Profiles showing the typical performance of various criterion groups often have been provided for other tests and inventories. Counselors are expected to use these profiles by noting the similarity of a counselee's profile to the profiles of the criterion groups. Anyone who has engaged in this process needs no description of what has long been known as the profile problem (Tiedeman, 1954).
Similarity scores take the guesswork out of profile comparison but, unless they are used in conjunction with discriminant analysis procedures, they fail to deal directly with important aspects of the profile problem; for instance, do the criterion groups actually look different on the measures involved? If so, what are the important measures and how should they be weighted? Unfortunately, a set of similarity scores can be obtained from purely irrelevant variables.
For the above reasons, discriminant analysis procedures often are used in conjunction with similarity scores. These procedures enable one to determine whether the criterion groups are, in fact, differentiated by the measures. If so, the measures can be weighted and combined into independent factors (discriminant functions) that maximize criterion group differentiation. Furthermore, the number of factors needed for criterion group differentiation can be determined. Thus, one may, and usually will, find that two factors account for most of the discriminatory power of a set of measures when applied to criterion groups relevant to educational and vocational counseling. Finally, the nature of the factors can be identified by noting the measures that correlate highly with them.
Equations resulting from discriminant analysis can be used to calculate criterion group positions on the discriminating factors. These positions, in turn, can be plotted on a coordinate grid with the vertical and horizontal axes representing the two major factors. In the same manner, the factor scores of a given student may be calculated and plotted. The student's position on the coordinate grid then may be compared visually with the criterion group positions.
This technique for graphically depicting a student's similarities and dissimilarities was implicit in early work on the profile problem (Tiedeman, 1954) and was specifically suggested more than 10 years ago (Dunn, 1959; Whitla, 1957). However, it has been mentioned only occasionally in the professional literature since then (for example, Baggaley and Campbell, 1967; Cooley and Lohnes, 1968) and has received little attention in testing texts. Rulon et al. (1967) have provided a detailed discussion of the rationale underlying discriminant analysis and similarity score procedures along with ample illustrations of the resulting graphical solution to the profile problem. However, in presenting the illustrations, emphasis was placed on representing the geometry of the statistical procedures. Little attention was given to test interpretation applications of the illustrations.
Data-Information Conversion via Similarity Score Profiles
In helping Fred understand the possible reasons underlying his similarities and dissimilarities, one is, in a sense, helping him to project certain aspects of his self into the choice options. This might be viewed as a vicarious exploration that tells Fred what persons who have exercised various choice options are like in terms of the characteristics that have been measured. The considerable variation in these characteristics among students who have made a specific choice will be clearly evident from the ellipse shown on the profile. If ellipses are shown for all of the vocational programs, overlap among the various groups also will be evident. Criticisms of counseling applications of trait and factor research sometimes are based on the fact that divergences within criterion groups and similarities among criterion groups are concealed. Similarity score profiles reveal these facts of life. At the same time, useful differences among criterion groups, if present in the data, are presented in a manner that permits the counselee to "try the various groups on for size."
Once the reasons underlying Fred's similarity scores have been determined, Fred and his counselor may be able to develop a program of activities and study that would increase his similarity score for a given criterion group. The feasibility of doing this would, of course, depend on the variables involved. However, the suggested strategy represents one of the few counseling applications of test data that facilitates change in the status quo rather than merely being a representation of it. Other strategies for computing the status quo have been presented by Prediger (1970) and Rulon et al. (1967). Since these strategies are institution oriented rather than counselee oriented, they will not be discussed here.
Some Technical Considerations
One obvious limitation of similarity score profiles is the difficulty in representing more than two test or factor dimensions at one time. Discriminant analysis, fortunately, results in a reduction in the number of dimensions needed to represent criterion group differentiation. Usually two dimensions are sufficient. Nevertheless, similarity score profile techniques can be used with three factors by developing a series of profiles representing group positions on the first two factors for successive values of the third (Prediger, 1970). Instances in which more than three factors would be required to represent criterion group discrimination are rare, judging from the results of discriminant analyses reported in the literature.
The discussion, so far, has involved only one of two general approaches that have been used to develop similarity scores. The centour score approach, which has been illustrated above, gives an independent estimate of a counselee's similarity to each of the criterion groups under consideration. The second approach, which is based on the maximum likelihood principle, provides probabilities that take into account the relative degree of a counselee's similarity to each of the criterion groups (Cooley and Lohnes, 1962). The resulting similarity scores are given as decimal probabilities that total 1.00. Thus, if five criterion groups of equal size were involved and a counselee was equally similar to all five, his similarity scores via the second approach would be 0.20 for each group. This would be true whether his similarity scores obtained via the centour method were all 99 or all 1. That is, relative degree of similarity rather than absolute amount is determined.