Population Invariance of Equating Functions

• Activity Number: 423
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Social Statistics Section
• Author(s): Zhaohui Sheng*+ and Yanyan Sheng
• Companies: and Southern Illinois University-Carbondale
• Keywords: Equating ; Population Invariance ; Sample Size ; Resampling Method

Abstract

The study investigates equating invariance in situations where some equating samples are considerably small. 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 illustrates that sample sizes have an impact on equating invariance. With samples unequal in size, equating functions developed from the total examinee sample tend to be influenced by the dominating examinee group, whereas equating functions obtained from small examinee samples are subject to larger sampling error. Linear equating has better equating precision for equating samples in size less than 1500 per form based on examination of equating precision.