status and rural versus urban)related simultaneously to family size and toIQ, thus resulting in a correlation withoutimplying direct causation.

Any one or a combination of thesedemographic factors such as family size andbirth order can spuriously create the ap-pearance of progressive decrement in oneor another subpopulation, or they cancounteract and hide a true decrement. All wecan be sure of with cross-sectional data isthat they reflect demographic rather thanstrictly psychological phenomena. One canslightly improve psychological inferencesfrom cross-sectional data by taking accountof certain demographic variables, but eventhis leaves much to be desired. For example,Jensen (1971) compared white, Negro, andMexican groups cross-sectionally on anumber of tests at every grade from 1 to 8 ina California school district and found no ap-preciable evidence of progressive decrementin the two minority groups; he claimedgreater validity for this finding by showingthat a fine-grained measure of socioeco-nomic status and home background factors(Cough's Home Index) did not show anysystematic differences across grades. But thequestion always lingers whether the reallyrelevant demographic variables have beentaken into account and, strictly speaking,one is left again with only a demographicrather than a psychological finding.

Longitudinal studies. Methodologically, lon-gitudinal studies are potentially far superiorto cross-sectional studies, but they, too, cansuffer some of the same disadvantages to theextent that there is nonrandom attrition ofsubjects over the course of time. Duller

pupils may drop out of public school and goto private schools, families may move awaybecause of changing employment op-portunities in the community, and so on.Longitudinal studies should always note theattrition rate and the relevant characteristicsof the subjects that were lost.

Sibling studies. With proper control of familysize and birth order, sibling comparisonshave less risk than cross-sectional and lon-gitudinal studies of reflecting demographicvariables. Progressive decrement is indicatedwhen the standard score difference betweenyounger and older sibs (i.e., the mean ofyounger minus older within each family) issignificantly greater than zero. To avoidreflecting a demographic feature, however, itis necessary to control for family size andbirth order. Because of the well-establishednegative correlation between mental testscores and family size (Anastasi, 1956), therewill be more possible sibling pairs con-tributed by low-scoring families. In otherwords, low-scoring families, having morechildren, would be overweighted in theoverall average of the differences betweenyounger and older sibs. This is easily over-come by weighting each family equally in theoverall mean, regardless of the number ofsibs (and paired differences) in each family.With this control and control for birth order,the sib method is probably the most satisfac-tory, with the one disadvantage that not avery wide age range can be spanned by thismethod. Few families today have childrenspaced more than 5 or 6 years apart, and inthe vast majority the children are spacedmuch closer.

The sib method controls for genetic fac-tors in the sense that, on average, youngerand older sibs do not differ in genotypicvalue. It also controls largely for en-vironmental factors, in that, on average,younger and older sibs do not enjoy better orworse environments, although it can beargued that firstborn children may receivemore parental attention, at least in infancy,than later borns. If this has any lasting ad-vantage, it should counteract the appearanceof progressive decrement using the sibmethod, depending as it does upon thedifference between younger and older sibs


and the fact that the supposedly advantagedfirstborn is always the oldest sib. Unless it istaken into account, this advantage of thefirstborn would work against detection ofprogressive decrement fey the sib method.There is a considerable literature claiming aslight average superiority of the firstborn(Altus, 1966). If true, the causes are uncer-tain, except that they cannot be due togenetic factors. They could involve prenatalas well as postnatal factors, bat the latterseem more likely (set Record, McKeown, &Edwards, 1969).

The mean within-family absolute dif-ference in IQ between all sibs in a samplereflects a composite of both the genetic andthe environmental factors that make for sibdifferences. The mean within-family signedIQ difference between younger and older sibsreflects only the cumulative effect of en-vironmental influences, since there is noknown or theoretically expeeted relationshipbetween birth ordfer and genotypes ofsiblings within a family. In a large sample,the average of the genotypic values for anygiven characteristic, like IQ, should be thesame for firstborns, secondborns, etc. forfamilies of any given size. Any within-familymean differences according to birth orderwould therefore reflect nongenetic or en-vironmental factors. In fact, the best con-trolled studies reveal a small but significantrelationship between IQ and birth orderwhen the evidence consists of siblingdifferences within families, thereby con-trolling family size and related demographicartifacts. The most definitive study, byRecord et al. (1969), found an IQ differenceof 1.5 between first and second born, of .9between second and third born, and .5 or lessbetween sibs after the thrid born; at BirthRank 5 and over there is no consistentdifference between sibs. Thus, properly used,the sibling method can provide perhaps thebest test of age decrement in IQ, certainlymore satisfactorily than the cross-sectionalmethod with its plethora of demographic ar-tifacts, and probably more rigorously thanthe logitudinal method if there has been at-trition of the sample.

Specificity of progressive decrement. Finally,it should be recognized that finding the

presence or absence of progressive decre-ment in one locality may not generalize to allother localities. Progressive decrement, if itexists at all, is a population characteristic,like IQ, the birth rate, income or the averagedaily school attendance. So, theoretically itcould vary from one locality to another,from one type of test to another, from onetime to another, and from one subpopula-tion to another. But in any case, progressivedecrement cannot simply be presumed to ex-ist. Its existence must be demonstrated bysome methodologically sound analysis.

