Measures of consistency for Holland-type codes

Journal of Vocational

Behavior 31, 37-44 (1987)

Measures of Consistency for Holland-Type Codes ROBERT

F.

STRAHAN

Iowa State University “Consistency” in Holland’s theory refers to the extent to which more closely related scale types are found together in codes of the Self-Directed Search sort. This paper describes two new measures of consistency. One is based on the hexagonal model and is for use with 3-point codes. The other is based on conditional probabilities and is for use with 2point codes. o 1987 Academic PWS, IIIC.

The first letter in a Holland-type code refers to that scale for which an individual receives the highest score on, say, the Self-Directed Search (SDS; Holland, 1985a). The second letter refers to the second-highest scale, and (in the case of 3-point codes) the third letter to the thirdhighest. Some of Holland’s six personality types are found together more often than are others. A realistic-Investigative (RI) code is much more common than an Artistic-Conventional (AC) code, e.g., while a Social-Conventional (SC) is intermediate in frequency. Holland (1985b)usesthe term consistency in speaking of “the degree of relatedness between personality types or between environmental models” (p. 4) and has suggested that more consistent profiles should be associated with more stable or mature vocational identity. MEASURES

OF CONSISTENCY

Most consistency research has used a measure based on Holland’s hexagonal (RIASEC) model. In that model (cf. Table 1) more commonly associated types are found adjacent on the hexagon, less commonly associated types are separated by another type letter, and least related types are separated by two other letters (opposite one another). Holland (198Sa)writes that “at best, the hexagons resulting from real-world data are misshapen polygons, but this arrangement is superior to the use of unrelated or unordered occupational categories.” The author thanks Michelle Iaffaldano Graef for bringing this research area to his attention. The comments of Paul M. Muchinsky and an anonymous reviewer were useful, as was the assistance of D. Jeff Johnson. Requests for reprints should be sent to Robert F. Strahan, Department of Psychology, Iowa State University, W204 Lagomarcino Hall, Ames, IA 5001 l-3180. 37 Oool-8791/87 $3.00 Copyright EB 1987 by Academic Press, Inc. All rights of reproduction in any form resaved.

38

ROBERT

F. STRAHAN

TABLE 1 Examples of Extremely Consistent (a), Moderately Consistent (b), and Extremely Inconsistent (c) 3-Point Codes (a) RIC

(b) RAC

(c) RSA

(1) R

(1)

(1) R 1 (2) A

(3) c E S

(3) c E S

R c E

1 A (2)

S

I A (3)

(2) Y = 6(2) + 2(2) + l(1) = 17 c, = 10

Y = 6(l) + 2(2) + l(0) = 10 c, = 5

Y = 6(O) + 2(l) + l(2) = 4 c, = 1

The simplest index for 2-point codes (Holland, 1973) in effect assigns the score “2” to codes for which the two letters are adjacent on the hexagon, and the score “1” in all other cases. Probably more commonly used has been a trichotomous rather than dichotomous measure. Here three points are scored for adjacent letters, two points for letters separated by one other on the hexagon, and one point for letters opposite one another (Holland, 1985b, p. 28). (Because their work involving students’ choices of two major subjects made it possible for the same letter to be seen in both first and second places of the code, Barak and Rabbi (1982) expanded this scoring method to a 4-level index.) Villwock, Schnitzen, and Carbonari (1976) used a consistency measure based on the correlations among the six SDS scales rather than on the hexagonal model (itself, as suggested above, a simplification based on those correlations). Their measure was roughly continuous in its employment of the square of the correlations arising from the 15 possible pairings of the six types. Erwin (1982) also used the pair-wise correlations, though indirectly, for a consistency measure. His index, based on the factor analytic work of Cole, Whitney, and Holland (1971), is essentially a Mahalanobis or generalized distance function measure (cf. Wiggins, 1973, ~99). An Hexagonal Model-Based Measure for 3-Point Codes

All the previously mentioned measures of consistency apply to 2-point codes. Described now is an hexagonal model-based measure for 3-point codes. Using the third letter permits a more sensitive (finely differentiated) index. Intuitively, a consistent 3-point code woud be one in which (a) the three highest letters are close together on the hexagon, and (b) the “closeness” is greater between the first and second letters than between

