역균형화 단일집단 설계를 사용하는 검사동등화에서 차별적 순서효과의 통계적 유의성 검정 및 검정력 분석

초록

When conducting equating of two test forms using the single group design, counterbalancing the order of administration of the forms is almost always required in practice. In the single group test equating design with counterbalancing, differential order (DO) effects refer to the interaction effects of test forms (A) and administration orders (B). The main purpose of this study is to present the principle and methods of conducting the statistical significance test for the DO effects in the counterbalanced single group design involving a total sample size of 2n. Main findings are as follows. One can conduct the significance test for the DO effects using a statistic , which follows an F distribution with the degrees of freedom of 1 and 2n-2. The statistic simplifies to the F statistic for the main effects of a random groups factor (G) in a 2x2 Latin square design including the three factors, G, A, and B. Also, the statistic is equal to the F statistic used for the significance test of the between-subjects effects in a ‘one between-subjects factor and one within-subjects factor’ repeated-measures design. Further, one can perform power analyses for the statistic at a significance level (alpha) once the noncentrality parameter and effect size for are identified or estimated with sample data.

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