The following study illustrates the use ofthe sibling method for analyzing progressivedecrement in white and Negro school pop-ulations.

Method

Subjects

The entire Berkeley Unified School District's elemen-tary school (kindergarten through Grade 6) population,consisting of some 8,000 children in 17 schools, wasgiven a battery of tests by 20 specially trained testers (12whites and 8 Negroes). (A separate analysis showed thatthe race of the examiner had a negligible effect on Lorge-Thorndike scores in both the white and Negro groups;Jensen, 1974.) The present analysis is concerned onlywith the white and Negro subpopulations, which are ap-proximately 60% and 40%, respectively.

From school records and from questionnaires sent tothe childen's parents, all full sibships within the elemen-tary school population were identified. Half-sibs werealso identified but were not included in the presentanalysis. The presence of half-sibs in the sample would,of course, increase the average difference amongchildren within families. If there was any contaminationof the full-sib sample by an admixture of half-sibs falselyidentified as full-sibs, it was either of statistically negligi-ble proportions or occurred to an approximately equalextent in the Negro and white samples. One possiblecheck of this is the full-sib correlation for height. Thetheoretical genetic correlation for full-sibs is close to .50;for half-sibs it is close to .25. Therefore, if there was anappreciably greater proportion of misidentified half-sibsin the Negro sample (since many more Negro half-sibswere identified in the total population), this should bereflected in4 significantly lower nominal sib correlationfor Negroes. But in fact this was not the case. The ob-tained intraclass correlation between full-sibs (un-corrected for attenuation) was ,42 for whites and .45 forNegroes. Corrected for unequal standard deviations(but not for attenuation), the intraclass correlations are.44 for whites and .43 for Negroes. Differences betweenthe white and Negro populations in the degree of assort-ative mating for height or IQ would affect the sib cor-relations but would have a negligible effect on the meanabsolute difference (or within-family variance) between


sibs (Crow & Kimura, 1970, pp. 158-159). The mean ab-solute difference in height between siblings, in standarddeviation units based on the total population within 6-month age intervals, is .846 a for the white group and.856 a for the Negro group, which is a negligible groupdifference of .01 a.

iSfN

Tests

Several tests of mental abilities and of scholasticachievement were used. All were group-administered tointact classrooms. However, the only tests to be con-sidered for the present discussion are the Lorge-Thorn-dike IQ tests, because they were the only tests in thebattery for which published nationwide age norms areavailable. Tests for which the national norms are ex-pressed as grade norms rather than age norms (e.g., theStanford Achievement Tests) are unsuitable for detect-ing progressive decrement, since the average age andthe age variance in each grade may differ from oneschool to another, depending upon the school's promo-tion policies. Though grade norms may be useful toschool personnel, they are practically worthless forresearch in developmental psychology, which requiresmuch more exact quantification of the chief independentvariable, namely, the time scale. This is provided only byshowing normative scores as a function of chronologicalage in months rather than by such an arbitrary and am-biguous scale as grade level in school. Local norms arenot suitable for progressive decrement analysis, becauseif there is some demographic shift in the nature of theschool population from the younger to the older agegroups, the local population age norms will not providea consistent frame of reference across all ages, and thiswill introduce some artifact into the magnitude of theyounger-older sib differences in the locally standardizedscores.

The promotion policy of the Berkeley schools is suchthat virtually all pupils in the regular classes are in theschool grade appropriate for their chronological age.The few exceptions found in the class rolls were ad-ministered the particular level of the Lorge-Thorndikeintended for their chronological age regardless of theirgrade placement, so that all of the pupils in any givenage group were tested on the same level of the Lorge-Thorndike, thereby avoiding any possible measurementartifact due to underageness or overageness in the whiteand Negro samples.

Lorge-Thorndike Intelligence Tests. This is a nationallystandardized group-administered test of general in-telligence. The normative sample was intended to berepresentative of the nation's school population. It isgenerally acknowledged to be one of the best standard-ized pencil-and-paper tests of general intelligence.

The Manual of the Lorge-Thorndike Test states thatthe test was designed to measure reasoning ability. Itdoes not test proficiency in specific skills taught inschool, although the verbal test, from Grade 4 andabove, depends upon reading ability. The reading levelrequired, however, is intentionally kept considerablybelow the level of reasoning required for correctlyanswering the test questions. Thus, the test is essentiallya test of reasoning and not of reading ability, which is to

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Table 2: Total Number of White and Negro Pupils in 9'A-12-Year Age Groups on the Lorge-Thorndike IQ Intermediate Test

Inter-mediate

test

VerbalNon-

verbal

9 to yrs. lOyrs.W N W N

265 156 289

263 175 308

150

168

lOto yrs.W N

271

271

222

231

1 1 yrs.W N

302

307

201

188

l i t e yrs. 12 yrs. TotalW N W N W N

322 198 262 177 1,711

334 194 256 183 1,748

1,104

1,139

Note. W = white; N = Negro.

say that it would have more of its variance in commonwith nonverbal tests of reasoning ability than with testsof reading per se.

