Using population invariance as a criterion to evaluate equating relationship for college basic academic subject examination

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] The study investigates population invariance of equating functions in situations where equating samples are considerably unequal in size. Using an equivalent groups equating design, the study compares equating functions developed from the linear equating procedure, the unsmoothed equipercentile equating procedure, and the three-parameter IRT true-score equating procedure on examinee samples that were formed based on gender and ethnicity as well as on the total examinee sample. Multiple evaluative measures were used to evaluate equating differences. Findings indicate that equating invariance was reasonably achieved across the gender groups, that lack of equating invariance was found for the ethnic groups, and that the IRT true-score equating did not perform better in terms of robustness to form or group differences. The study findings suggest that sample sizes do influence equating invariance. With samples unequal in size, equating functions developed from the total examinee sample tend to be influences by the dominating examinee group, whereas equating functions obtained from small examinee samples are subject to larger sampling error. The study recommends linear equating for small equating samples based on examination of equating precision. Investigation of invariance of score classifications supports the use of linear equating with small equating samples becuase of better classification consistency. Higher consistency was found at passing scores that are farther away from the mean, suggesting that the location of cutoff scores impacts classification consistency. When equating samples are small, using cutoff scores may be a practical alternative to better equating invariance.