HOLLAND-TYPE

CODES

39

the first and third or the second and third (reflecting the ordering of the code). This intuitive conception of consistency is operationalized as follows. The method begins by considering the first and second letters. Two points are scored if they are adjacent on the hexagon (Table 1). One point is scored if one other letter stands between them, and zero points are scored if two letters stand between them. (This is the same procedure followed for Holland 2-point codes.) This procedure is repeated for the first and third letters, then for the second and third. These three distance scores are labeled x1, x2, and x3. Next, the linear combination Y = clxl + c2x2 + cqx3, where the c’s are weighting constants, is formed. Y, or some transformation of Y, is a measure of consistency whose specific distribution depends on the values chosen for the c’s. As noted, cl is selected to be larger than c2 and c3. If one considers a more consistent code to be that for which the third letter is closer to the first than to the second, then c2 is chosen to be greater than c3. If one is undecided on the relative weighting to be given x2 and x3, then c2 and c3 are given the same value. (It seems unlikely that one would wish to make c2 less than c3, but that of course could be done.) The distributions of a number of different combinations of c’s were examined. The combination c, = 6, c2 = 2, c3 = 1 seemedmost attractive, and so was used for generation of Table 2. The entries of this table need some explanation. For the particular c’s chosen, Y has the 10 possible values 4, 5, 8, 9, 10, 12, 13, 14, 16, and 17. Note the “gaps” of 6, 7, 11, and 15. Because this consistency measure is no more than ordinal in scale level, the final consistency measure C1 was defined as the rank transform (rank order) of Y. Thus C, ranges from 1 to 10 (low to high consistency)with no gaps. Table 1 shows examples of extremely consistent, moderately consistent, and extremely inconsistent codes, together with the calculations of Y and C,. The set of weights 6, 2, and 1 indicates that the distance between the first and third letters is considered more important than the distance between the second and third. A reasonable set of c’s that does not distinguish between the importance of x2 and x3 is c, = 4, c2 = 1, c3 = 1. This combination results in the less-differentiated, 5-level measure C2, whose values are given in Table 2 along with, for comparison, those of the Holland 2-point code measure, abbreviated H herein. As Table 2 shows, Cl, C,, and H are monotonic functions of one another. H is in fact a special case of the general linear combination procedure dealt with in this section, that for which only the distance x1 is considered and for which c, = 1; that is, the case for which Y = x1. Inspection of Table 2 reveals that C1 and C2 differentiate more finely than the Holland 3-level measure, especially at higher levels of consistency.

40

ROBERT

Hexagonal

RIA RIS RIE RIC RAS RAE RAC RAI RSE RSC RSI RSA REC REI REA RES RCI RCA RCS RCE Note. Holland

IAS IAE IAC IAR ISE ISC ISR ISA IEC IER IEA IES ICR ICA ICS ICE IRA IRS IRE IRC C, = 3-level

ASE ASC ASR AS1 AEC AER AEI AES ACR AC1 ACS ACE AR1 ARS ARE ARC AIS AIE AIC AIR IO-level (Zpoint

TABLE Consistency

Mode&Based 3-point

F. STRAHAN 2 Measures

codes SEC SER SE1 SEA SCR SC1 SCA

SCE SRI SRA SRE SRC SIA SIE SIC SIR SAE SAC SAR SAI

ECR EC1 ECA ECS ERI ERA ERS ERC EIA EIS EIC EIR EAS EAC EAR EAI ESC ESR ES1 ESA

CR1 CRA CRS CRE CIA CIS CIE CIR CAS CAE CAR CA1 CSE CSR CSI CSA CER CEI CEA CES

consistency measure, C, = 5-level code) consistency measure.

for 3-Point

Codes

Cl

G

H

9 I 8 IO 3 4 5 6 1 2 2 1 6 5 4 3 10 8 I 9

5 4 4 5 2 2 2 3 1 1 1 1 3 2 2 2 5 4 4 5

3 3 3 3 2 2 2 2 1 1 1 1 2 2 2 2 3 3 3 3

consistency

measure,

H

=

A Conditional Probability-Based Measure for 2-Point Codes

The consistency measures so far discussed are all based more or less directly on correlation coefficients. Rose (1984) has observed, however, that in some instances there are rather dramatic differences in judgment about relations among scale types depending on whether correlations or conditional probabilities are used. A correlation coefficient is nondirectional in the sense that it does not distinguish between, for example, the consistency of an RI and an IR code. For the hexagonal model-based Holland index, H, each of these two codes receives the same score (3). Empiricahy, however (Rose, 1984, middle part of his Table I), P(1 1R) = .63, whereas P(R 1 I) = .40. That is, the probability of R being the first point in the code and I the second is greater than the probability of I being the first and R the second. Conditional probabilities provide the basis for another hind of consistency index for 2-point codes. SDS conditional probabilities (Table 3) were calculated from Tables B14-B17 of the SDS manual (Holland, 1985a, pp. 71-74) separately for college males, college females, high school males, and high school females. Also given in Table 3 are frequencies for each of the 30 possible 2-point codes and corresponding H scores. The codes are arbitrarily ordered according to magnitude of conditional probability for college males.

