Comparison of Several Small Sample Equating Methods under the NEAT Design

Abstract

The aim of this study is to compare the performances of Identity, Nominal Weights Mean (NMW), and Circle-Arc (CA) equating methods under the Non-Equivalent Groups Anchor-Test (NEAT) design. Synthetic equating functions (SFs) of the NWM and CA (NWS and CAS) were also created using an equal weighting system (w = 0.5). Different sizes of small examinee samples (n = 10, 20, 50, 100) were used to equate new test forms to base test forms. Chained Equipercentile (CE) with bivariate log-linear presmoothing was used as population criterion equating function to compare the performances of the equating methods. Overall, the identity (ID) equating was the most favorable, but the NWS method produced less equating error than the ID and Tucker Linear (TL) equating methods under specific simulation conditions. The use of the SF of the NWM method can be used in practice to equate the test forms with samples less than 25 examinees. In future studies, the SFs of other existing equating methods should be tested to determine the best performing equating method(s) for small sample equating.

Equating Method for Learning Outcomes of Elementary School/Madrasah Students

“…(8) and ( 9) Thus the nominal weight replaces the variance and covariance in the Tucker method in the form of total items and anchor items to be the number of respondents (Caglak, 2016), where K indicates the number of items on the test device. While w is related to the number of samples/respondents (N), which is the ratio of the number of samples from X and Y to the total number of samples (Babcock et al, 2012;Caglak, 2016) (10) and ( 11) By substituting equations ( 8) and (9) to equation ( 2) is obtained, Moreover, using the weights of the number of samples in equations ( 12) and (13), the above equation becomes: so the equation for the Nominal Weight Mean Equating method will be obtained as follows:…”

Equating Method for Small Sample: Comparative research on nominal weight mean and linear method

“…This method is one simple method aimed at aligning with small samples [35]. The NWM method replaces the covariant terms and variants with the ratio of the number of items in the total test to the anchor text, making the weight effective [36]. The following is the formula for equalizing scores using the NWM method: The use of equalization methods in small samples can be used at the school level, which in general is the number of students in the small sample category.…”