The tests for Kindergarten-Grade 3 do not depend atall upon reading ability but make use exclusively of pic-torial items. The tests for Grades 4-8 consist of twoparts, Verbal and Nonverbal. They are scoredseparately. The chief advantage of keeping the twoscores separate is that the Nonverbal scale does notoverestimate or underestimate the child's general levelof intellectual ability because of specific skills or dis-abilities in reading.

The following forms of the Lorge-Thorndike In-telligence Test were used:

Level 1, Form B. Primary, Nonverbal. Grades K.-1Level 2, Form B. Primary, Nonverbal Grades 2-3Level 3, Form B. Verbal and Nonverbal Grades 4-6.

The "consumable" form of the test was used to obviateseparate answer sheets and the added difficulty they mayinvolve for the testees.

Results and Discussion

Raw Scores as a Function of Age

Tables 1 and 2 show the white and Negrosample sizes within each 6-month age inter-val on each of the Lorge-Thorndike tests.

Figure 1 shows the raw test scores (i.e.,number of items right) on each of the formsas a function of age. It can be seen thatwithin each form the scores increase quitelinearly with age and that the slopes of theincrease are very nearly parallel in the whiteand Negro samples. This parallelismsuggests the absence of any progressivedecrement in the Negro sample, relative tothe white. But it is inconclusive for tworeasons: (a) Since these are cross-sectionaldata, population characteristics may shiftfrom one age to another, and (b) the wideseparation of the white and Negro means(amounting to about 20 IQ points) at all agesindicates that the discriminating items in agiven test are different, on the whole, forwhites and Negroes. It cannot be presumed

that the raw score increments in the first halfof the test are equal to those in the secondhalf, or, or in other words, we cannot assumea priori an interval scale for the raw scores.Therefore the parallelism seen in Figure 1,strictly speaking, is uninterpretable withrespect to the possible presence or absence ofa progressive decrement in the Negro sam-pie.

Sibling Analysis

The sibling analysis satisfies the main re-quirements for detecting progressive dec-rement: (a) It assures comparisons betweenyounger and older children in the samepopulation at all age levels, since all of thecomparisons are within families, and (b) theage differences in IQ are expressed in termsof nationally standardized age norms, andthe normative samples were speciallyselected to be demographically homogene-ous across the entire range of these tests.

Since the average number of siblings tak-ing any particular form of the Lorge-Thorn-dike test differs in the white and Negrofamilies (2.25 and 2.35, respectively), it is

PRIMARY Ml

WHITENEGRO

PRIMARY (2}

^

INTERMEDIATE (j). VEflBAL

^f~

^^^

^-

• r i — i — r -INTERMEDIATE (3).

NON-VERBAL

- »•''* '

\\\ M

Figure 1. Raw scores (i.e., number right) of white andNegro children on Primary and Intermediate forms of theLorge-Thorndike Intelligence Test as a function ofchronological age. The Ns for each data point are given inTable 1.


Table 3: Mean Sibling Difference (YoungerIQ difference (Y - O)

Test form taken by W NYounger sib Older sib % SD X SD

t test"ofW-N

difference

Age differenceW

Jf SD

Younger brother - older brother

PrimaryVerbalPrimaryNonverbalPrimary



PrimaryVerbalVerbalNonverbalNonverbal



3.62***-5.05-3.77***-3.34-4.86***

-.84'.80

-2.85***.19

-3.35***

1.66-.56

-2.77***-2.74-4.31***

16.5119.3016.9413.5815.71

Younger

15.5616.9115.8816.9715.74

Younger

15.8412.7614.8713.7715.19

.436.943.22*

-2.71-1.21

12.4118.5115.3220.8816.46

1.25-2.22*-3.87***-.15

-2.13*

23.1919.4630.3919.6630.56

9.125.54

13.565.05

13.70

sister - older brother

1.414.761.77

-6.60***-2.77

16.9516.2117.2315.8918.19

-.76-.91

-2.52*1.68

-.33

21.1218.8029.2219.3730.05

7.0514.6713.215.96

13.95

brother - older sister

3,55-.171.48

-3.77-1.07

15.0714.0114.6817.7315.55

-.68-.11

-2.55*.25

-1.88

21.3018.9828.8019.1328.71

7.075.59

12.345.93

12.13

Younger sister - older sister



-.041.45

-4.48***-1.59-6.41***

14.9316.8316.3916.3115.16

1.273.55

-.396.38

-2.28

All younger - older



Note. Y = younger; O =" Two-tailed." One-tailed.

1.72-.41

-3.19***-1.30-4.53***

15.4416.6515.3215.1514.98

1.623.94**1.64*

-2.05-1.36

11.7512.7613.6016.4114.67

siblings

14.0315.9315.1118.6215.84

.-52-.49

-2.34*-1.72-2.41*

.07-1.88-4.98***

.33-3.33***

older; W = white; N = Negro. * P "

21.0720.0630.3320.7630.57

21.6219.3629.7219.7330.02

.05.