HOLLAND-TYPE

Conditional 2-point code RI AS ES CE SE IR IS cs SI AI RS CI EI SA IA SR EC ER AR AE RA IE RE EA SC RC IC CR AC CA

TABLE 3 Frequencies, and Holland Consistency Scores for the SDS

Probabilities,

Holland consistency score (H) 3 3 3 3 3 3 2 2 2 3 2 3 3

41

CODES

Freq

Fw

Freq

Freq

CM

CM

CF

CF

HSM

HSM

HSF

HSF

171 61 86 21 136 190 167 15 80 26 49 8 23 50 61 42 19 15 10 10 23 39 18 10 17 10 17 2 2 0

.63 .56 .56 .46 .42 .40 .35 .33 .25 .24 .I8 .I7 .15 .15 .13 .13 . .12 .lO .09 49 .08 .08 .07 .07 .05 .04 .04 .04 .02 .oo

9 199 14 3 186 11 142 35 205 40 2 9 4 417 61 13 1 0 1 7 1 4 0 5 122 0 12 0 2 4

.75 30 .58 36 .20 .05 .62 .69 .22 .16 .17 .18 .17 A4 .27 .Ol 34 .oo .oo .03 38 .02 30 .21 .13 .oo .05 .oo .Ol .08

290 89 68 17 138 202 171 21 % 38 301 9 16 67 61 102 15 24 31 20 111 46 128 10 32 39 13 13 0 1

.33 .50 .51 .28 .32 .41 .35 .34 .22 .21 .35 .15 .12 .15 .12 .23 .ll .18 .17 .ll .13 .09 .15 .08 .07 .04 .03 .21 .oo .02

5 251 18 13 274 11 138 231 307 31 8 5 3 595 37 23 4 1 4 9 0 2 1 1 433 0 7 3 13 19

.36 .81 .67 .05 .17 .06 .71 .85 .19 .lO .57 .02 .11 .36 .19 .Ol .15 A4 .Ol .03 .oo .Ol .07 .04 .27 a0 .04 .Ol .04 .07

Note. CM = college males, CF = college females, HSM = high school males, HSF = high school females.

A conditional probability consistency score for an individual is simply the conditional probability associated with the given code type (with perhaps the decimal omitted for convenience of data transcriptionMr possibly the rank transform of the conditional probability. What is clear from Table 3, however, is that such scores will differ, at least somewhat, depending on which norm base is used. For example, an RI conditional probability consistency score will be $3 (or 63) if the college males norms are used, but .75 if college females norms are applied; and still other figures (.33 and .36) are seen with high school males’ and females’ norms.

42

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Pearson Product-Moment

College males (CM)

TABLE 4 and Spearman Rank-Order (in Parentheses) Correlations among Consistency Measures CF

HSM

HSF

.73

.87 (.86) .65 (.45)

.61 (.61) .87 (.79) .70 (.51)

t.67) College females (CF)

F. STRAHAN

High school males (HSM) High school females (HSF)

Holland consistency score (H) SO (.43) .31 (.24) .39

C.36) .16

C.23)

Casual examination of Table 3 shows general congruence in conditional probabilities among the four norm groups, but also some rather striking incongruences. A summary view of the degree of similarity among groups is provided by the Pearson product-moment (r) and Spearman rank-order (r,) correlations of Table 4. There it is seen that college and high school males and college and high school females are most like one another in the conditional probability consistency sense. College males and females are next most alike. What this table shows in addition is the rather low correlation between conditional probability consistency and H consistency measures. Scatterplot inspection shows greater conditional probability variation for H scores of two than for one, and greater still for H scores of three. That is, the conditional probability index is discriminating more finely than Holland’s 2-point code measure at higher levels of consistency, just as does the 3-point code measure previously described. Although different conditional probability norms are a methodological inconvenience, they are also a reflection here of real differences between the sexes and between college and high school students. If one were willing to blur those differences, collapsed tables of conditional probabilities (one, say, for college students, another for high school students; or one for males, another for females) could be generated from the Holland (1985a) basic data. If VP1 (Vocational Preference Inventory; Holland, 198%) conditional probabilities are desired, they can be calculated from Table B19 of the SDS manual (Holland, 1985a, p. 75). Some of these conditional probabilities are found in Rose’s (1984) Table 1. DISCUSSION

