Level I/Level II: Factors or Categories?

Arthur R. Jensen Institute of Human , University of , Berkeley

An explanation is sought for the striking apparent failure of the interactions of and memory factors with socioeconomic status predicted by Jensen's Level I/Level II theory, in a study by Stankov, Horn, and Roy (1980). It is suggested that Level I ability may not be a higher-order factor, like Spear- man's g or Level II but rather a category of narrower abilities involving rote learning and primary memory, with little transformation between input and output. Orthogonal! zed hierarchical of the abilities domain is recommended as potentially the most fruitful method for discovering the na- ture of Ability X SES (or Race) interactions.

The recent article in this journal "On the the phenomena that it has helped to reveal. Relationship Between Gf/Gc Theory and When the theoretical scaffolding is torn Jensen's Level I/Level II Theory" by Stan- down, are the established empirical findings kov, Horn, and Roy (1980) merits a critical that are left standing of interest, scientifi- comment. These authors (henceforth sig- cally or practically, and worthy of attempts nified as SHR) investigated Level I/Il in a at better theoretical formulation? If so, the factor analytic framework that seems to theory has served its legitimate purpose. highlight certain aspects of the Level I/II I believe this is the case with the Level I/II theory thai have been neglected in previous theory. A large number of studies, of which studies. This is indeed valuable. But what my own studies of Level I/II are only a minor I see as the main contribution of their study fraction, have now established certain phe- is apt to be lost in the article's clutter of side nomena that must be understood by differ- issues, including some confusions about the ential psychologists. A recent comprehen- Level I/II theory and all the previous em- sive review of this research literature con- pirical research on it. cludes: Level I/II is more a set of empirical gen- eralizations than it is a theory, although the The majority of studies . . . provide support for the attempt to explain these generalizations, major hypotheses of Jensen's [Level I/II] theory. Dif- which so far has not been uppermost, can ferent socioeconomic status (SES) and racial groups fend to obtain equal average scores on Level I, whereas loosely be termed a theory. I regard theories middle SES and white groups obtain higher scores on merely as tools and scaffolding for the dis- tests of Level 11, on average, than groups of low SKS and covery of previously unnoticed phenomena. black individuals. Among the mentally retarded, low A theory is useful so long as it serves this SES children consistently outperform middle SES purpose, and it is defensible on this ground children on measures of Level 1. (Vernon, 1981) alone. As the phenomena that a theory re- Also, the results of other large-scale studies veals increase in extent and complexity, the of Level I/II (Hall & Kaye, 1980; Scarr, 1981) theory must undergo revision or be discarded too recent for inclusion in Vernon's review and replaced by some other theory, if our are consistent with the major hypotheses aim is to go on probing reality. The danger derived from Level I/II theory—for example, of a theory is not that the theory is wrong or much smaller race and SES differences on inadequate in light of further discovery, for Level I (memory) than on Level II (intelli- that is inevitable and necessary. The danger gence). is that proving the theory to be deficient may That the SHR study apparently did not be misconstrued as justification for ignoring yield results consistent with expectations from Level I/II, as so many other much Requests for reprints should he sent to Arthur R. larger studies have done, is itself in need of Jensen, Institute of Human Learning, University of explanation. SHR's findings do not "dis- California, Berkeley, California 94720. prove," or even bring into question, the main

