Effects of sample size and item format on eighth grade ABIDE tests equating

In this study, preservation of same distributions property (SDP) and equity properties in non-equivalent groups common-item design was investigated for true score (True_Sc) and observed score (Obs_Sc) equating. Samples of 1000, 3000 and 5000 participants selected randomly from 34000 students having participating in 2016 Eighth Grade Monitoring and Evaluating Academic Skills (MEAS) research were used for analysis. In equating A and C forms of Math and Social Studies tests to B form in MEAS research, preservation of SDP and equity properties was evaluated according to sample size, item format, sub groups of test takers, true/observed score equating and scale transformation methods (Mean-Mean, Mean-Sigma, Haebera, Stocking-Lord). Since MEAS tests were mixed-format, to evaluate the effects of item format, tests were transformed into dichotomous format by giving 1 point for maximum score and 0 point to the others. After transformation, effects of mixed-format and dichotomous format on SDP, first-order equity (FOE) and second-order equity (SOE) values were compared. The results obtained were as follows: In Math and Social Studies tests; (i) Sex of student wasn't unidirectionally effective for preservation of SDP, FOE and SOE. (ii) Characteristic curve methods generated mostly stable results, but the smallest FOE ad SOE values were estimated in moment methods in some cases. (iii) Whether cumulative distribution functions (cdf) of the forms were similar or different prior to equating affected preservation of SDP after equating. (iv) Format affected tests differrently. (v) Effect of Obs_Sc and True_Sc equating on preservation of SDP, FOE and SOE changed according to tests.