Holland (1985b) remarks that “consistency has had a checkered careerabout as many negative as positive results” (p. 73). It is conceivable that these new measures of consistency might contribute to the positive

HOLLAND-TYPE

CODES

43

box score, either in new studies or through reanalyses of earlier research. This is, of course, an empirical matter. And even if the measuresdescribed here were to improve on previous ones (in the senseof supporting Holland’s theoretical notions), the improvement might prove to be trivial. It is worth noting in this connection the fairly appreciable redundancy between consistency measures and frequencies of the associated code types (not surprising given the conception of consistency in terms of most frequently observed codes). For example, correlations between the thirty 3-point code frequencies and C, are r = .71 (r, = .76) for college males, 44 (.75) for college females, 56 (64) for high school males, and .42 (66) for high school females. Relevant to this issue as well are the relations among consistency and the several other constructs that are part of Holland’s theory. Holland (1985b) writes, “Identity, consistency, and differentiation are all concerned with the clarity, definition, or focus of the main concepts-types and environmental models. They probably represent three techniques for assessing the same concept” (p. 5). The measurement of identity is discussed by Holland (1985b). Measurement of differentiation is dealt with by Holland (1985a, 1985b), Frantz and Walsh (1972), Iachan (1984c), and Spokane and Walsh (1978). Also pertinent is work on the concept of congruence, discussed by Holland (1985a, 1985b), Iachan (1984a, 1984b), Kwak and Pulvino (1982), and Zener and Schnuelle (1976). (The rationale underlying the hexagonal model-based consistency measure of this paper is very similar to that of Iachan’s congruence measure.) The power of modern computing facilities should enable investigators with reasonably large data bases to clarify the relationships among the various measures of the several Holland concepts. Empirical clarification might in turn lead to theoretical clarification or refinement. REFERENCES Bat-ah, A., t Rabbi, B.-Z. (1982). Predicting persistence, stability, and achievement in college by major choice consistency: A test of Holland’s consistency hypothesis. Journal of Vocational Behavior, 20, 235-243. Cole, N. S., Whitney, D. R., & Holland, J. L. (1971). A spatial configuration of occupations. Journal of Vocational Behavior, 1, l-9. Erwin, T. D. (1982). The predictive validity of Holland’s construct of consistency. Journal of Vocational Behavior, 20, 180-192. Frantz, T., & Walsh, E. (1972). Exploration of Holland’s theory of vocational choice in graduate school environments. Journal of Vocational Behavior, 2, 223-232. Holland, J. L. (1973). Making vocational choices: A theory of careers. Englewood Cliis, NJ: Prentice-Hall. Holland, J. L. (1985a). The self-directed search professional manuaC1985 edition. Odessa, FL: Psychological Assessment Resources, Inc. Holland, J. L. (1985b). Making vocational choices: A theory of vocational personalities and work environments (2nd ed.). EngIewood Cliffs, NJ: Prentice-Hall.

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Holland, J. L. (1985c). Vocational preference inventory (VPI) manual-1985 edition. Odessa, FL: Psychological Assessment Resources, Inc. Iachan, R. (1984a). A measure of agreement for use with the Holland classification system. JOWM~ of Vocational Behavior, 24, 133-141. Iachan, R. (1984b). Measures of agreement for incompletely ranked data. Educafionaf and Psychological Measurement, 44, 823-830. Iachan, R. (1984c). A family of differentiation indices. Psychometrika, 49, 217-222. Kwak, J. C., & Pulvino, C. J. (1982). A mathematical model for comparing Holland’s personality and environmental codes. Journal of Vocational Behavior, 21, 232-241. Rose, R. G. (1984). The use of conditional probabilities in applications of Holland’s theory. Journal of Vocational Behavior, 25, 284-289. Spokane, A., & Walsh, W. (1978). Occupational level and Holland’s theory for employed men and women. Journal of Vocational Behavior, 12, 145-154. Villwock, J. D., Schnitzen, J. P., & Carbonari, J. P. (1976). Holland’s personality constructs as predictors of stability of choice. Journal of Vocational Behavior, 9, 77-85. Wiggins, J. S. (1973). Personality and prediction: Principles of personality assessment. Reading, MA: Addison-Wesley. Zener, T. B., & Schnuelle, L. (1976). Effects of the self-directed search on high school students. Journal of Counseling Psychology, 23, 353-359. Received: October 30. 1986.