.025.

.01.

7.364.77

13.354.34

13.18

7.355.12

12.345.21

12.48

necessary to make the average sibling IQdifference (younger-older sib) independentof family size. Since the number of paired sibcomparisons within a family is (N1 — N)/2,where N is the number of sibs in the family,larger families would disproportionatelyweight the mean sib IQ difference, therebyconfounding mean sib difference with familysize. To overcome this, one simply obtainsthe mean sib IQ difference within each familyand averages these mean differences over allfamilies in each racial group.

Table 3 shows the mean IQ differencesbetween younger and older siblings withinfamilies, as well as the mean age differencesbetween the older and younger sibs. The

differences are presented for each of the fourpossible combinations of Younger-Older XSex, and for all younger-older sibs re-gardless of sex. Sib differences are given foreach form of the test separately, whichrestricts the number and age range of sibdifferences, and $lso across the Primary andIntermediate (Verbal awj Nonverbal) forms,in order to increase the potential number ofsib comparisons. Sib IQ differences thatcross the Primary and Intermediate forms, ofcourse, involve same risk of reflecting apossible change in the factorial compositionof the different test forms. The test formatsand style differ: The Primary material issomewhat less abstract and requires no


— Older) in Lorge-Thorndike IQ

(O - Y) in monthsN

JP SD

t test"of age

difference

Absolute difference in IQ t test* ofW N absolute

X SD X SD difference in IQNo. familiesW N

Younger brother - older brother

21.5518.5027.9017.6227.41

20.375.50

25.9015.6226.30

9.125.79

12.416.72

12.35

8.983.73

12.753.54

12.75

1.05.60

1.71*1.372.22**

.523,15***2.27**2.94***2.57***

12.81 11.2816.40 12.0514.11 10.9011.03 8.5912.99 10.56

Younger sister

12.85 8.8913.40 10.3413.40 9.1614.15 9.3813.24 9.39

10.2616.0612.7917.1213.40

7.5711.539.71

12.2510.25

1.50.12

1.14-2.32*

-.37

8341

24139

241

5818

12524

136

- older brother

13.3414.1914.0214.2914.96

Younger brother - older

19.9317.4426.7717.5526.29

21.0118.2327.9119.2227.72

20.5517.2027.1117.3926.99

6.766.14

13.216.26

12.92

8.496.19

11.976.15

12.18

7.875.74

12.305.83

12.36

1.11.94

1.43.98

1.74*

.051.221.66*1.001.95*

1.482.87***3.34***3.13***3.90***

12.67 9.7710.02 7.9112.49 9.2611.16 8.5313.21 9.34

Younger sister

11.56 9.4613.58 10.0513.98 10.3012.97 10.0213.79 9.65

All younger -

12.41 9.9013.10 10.4513.47 9.4812.32 8.9513.44 9.42

11.7912.1111.8015.0512.44

10.649.17

10.429.58

10.96

sister

10.047.059.03

10.169.54

-.28-.30-.58-.62

-1.60

.50-.96-.66

-1.59.73

7450

23748

247

9641

25838

255

4921

12026

133

4718

11522

115

- older sister

10.349.64

11.1215.5012.84

6.109.088.228.698.27

.811.462.63***-.89

.91

7531

19629

199

5122

12718

124

older siblings

11.6113.2412.7315.8113.67

8.699.709.27

10.469.55

.89-.091.25

-2.27*-.39

295155735148741

17475

37583

393

reading, the Intermediate Verbal test in-volves reading, the Nonverbal involvesabstract figural material.

A progressive age decrement in IQ,relative to the normative population, wouldbe indicated by a positive difference betweenthe IQs of younger and older sibs.

It should be emphasized that the test of aprogressive decrement is essentially a com-parison of younger-older sibling IQs whenthe IQ is based on national norms; it is notbased on a comparison of sibling IQdifferences between the local white andNegro samples. In Table 2 the t tests for thesignificance of the difference between thewhite and Negro groups is not the test of the

cumulative deficit hypothesis. It indicates,however, that the white group in this studyshows a significant progressive increment(i.e., older sibs score higher than theiryounger sibs) relative to the Negro group.But it does so not because the Negro groupshows a progressive decrement, but becausethe white group shows a progressive incre-ment relative to the national norms.

We are concerned primarily with evidenceof progressive decrement in the Negro grouprelative to national norms. It can be seen thatfor the Negroes there is a significantyounger—older difference involving the Ver-bal IQ, which is significant at the .05 level forthe combined sexes and for the younger-


brother-older-brother group. It is not signifi-cant for the other three sex combinations.The discrepancies in significance level for thevarious mean sib differences involving Ver-bal IQ appear to be more related todifferences in sample sizes than tomagnitudes of the differences themselves.The fact that the younger-older sib differ-ence appears as significant for the combinedsexes, however, means that it must be inter-preted as a real effect, albeit not of consistentmagnitude for all sex combinations of theyounger-older sib differences. The VerbalIQ, it should be noted, is the only form of theLorge-Thorndike test that involves readingcomprehension.

