Persistence of Performance‐Approach Individuals in Achievement Situations: An application of the Rasch model

Abstract

Research in goal theory has often relied on the general linear model, ignoring some central assumptions of the theoretical framework under investigation. The purpose of the two studies reported here was to illustrate how the Rasch model can supplement traditional statistical analyses when evaluating the effects of goal orientations on persistence. In Study 1, 41 adolescents participated in a series of insolvable puzzles. Means analyses failed to reveal differences between mastery‐approach and performance‐approach students. Application of the Rasch model, and in particular the differential item functioning procedure, indicated that mastery students were more severely challenged by the last puzzle, compared to performance approach students, with their probability of persisting being significantly lower. The findings of Study 1 were replicated in Study 2 with a sample of 37 college students who were also given a series of insolvable puzzles. The findings suggest that use of the Rasch model can be particularly fruitful for our understanding of the complex achievement‐goal relationship.

Acknowledgements

I am grateful to Athanassios Mouratidis for collecting the data for Study 1, and to my psychology students who took part in Study 2 by participating in my “Motivation in Education” laboratory. Last, I am indebted to Educational Psychology editor Professor Wheldall and two anonymous reviewers, who provided constructive feedback on an earlier draft of this paper.

Notes

1. The logit has been defined as a person's natural log odds for succeeding on items that belong at the middle of a scale (Wright, 1993; Wright & Stone, 1979), and is based on odds ratios. A logit is the natural log of an odds ratio. Thus, it describes the relative frequency of an event compared to the relative frequency of non‐occurrence (Ludlow & Haley, 1995). For example, if the weather is likely to be forecast correctly five out of a total of six times, then the odds are 5/1 (five times occurrence vs. one time non‐occurrence) = 5, and the natural logarithm of these odds gives us a logit of 1.61. Getting heads when dropping a coin reflects chance occurrence (i.e., one out of two) or an odds ratio of 1/1, which equals zero. The natural log of zero is also zero; thus, the likelihood of getting heads is zero on the logits scale (which means the average for that metric). Similarly, when the probability of occurrence is lower than the probability of non‐occurrence, logits take negative values and the probability of success would be less than .5 (Ludlow, Haley, & Cans, 1992).

2. The difference B–D does not necessarily have to be positive. The hypothesis posited is that the B–D difference for the performance‐approach group would be larger than that for the mastery‐oriented group.

3. As a thoughtful reviewer stated, ability is considered a fixed entity in the Rasch model and thus applying the model to persistence, if persistence is malleable, may contradict the basic tenets of Rasch modelling.

Two comments can be offered in response. First, theoretically speaking, ability has been subjectively considered as a fixed and as a malleable entity in goal theory (Dweck, 1986; Dweck & Leggett, 1988). Thus, involvement and achievement have been a function of how ability is perceived, not how it actually is. Second, as Wright and Stone (1979) nicely put it: “[T]he more the item overwhelms the person, the greater this negative difference becomes and the nearer the probability of success comes to zero” (p. 16). Thus, failure on an item is a function of ability and of all the other elements that result in a person failing an item. These elements can be motivational and emotional factors, and not ability only. This proposition can easily be amplified with the example of two students of unequal ability, one a low achiever and one a high achiever, who both flunk an exam because of stress, which suggests that the probability of success is related to more than ability (unless we consider ability a global estimate of subject‐matter ability as well as ability to regulate emotions, stress, etc.—and if this is the case then persistence is certainly an aspect of a person's ability to keep going in the presence of a challenge). Thus, implicitly, the Rasch model allows us to estimate success as a function of factors such as motivation, possibly by incorporating it into the ability estimate.

4. Based on the Gutman pattern, across a continuum of items based on ability an individual is expected to be successful in the first one‐third, be partially successful in the middle items, and fail the last third. In other words, an individual is expected to display a 11101010000 pattern of responding, with 1 indicating success and 0 indicating failure.

5. The items assessed both normative and non‐normative performance goals, in accord with the conceptualization of performance goals posited by Elliot and colleagues (e.g., Elliot, 1999; Elliot & Harackiewicz, 1996). Recently, Grant and Dweck (2003) pointed to the existence of both performance goals with a focus on normative standards (i.e., be better than others) and performance goals with a focus on non‐normative, outcome‐based standards of performance (e.g., solve all the problems). To date, no studies have examined these in detail.

6. As a reviewer suggested, the apparent differences pointed out by the Rasch model can be misleading because of the differential scaling used by the two models (i.e., the Rasch uses logits, which can inflate or deflate actual findings). However, the point to be made here is that the Rasch model did provide unique information not apparent from the GLM analyses, and information regarding person behaviours, which were again confounded in the means analyses.