A CROSS-VALIDATION OF PRIMARY PERSONALITY STRUCTURE IN THE 16 P.F. BY TWO PARCELLED FACTOR ANALYSES

Since most recent factorings of primary personality structure as based on the 16 P.F. item domain have been by scales, they just conceivably could yield a simple . structure perpetuating a past structure. Two new analyses have been made, one here, one prior, setting scales aside and using 46 "radial parcel" variables covering the 184 items. Radial parcels of four items each have built up quite regardless of scale groupings. The present analysis on 250 students and the prior one on 780 adults yielded 22 and 21 factors respectively, statistically significant simple structures in both and a substantial invariance (matching) of factors between them by congruence and salient variable similarity coefficients. Further analysis, beyond the present, shows that the factors found here (a) match when converted to loadings on items, the recognized 16 P.F. factor patterns, and (b) yield the patterns of second-order factors that would be expected from the identification by item content given them as primaries. Additionally, new primaries appear here beyond those in the 16 P.F. , and they also match from the present to the prior parcelled analysis. However, one or two poor matches E, H, M, Q 2 , and Q 4 also result, which could be due to the substantial differences of population in the studies used in the cross validation. CLARIFICATION OF THE ISSUES IN DEBATE For over 25 years, Cattell's theory (1946, 1947, 1950, 1957) of personality structure has been that there are between 20 and 25 primary and 8 to 12 secondorder factorial source traits in items of "normal" behavior. The theory further asserts that the particular concepts involved which have received much experimental development appear equally in Qand L-data. That is to say, the same instrument:-free factors can be found from jointly factoring questionnaire and life ratings by observers (Cattell, 1973). Although more than a dozen other investigators have supported these general conclusions, a minority Eysenck ( 1971 ), Comrey and Duffy (1968), Howard and Browne (1971)have categorically disagreed, asserting that there are only 3 to 10 primaries, several of them alleged181 il l ~· ~: " . MULTIVARIATE EXPERIMENTAL CLINICAL RESEARCH ly different in nature from the 16 P.F. concepts. ·Sells, Demaree and Will ( 1970), on larger samples, believed 11 factors to-exist and took an intermediate position identifying most with one or another of the primaries A through Q6 located by Cattell. Naturally, the number of factors discovered will increase somewhat with larger item coverage encompassed, and it is fortunate for sanity and progress in this often methodologically crude and chaotic realm that the chief protagonists ·have recognized the need for referring to a standard basis-in fact, the personality sphere of variables as initially defined (Cattell, 1946, 1950) and now represented in 184 items in the 16 P.F. As further research shows (Cattell & Gibbons, 1968); Sells, Demaree & will, 1970), much the same domain is covered in Guilford, s questionnaire (Guilford & Zimmerman, 1949-55) and in the "normal,, part of the MMPI (Cattell & Bolton, 1969; Delhees & Cattell, 1971). The disagreement does not arise primarily about the basis of variables, therefore, but about (a) the required dimensionality and (b) the rotation within it. The debate between the two groups of questionnaire researches is thus not merely one of number of factors, but also of nature of factors, because the rotational positions with underfactoring (Eysenck, Howarth & Browne, 1970) are unable to find a really tight simple structure (Cattell, 1966) and lead to conglomerates of primaries and second orders. The chief argument that recurs on the opposite side, when Comrey, Howarth, and Eysenck have been unable to find and support the primaries in the 16 P.F. , the High School Personality Questionnaire, etc., is that the programmatic research that for 20 years and 40 researches has checked the structure and increased the scale validity for these 16 to 20 primaries is in some way bound by the traditions of an "establishment. ,, Since the same span of actual items has now been covered by both groups, this can no longer be ascribed to a choice of items favoring one structure, and the second group has therefore concentrated its attention on objections to factoring of scales as variables, instead of items. It is, prima facies, a possible argument that a set of 64 scales (as in the 16 P.F., forms A, B, C, and D), growing out of simple structure found in items, will tend to perpetuate any falsities in the original simple structure position. However, this argument has perhaps been sufficiently refuted by (a) Cattell' s point that the number of altern~tive possible 60 variable hyperplanes in 64 variables is enormous, permitting other structure to emerge if they are, in fact, better; (b) the demonstration (Cattell & ~aughan, in press) that factoring by items and factoring by parcels yields the same (congruent) conclusions, as theory would expect; and ( c) the psychometric argument that factoring by parcels, such as has predominated in this last 10 years, can lead, by progressive rectification (Cattell, 1973), to item substitutions that lead to the same improvements as would result from item factoring. Faced with this accumulating refutation of attacks, there remains for the opposition, i.e., those opposing the 20and primary-factor solution, with the identities given to traits A, B, C, etc., on the 16 P.F. , only one possible far-out style of attack. It is to assert that the blind rotations to simple structure have achieved their matching coherence by some kind of accidental recognition of variables in the rotation process_. In all our practice, variables at the rotation stage are represented only by numbers, and in the plots only by points. Of course, in a