The Nonverbal IQ in the Negro group, onthe other hand, shows no evidence of aprogressive decrement. Thus, the presentevidence for a progressive IQ decrement inthe Negro group appears significant only incomparisons involving the Verbal IQ. Themagnitude of the effect can be comparedwith the overall mean white-Negro IQdifferences (Primary 18.05, Verbal 21.38,Nonverbal 21.63).

Table 3 also shows the mean absolute IQdifference between sibs within families, thatis to say, the mean difference between sibsregardless of whether the difference ispositive or negative. While the overall meansigned difference between younger and oldersibs can reflect only nongenetic or en-vironmental factors (since there is notheoretical basis for assuming a correlationbetween genotyptic values and birth order),the mean absolute difference reflects allsources of difference between siblings,genetic and environmental, as well as errorsof measurement. It is therefore instructive tocompare the mean absolute sib differences inthe white and Negro groups. If it ishypothesized that the distributions ofgenotypes for IQ are the same in both racialgroups, then any racial group disparity in theabsolute difference between sibs would haveto reflect nongenetic influences on IQ. Allfactors that potentially could affect IQ arereflected in the absolute sib difference—sexdifferences, age differences, birth orderdifferences, etc.

As shown in Table 3, a two-tailed t test ofthe white-Negro difference in the mean ab-

solute sib IQ differences reveals mostly non-sigificant racial differences. The couple ofdifferences that are significant in two of thesex combinations are of opposite sign andoccur for different tests. Any interpretationof them, against the background of so manynonsignificant differences, would necessarilybe very tenuous and speculative. It seemsreasonable to conclude from these data thatin general, the mean absolute sib IQdifference is about the same in the white andNegro groups. This finding implies prac-tically equal influence in the two racialgroups of the sum total of genetic and en-vironmental factors contributing to within-family IQ differences. Under the assumptionof equal genotypic distributions in the tworacial groups, it is therefore inconsistent withthe cumulative deficit hypothesis, whichshould predict a larger absolute differencebetween Negro siblings' IQs, since the oldersibs, on the average, should have lowerIQs—a source of within-family variance thatwould not exist, on the average, in the whitenormative population.

The mean age difference between youngerand older sibs is significantly greater in thewhite group compared to the Negro, asshown by the ; tests for the age difference inTable 3. This point is relevant to com-parisons of the white and Negro samples, butit does not affect the test of progressivedecrement in the Negro group in relation tothe general population norms. In any case,within the range of sibling age differences inthe present samples, the correlation betweenage difference and IQ difference is so small asto be practically negligible. This fact con-stitutes still another test of the cumulativedeficit hypothesis.

Correlation between age difference and IQdifference. It also follows from thecumulative deficit hypothesis that thereshould be a positive correlation between thesib age difference (older-younger) and the sibIQ difference (younger-older). To test thishypothesis, Pearson's correlation was com-puted between age difference (older-younger)and IQ difference (younger-older) withineach of the four possible sex combinations ofsibs and for each pair of tests involved. Sothat family size would not be confounded in


this correlation, each family is weightedequally in determing the r, regardless of thenumber of sib pairs within each family. Thers were tested for significance by a one-tailedt test, since only a positive r is consistent withthe progressive decrement hypothesis. Theresults are shown in Table 4. There is onlyone significant (.05 level) correlation in theNegro group and it occurs only on the Ver-bal IQ in the brother-brother comparison.The r is negligible (and at times reversed insign) in all the other comparisons. The 1significant r out of a possible 20 could well bea fluke, but the fact that it involves the Ver-bal IQ at least makes it somewhat consistentwith the evidence in Table 3 for a progressivedecrement in Verbal IQ. However, the hy-pothesized effect shows up not at allsignificantly in the correlation for all Negrosiblings combined (see last two columns ofTable 4).

Family size and sib IQ difference. The factthat there are more children in the Negrothan in the white families could affect theresults of the preceding analyses if there werea significant correlation between the sib IQdifference and the number of children in thefamily. If such a correlation exists, it wouldnot be proper, however, statistically to con-trol or partial out the variable of family sizein the preceding analyses, since family sizecould itself be a causal factor in the directionand magnitude of sibling differences. Thatthis is not the case, however, is shown by theconsistently negligible correlations betweenfamily size (i.e., total number of children inthe family) and sib IQ difference—both thesigned younger-older difference and the ab-solute difference, presented in Table 5. Itseems safe to conclude that in this study,family size is an unimportant factor in sib-ling IQ differences, both for whites andNegroes.

