This article discusses the five studies included in this issue. Each article addressed the same topic, population invariance of equating. They all used data from major standardized testing programs, and they all used essentially the same statistics to evaluate their results, namely, the root mean square difference and root expected mean square difference (Dorans & Holland, 2000). The major premises underlying all of these articles are that population invariance is a prerequisite for equating, and lack of population invariance can be taken as evidence that a linking is not an equating.
Braun, H.I., & Holland, P.W. (1982). Observed score test equating: A mathematical analysis of some ETS equating procedures. In P. W. Holland & D. B. Rubin (Eds.), Test equating (pp. 9-49). New York: Academic Press.
2.
Cook, L.L., & Petersen, N.S. (1987). Problems related to the use of conventional and item response theory equating methods in less than optimal circumstances. Applied Psychological Measurement, 11, 225-244.
3.
Dorans, N.J., & Holland, P.W. (2000). Population invariance and equatability of tests: Basic theory and the linear case. Journal of Educational Measurement , 37, 281-306.
4.
Dorans, N.J., Liu, J., & Hammond, S. (2008). Anchor Test Type and Population Invariance: An Exploration Across Subpopulations and Test Administrations. Applied Psychological Measurement, 32, 81-97.
5.
Liu, M. & Holland, P.W. (2008). Exploring Population Sensitivity of Linking Functions Across Three Law School Admission Test Administrations. Applied Psychological Measurement, 32, 27-44.
6.
Lord, F.M. (1980). Application of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.
7.
Petersen, N.S., Kolen, M.J., & Hoover, H.D. (1989). Scaling, norming, and equating. In R. L. Linn (Ed.), Educational measurement (3rd ed., pp. 221-262). New York: Macmillan.
8.
von Davier, A.A., & Wilson, C. (2008). Investigating the Population Sensitivity Assumption of Item Response Theory True-Score Equating Across Two Subgroups of Examinees and Two Test Formats. Applied Psychological Measurement, 32, 11-26.
9.
Yang, W.-L., & Gao, R. (2008). Invariance of Score Linkings Across Gender Groups for Forms of a Testlet-Based College-Level Examination Program Examination . Applied Psychological Measurement, 32, 45-61.
10.
Yi, Q., Harris, D.J., & Gao, X. (2008). Invariance of Equating Functions Across Different Subgroups of Examinees Taking a Science Achievement Test. Applied Psychological Measurement, 32, 62-80.