868 LEVEL I/LEVEL II 869 empirical generalizations of Level I/II that as Level I, and in fact one of the tests (free are well supported by a host of other studies. recall of categorized lists) was used as a Level But a more careful examination of how and II test in one study (Jensen & Frederiksen, why the SHR results differ from those of 1973), and it behaved as a Level II measure other studies might well throw important should behave in relation to other variables, new light on the Level I/II formulation. in terms of the theory—this, despite the fact that the Mm primary is as substantially The SHR Study loaded on the second-order SAR factor as are the other two primaries, Ms and Ma, that Essentially, what SHR did was as follows: also define the SAR factor. SHR thus wisely They began with 12 primary (first order) dropped the free recall tests in their subse- factors that had already been established in quent analyses because of their ambiguity as earlier studies. Each of these primary fac- a SAR factor. tors is measured by a small group of tests. Factor scores were then obtained on the Three of the primaries involving memory oblique second-order factors Gf, Gc, and tests were identified as characteristic of SAR. These factor scores were then used to Level I ability: Memory Span (Ms), mea- compare the means of three SES groups sured by auditory and visual number and after the total sample of 201 high school letter span; Associative Memory (Ma), students was divided into high (n = 45), measured by low association word paired- medium (n = 75), and low (n = 81) SES associates, word-number pairs, and free re- groups on the basis of father's occupation. call of uncategorized lists; and Meaningful The main prediction from Level I/II Memory (Mm), measured by high associa- theory, which many other studies have borne tion word pairs, emphasized word recall, and out (Vernon, 1981), is that the SES groups free recall of categorized lists. The 12 pri- should differ very much less on Level I mary factors (including Ms, Ma, and Mm) ability (as here measured by SAR factor were factor analyzed, and three second-order scores) than on Level II ability (as measured factors with eigenvalues larger than 1 by Gf and Gc factor scores). The results of emerged. These three second-order factors, the SHR study, however, did not bear out obliquely rotated to approximate simple this prediction. The SES groups differ structure, were identified as Fluid Intelli- consistently and significantly on all of the gence (Gf), Crystalized intelligence (Gc), factor scores, and the SES differences are of and Short- Term Acquisition and Retention about the same magnitude on Gf, Gc, and (SAR). The Gf and Gc factors are both es- SAR. This striking result is virtually sentially Level II ability, which I have always unique, so consistently has this particular considered to be much the same ability as prediction from Level I/II theory been sub- Spearman's . Gf and Gc are differ- stantiated in previous studies comparing ent (although usually highly correlated) SES and racial (white/black) groups on phenotypic expressions of the same ge- measures of Level I and Level II. Unfortu- notypic Spearman's g. The SAR factor, nately, SHR's explanation for this surprising being defined by tests of short-term memory, finding is inadequate and inaccurate. It is presumably a factor analogue of Level I requires a closer, more careful look than they ability. That is to say, the SAR factor rep- gave to it. It is even possible that they have resents mainly the common variance among found something more interesting than they three primary factors derived from nine had apparently realized. various tests of short-term memory. At least two of the primary factors—Ms and False Explanations Ma—would surely appear to qualify as Level I; their defining tests, or something very SHR suggest that their results are a result equivalent, have all been used as Level I of their better, less biased sampling. They measures in previous studies. In terms of state that Level I/II theory, however, the Mm (Mean- ingful Memory) primary is not as clearly when sampling does not produce a contrast between defined by tests that would be characterized only one extreme group and a midgroup with respect to 870 ARTHUR R. JENSEN the abilities of interest, the differences between SES ferences (see next section) from I/II groups are significant for LI (i.e., SAR) as well as for IJI theory tested in this study, the sample sizes (i.e., Gf or Gc), and the differences between the differ- ences are neither noteworthy nor significant." (p. cannot be held responsible for the failure of 807) the main hypothesis, that is, the absence of a significant and appreciable Level I/II X And they then go on to explain the statistical SES interaction. However, it is noteworthy effects and possible artifacts that could re- that the SES classification into high, medi- sult from selecting extreme groups, con- um, and low SES groups in this Australian cluding that sample does not result in as large mean SES differences on the Level II factor scorers (Gf the present analyses and results differ from those of Jensen in one notable respect: Groups are selected at and Gc) as are typically found in American both extremes and in the middle with respect to each samples that are stratified in much the same of the three major factors. This means that selection way. For example, Jensen (1974) found at one extreme has not occurred. differences between high and low SES groups on Level II (Lorge-Thorndike Verbal They fail to note that only three of my ear- and Nonverbal IQ) of about .90

Level I characteristics (e.g., forward digit if incorrect inferences from it are not borne span, serial and paired-associate rote out empirically, or if the theory allows pre- learning, and free recall of unrelated items) diction of certain effects that are only very behave differently than Level II (intelli- weak and would require an unusually large gence) tests in relation to SES and race. sample for an adequate statistical test. Such The fact that some other types of tests (or is the case with two of SHR's predictions. factors) besides Level I tests might also be First, they expected (p. 805), supposedly found that do not discriminate SES or racial from Level I/II theory, that the variances of groups in the same way as do standard in- Gf and Gc (or Level II) should be positively telligence tests is simply further grist for related to SES level. They found just the research and theoretical understanding, not opposite trend, although the variances did a contradiction of Level I/II. I would be the not differ significantly. But their theoretical first to agree that when the nature of SES expectation was the opposite of what Level and racial differences in mental abilities (not I/II theory should predict. What they ac- just in intelligence or g) is much better tually found thus accords with the theory. known, the Level I/II theory will most likely As noted elsewhere (Jensen, 1974), it was be discarded for some better, more compre- hypothesized that social mobility in an in- hensive formulation. But the phenomena dustrialized is more dependent upon to which Level I/II theory has drawn atten- Level II than upon Level I abilities. SES is tion, unless proved an outright method- indexed mainly by attained occupational ological artifact, will have to be compre- status. High and low prestige occupations hended by any new formulation. differ in the intelligence threshold below The failure of the second-order SAR fac- which entry into, or successful performance tor to replicate the predicted Level I/Level in, the occupation is impossible or highly II X SES interaction should have led SHR to improbable. Consequently, the variance in investigate whether any one of the purported intelligence (Level II) should decrease, going Level I primary factors (Ms, Ma, or Mm) from lower to higher occupational levels (and separately would conform to the theoretical hence from lower to higher SES). This, in prediction. If Ms, for example, did not, we fact, is what is reported in a number of large would be faced with an inexplicable failure studies (Jensen, 1974; Jensen, 1980, p. of the SHR study to replicate a finding that 344). has been substantiated in much larger SHR also predicted that the variance of studies. And if none of the primary Level I SAR (Level I) should increase going from low factors accorded with theoretical prediction, to high SES. This is theoretically correct, would any of the separate tests do so? If but the theory would predict only a very not, then the results of the SHR study would weak relationship that would not likely be seem even more surprising and puzzling. significant in a sample as small as SHR's. But these further analyses should have been The directional prediction is borne out in done by SHR to help locate more precisely much larger samples (Jensen, 1974). the failure of the theoretical prediction. SHR warn against interpreting Level I as Another procedure that might enlighten "a kind of intelligence" (p. 808). I am not these data is an orthogonalized hierarchical aware that I have ever referred to Level I as factor analysis, as is provided by the a kind of intelligence, which I equate with Schmid-Leiman (1957) transformation, in Level II—in contrast to Level I. But both, which each factor at each level of the hier- of course, are surely mental abilities. archical structure is uncorrelated with every other factor. Then see if factor scores on Future Research Level I and Level II types of factors, what- ever their level in the hierarchy (if such fac- Level I/II theory has successfully identi- tors indeed emerge) interact with SES in the fied a class of mental abilities (whether they way predicted by Level I/II theory. qualify as broad factors or not) on which social classes and racial groups generally do Incorrect and Weak Inferences not differ nearly as much as they differ on tests of intelligence. What is now needed is A theory should not be held accountable a more complete analysis of SES and race LEVEL I/LEVKL II 873