Effect of birth order on IQ. If there were asignificant effect of birth order on IQ andthis effect interacted significantly with race, itwould complicate or obfuscate the inter-pretation of the foregoing results. For exam-ple, if the earlier born (i.e., older) sibs hadhigher IQs than the later born, this wouldcounteract or mask the appearance of a

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Table 5: Correlation between Sibling IQ difference (Younger - Older) and Number of Childrenin Family

CorrelationTest form taken by

Younger sib


Older sib


No.W

295155735148741

familiesN

17475

37583

393

Sib IQ Difference XNo. Children in

W

-.021-.030-.061-.127-.055

FamilyN

,077.072.037

-.046-.037

Absolute Sib IQNo. Children

W

-.041-.007

.044-.053

.015

Difference Xin Family

N

-.075-.010-.068-.033

.010

Note. W = white; N = Negro. Number of children in family is all children, including those who were not testedin this study. Mean number of children per family: White = 3.05, a = 1.41; Negro = 3.39, a = 2.3.3. (Single-childfamilies are necessarily excluded from this analysis.)

progressive decrement as evidenced by theyounger-older sib IQ difference. And ifthere were a significant interaction of Race XBirth Order, the degree of masking of theprogressive decrement would be different forNegroes and whites.

To examine this possibility, the effects ofbirth order on IQ and the interaction of thebirth order effect with race were tested by ananalysis of variance. So as not to confoundbirth order effect with family size, theanalysis of variance was performed sep-arately for each family size, using all fam-ilies having at least two children and atmost six. (Families of more than six childrenwere too few to warrant statistical analysis.)For each family size, a two-way analysis ofvariance was used, yielding main effects forrace variance and birth order and the Race XBirth Order interaction. The results of the

analyses of variance are summarized inTable 6, which gives the mean square, the Fvalue, the degrees of freedom, and the exactp values for each F.

It can be seen that the main effect of race ishighly significant throughout all sizes offamily. The birth order effect is surprisinglysmall, and in fact attains significance (forboth Verbal and Nonverbal IQ) only in four-child families, in which the firstborn chil-dren have slightly higher IQs than later born.In no instance, however, is there a significantinteraction of Race X Birth Order, and infact the exact p values show that this interac-tion does not even approach significance.The same kind of analysis of variances wasperformed on each of the four possible sexcombinations of sibs, all with highly similarresults. Therefore, the effects of birth orderon all the preceding analyses are almost cer-

Table 6: Analysis of Variance of Verbal and Nonverbal IQ as a Function of Race, Birth Order,and the Race X Birth Order Interaction for Families with Two to Six Children

Familysize MS

RaceF* df

Birth orderMS P P

Race X Birth OrderMS F° p

Verbal IQ

23456

99,917.44140,007.4483,057.9032,403.5311,431.69

471.92681.18399.33146.2848.31

1/12641/12411/8231/3401/151

15.9343.45

530.90266.03303.37

.07

.212.551.211.28

.78

.81

.05

.31

.27

489.71415.46207.90254.62184.28

2.312.021.001.15.78

.13

.13

.39

.33

.57

Nonverbal IQ

23456

97,964.58131,166.3977,664.2133,413.5511,303.06

485.91653.95374.20122.7642.43

1/12641/12411/8271/3431/155

1.3987.26

870.6755.66

274.84

.01

.434.19

.201.03

.93

.65

.01

.93

.40

130.89117.7591.22

210.09174.66

.65

.59

.44

.77

.65

.42

.55

.72

.54

.66

" All Fs significant at p < .0001."The ^numerator is 1 less than family size, the denominator is same as under Race.

Table 7: Correlations of Lorge-Thorndike IQ With Family Size and Birth Order in White and Negro Groups

Family size Birth order Sample sizeTest Males Females Total Males Females Total Males Females Total

W N W N W N W N W N W N W N W N W N

Primary -15*** -04 -09** -10** -12*** -07* -09** 00 -09** -03 -09*** -01 926 502 835 514 1,761 1,016

Verbal -12*** -04 -19*** -07 -16*** -05 -11** -03 -18*** -04 -14*** -03 601 277 578 302 1,179 579

Non-verbal -14*** -02 -13*** -05 -14*** -04 -08* -07 -11** -07 -09*** -07 607 304 586 295 1,193 599

PrimaryorVerbal -11*** -05 -11*** -07* -11*** -06** -09*** -01 -13*** -03 -11*** -02 1,527 779 1,413 816 2,940 1,595

Primaryornon-verbal -10*** -02 -08*** -05 -09*** -03 -08*** -03 -11*** -04 -09*** -04 1.533 806 1,420 809 2,953 1,615Note. Decimals omitted. W = white, N = Negro.

*p < .05."p < .01.

*** p < .001.

Table 8: Correlation between Birth Order and Family Size, and Partial Correlation between Birth Order and IQ with Family Size Partialed Out

Variables MalesW N

Birth Order XFamily Size 72

Birth Order X IQ(partial correlation)Primary 03Verbal -03Nonverbal 03Primary or Verbal —03Primary or nonverbal —02

78

0500

-0905

-02

CorrelationFemales

W N

73

-04-06-01-07**-07**

49

03-01-05

01-02

TotalW N

74

00-06*

01-05**-04*

59

0400

-0602

-02

MalesW N

1,574

926601607

1,5271,533

829

502277304779806

Sample sizeFemales

W N

1,457

835578586

1,4131,420

845

514302295816809

TotalW N

3,031

1,7611,1791,1932,9402,953

1,674

1,016579599

1,5951,615

Note. Decimals omitted. W = white; N = Negro.*/> < .05.

