The two commonly used criteria in assessing equating consistency for a potential scale drift-direct equating (versus indirect equating) and equating in a circle (versus identity equating) were studied through simulation. The chained equipercentile and linear methods were used for equating when population difference in ability in terms of the standardized mean difference (SMD) in anchor scores were observed with a wide range of values in the anchor test equating design. For the equipercentile method, when the obtained SMD values were less than 1, the differences between the direct and indirect equatings, or between the circular and identity equatings were small and trivial. When the obtained SMD values were greater than 1, the differences of the conversions between the indirect and direct equatings, or between the circular and identity equatings appeared to be substantially large. For the linear method, the differences between the two conversions appeared to be substantially large when the SMD values were very small.
The two commonly used criteria in assessing equating consistency for a potential scale drift-direct equating (versus indirect equating) and equating in a circle (versus identity equating) were studied through simulation. The chained equipercentile and linear methods were used for equating when population difference in ability in terms of the standardized mean difference (SMD) in anchor scores were observed with a wide range of values in the anchor test equating design. For the equipercentile method, when the obtained SMD values were less than 1, the differences between the direct and indirect equatings, or between the circular and identity equatings were small and trivial. When the obtained SMD values were greater than 1, the differences of the conversions between the indirect and direct equatings, or between the circular and identity equatings appeared to be substantially large. For the linear method, the differences between the two conversions appeared to be substantially large when the SMD values were very small.