differences over a much broader range of and Anglo-American children. California Journal mental abilities. I believe that factor anal- of Educational Research, 1961,12, 147-159. Jensen, A. R. Learning abilities in retarded, average, ysis is not only the most useful tool for such and gifted children. Merrill-Palmer Quarterly, exploration but is now indispensable for any 1963, 9,123-140. economy and clarity in such investigation. Jensen, A. R. Patterns of mental ability and socio- What we wish to discover is all of the inter- economic status. Proceedings of the National Academy of Science, 1968,60, 1330-1337. actions of race (white-black or other racial Jensen, A. R. How much can we boost IQ and scho- contrasts) and SES with all of the main in- lastic achievement? Harvard Educational Review, dependent factors of ability. I emphasize 1969, 39,1-123. "independent," because, as I have argued Jensen, A. R. Level I and Level II abilities in the three elsewhere (Jensen, 1980, pp. 729-736), group ethnic groups. American Educational Research Journal, 1973, 4, 263-276. mean profiles of abilities based on correlated Jensen, A. R. Interaction of Level I and Level II abili- tests (or oblique factor scores) are virtually ties with race and socioeconomic status. Journal of meaningless and can only obscure the anal- , 1974, 66, 99-111. ysis of population differences. Therefore, Jensen, A. R. Kias in mental testing. New York: orthogonalized hierarchical factor analysis, Free Press, 1980. Jensen, A. R., & Figueroa, R. A. Forward and backward a la Schmid-Leiman (1957), would seem to digit span interaction with race and IQ: Predictions be the preferred method. The hope re- from Jensen's theory. Journal of Educational mains, as I stated originally (Jensen, 1969), Psychology, 1975,67, 882-893. that we may discover other abilities, besides Jensen, A. R., & Frederikson, J. Free recall of catego- rized and uncategorized lists: A test of the Jensen Spearman's g, on which the direction or hypothesis. Journal of Educational Psychology, magnitude of SES and race differences are 1973, 65, 304-312. less disadvantageous to the traditionally Jensen, A. R., & Inouye, A. R. Level I and Level II unfavored groups in school, and which may abilities in Asian, white, and black children. Intel- ligence, WSO, 4, 41-49. be used to their advantage in the instruc- Scarr, S. IQ: Race, social class and individual dif- tional process. ferences: New studies of old problems. Hillsdale, N.J.: Erlbaum, 1981. Schmid, J., & Leiman, J. M. The development of References hierarchical factor solutions. Psychometrika, 1957, 22,53-61. Garrett, H. E., Bryan, A. I., & Perl, R. E. The age factor Stankov, L., Horn, J. L., & Roy, T. On the relationship in mental organization. Archives of Psychology, between Gf/Gc theory and Jensen's Level I/II theory. 1935, No. 176. Journal of Educational Psychology, 1980, 72, Hall, V. C., & Kaye, D. B. Early patterns of cognitive 796-809. development. Monographs of the Society for Re- Vernon, P. A. Level I and Level II: A review. Edu- search in Child Development, 1980, 45(2, Serial No. cational Psychologist, 1981, 16, 45-64. 184). Jensen, A. R. Learning abilities in Mexican-American Received April 10,1981 •