**.P < -01.


Table 9: Mean Sibling Difference (Younger - Older) in Lorge-Thorndike IQ With All Firstborn

Younger sib Older sib



IQ difference (Y - O)W N

Jf SD X

1.38-1.13-2.94**-3.15-4.75**

16.3917.2315.9115.5715.72

2.291.242.19*

-4.13-.43

SD

13.6414.4714.0316.1714.74

/ test"of W-N IQdifference

-.45-.74

-3.88**.32

-3.30**

Age differenceW

# SD

21.8119.8929.9120.3330.58

7.545.07

12.035.24

12.40

Note. Y = younger; O" One-tailed." Two-tailed.

* p = .05.**/» = .01.

older; W = white; N = Negro.

tainly negligible. A trend analysis for birthorder effects within each family size was alsoperformed on the white and Negro groups todetect possibly significant linear, quadratic,cubic, quartic, and quintic components. Theonly significant effect of birth order revealedin this analysis was for four-child families inthe white sample (as shown also by theanalysis of variance in Table 6), in whichthere was a significant (p < .05) linear com-ponent, with the firstborn having higher Ver-bal and Nonverbal IQs. There were nosignificant effects of birth order amongNegroes for any family size.

Further evidence of the small effect ofbirth order on IQs in this study can be seenin the correlations between birth order andIQ, with family size partialled out of the cor-relation. Table 7 shows the zero-order cor-relations of IQ with family size and birthorder. It is noteworthy that the correlationbetween IQ and family size is consistentlygreater for whites than for Negroes. As inmany other studies reported in the litaratureon IQ and family size, all the correlations arenegative, but here they are of somewhatlesser magnitude than those usually re-ported, which average close to -.30. Partof the reason may be that the presentanalysis is limited to family sizes of from twoto six children.

The correlations of IQ with birth order areall quite small. But the Birth Order X IQCorrelations in Table 7 are confounded bythe variable of family size. What we actuallywish to know is the correlation between IQand birth order independently of family size.This is given by the partial correlation

between IQ and birth order, statisticallyremoving the variable of family size. Thesepartial correlations are shown in Table 8.Despite the large Ns all of the partial rs arenonsignificant, with the exception of whitefemales (r = -.07, p < .05). Since the cor-relations in the Negro group center closelyaround zero, it surely cannot be argued thatthe failure of the younger minus older sib-ling difference to reveal any evidence of aprogressive IQ decrement in the Negrogroup is due to a masking of the decrementby the effect of birth order on IQ.

Since it is most frequently found that thelargest birth order effect on IQ is betweenfirstborn and all later-born, who differ littlefrom one another, and since the first-borns inthe present study had a slightly (though non-significantly) higher IQ than the later-bornsibs, the data summarized in Table 3 were re-analyzed omitting all firstborn sibs. Theresults for all four possible Sex XYounger-Older sib comparisons are essen-tially the same as the results in Table 3,which includes first-borns. The analysis of allyounger-older siblings, omitting firstborns,yields results which give essentially the samepicture as the full data shown in the lowerpart of Table 3. The analyses with firstbornsomitted are shown in Table 9 for com-parison. Clearly, omitting firstborns fromthe analysis leaves unchanged the conclusionof no positive younger-older sibling IQdifference for the nonverbal IQ, contrary tothe prediction from the cumulative deficithypothesis. The Lorge-Thorndike Primaryand Verbal tests, however, give some indica-tion of progressive decrement averaging


Siblings Omitted(O - Y) in month

NJf SD

20.6016.3626.2816.8626.08

8.155.04

11.805.56

11.87

t test"of age

difference

1.183.57**3.51**3.40**4.33**

Absolute difference in IQ t test"W N of absolute No. families

# SD Z SD difference in IQ W N

12.7413.5113.5412.7414.00

10.9910.9210.049.509.93

11.4112.2711.9913.8612.73

8.397.778.429.438.57

1.01.64

1.90-.621.58

13775

36367

367

10040

21147

221

about 2 IQ points.Also, the correlations between Negro sib-

ling age differences and sibling IQ differencefor all siblings in the various combinations oftests remain negligible and nonsignificant(just as they are in the last two columns ofTable 4) when all firstborns are omitted.

Only child versus siblings. Finally, we mustinquire as to whether the omission of sub-jects who are only children from all thepreceding analyses based on siblingdifferences seriously biases the sample sothat it is not representative of the wholeBerkeley school population as regards IQ.Only children comprise about 7% of the totalwhite and about 11% of the total Negroschool population in Berkeley. The mean IQdifferences between only children and chil-dren with sibs are shown in Table 10. Onlyone of the differences isjust barely significantat the .05 level; that is, Negro only childrenaverage slightly higher IQs than Negro chil-dren with sibs, an effect which is significantonly for Verbal IQ. Thus, there is practicallyno basis for assuming that the IQs of the sib-ling sample are unrepresentative of the totalschool population.

Summary and Conclusions

Cumulative deficit refers to the hypothesiswhich attempts to explain the purported in-creasing disparity throughout the ages fromearly childhood to maturity between theaverage mental and scholastic achievementtest scores of Negroes and whites or, ingeneral, between more and less culturallyand environmentally disadvantaged seg-ments of the population. The existence ofthe phenomenon supposedly in need of ex-planation, here called progressive decrement(in rank, percentile, or standardized score),has not been unequivocally established inany samples of the U.S. Negro population.Most of the data and analyses usuallypresented as evidence for a progressivedecrement are riddled with artifact. Themost common method—white-Negro com-parisons of cross-sectional age sam-ples—confounds demographic and psycho-logical variables; the results of such studiesare conflicting, ambiguous, and generallyuntrustworthy.

Longitudinal studies of standardized test-score changes with age are scarce, un-fortunately, for they are much less liable to

Table 10: IQ Difference between Only Children and All Children with Siblings in Total Whiteand Negro Groups

IQ Test

PrimaryPrimary or VerbalPrimary or NonverbalVerbalNonverbal

Only

165249251

8486

WhiteN IQ

Sibs Difference"

1,7612,9402,9531,1791,193

-1.18-.97

-2.00.87

-1.67

t

-.93-0.91-1.90

.50-.99

NegroN IQ

Only Sibs Difference" <

150205205

5555

1,0161,5951,615

579599

1.482.101.773.533.77

.24

.99*

.70

.61

.90

* Mean IQ of only children minus mean IQ of siblings.*p < .05.


demographic selection artifacts, unless thereis significant nonrandom attrition of thesample over time, which would introducemany of the same artifacts that vitiate cross-sectional studies. The few existing lon-gitudinal studies are quite inconclusive withrespect to the progressive decrementphenomenon.

The sibling method, which is based on theaverage within-family sib differences in testscores between younger and older sibs, over-comes these artifacts and permits perhapsthe most satisfactory test of the existence of aprogressive decrement, provided proper ac-count is taken of the effects of family size andbirth order on siblings' IQs. This method isillustrated here by making all possible sib IQcomparisons within the Negro and whitepopulations (40% and 60%, respectively) inall the elementary grades (kindergarten toGrade 6) of a California school district. Thevariables of family size and birth order werecontrolled so as to rule out any biasing ar-tifact from these sources.

The sibling analyses revealed evidence of astatistically significant progressive decrementin the Negro group only for the Lorge-Thorndike Verbal IQ, and the effect is moreevident in boys than in girls. There is not theslightest evidence of a progressive decrementin Negroes' Nonverbal IQ. Yet the meanwhite-Negro difference is about the same forVerbal and Nonverbal IQs. Since the VerbalIQ test requires reading, it seems a likelyconjecture that the progressive decrement in-volves reading skills per se, rather than theabilities essentially defined as intelligence. Inany case, the small magnitude of the VerbalIQ decrement, as well as the total absence ofthe hypothesized decrement on the Non-verbal tests, renders the cumulative deficithypothesis, at least in the age range of 5 to 12years, an unlikely explanation of the morethan one standard deviation IQ differencebetween the white and Negro means.

The main expectations that should followfrom the cumulative deficit theory or fromthe hypothesis that environmental effects onmental development cumulate like com-pound interest, when rigorously tested, arenot borne out in general by the evidence. IfNegro IQ were significantly depressed bylack of proper stimulation in the home en-

vironment, by poorer schooling, by lowerteacher expectations, by cumulative effects ofrepeated frustrations of failures in the schoolsetting, and by decreasing motivation andcooperativeness in the learning and testingsituation with each successive year in school,then we should indeed expect to find aprogressive decrement in IQ with increasingage, in accordance with the cumulativedeficit hypothesis. The failure of the data tosupport this expectation except for the Ver-bal IQ test involving reading, implies thatthe hypothesized cumulative effect of en-vironmental disadvantages either does notaffect highly g-loaded nonverbal intelligencetest performance or has made all of its im-pact prior to about 5 years of age. Yet itwould seem unlikely, if environmental effectson intellectual development act cumulativelylike compound interest, that such cumulativeeffects would not continue beyond age 5.

No study, of course, can ever prove thenull hypothesis. A progressive age decrementin Negro IQ could exist. But it is noteworthythat the prevailing general acceptance of thecumulative deficit hypothesis as an explana-tion for the generally lower IQ of Negroes ascompared with Whites remains unsupportedby any methodologically sound evidence inthe literature. The results of the presentstudy, in addition to the lack of contradic-tory evidence in the previous researchliterature, suggest that the causes of theNegro IQ deficit, whatever they might be, arenot reflected in age decrements beyond aboutage 5 but appear largely to involve factorswhose influences are already establishedbefore school age.

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(Received December 26, 1973)

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