Asymptotic sampling distributions (means and vari ances) of estimated signed and unsigned areas between two item response functions (IRFS) are presented for the Rasch model, the two-parameter model, and the three-parameter model with fixed lower asymptotes. In item bias or differential item functioning research, it may be of interest to determine whether the estimated signed and unsigned areas between IRFS calibrated with two different groups are significantly different from 0. The usefulness of these sampling distributions in this context is discussed and illustrated. More em pirical research with the proposed significance tests is necessary.
Cook, L.L., & Eignor, D.R. (1983). Practical considerations regarding the use of item response theory to equate tests. In R. K. Hambleton (Ed.), Applications of item response theory . Vancouver: Educational Research Institute of British Columbia.
2.
Hambleton, R.K., & Swaminathan, H. (1985). Item response theory: Principles and applications. Boston: Kluwer-Nijhoff .
3.
Holland, P.W., & Thayer, D.T. (1988). Differential item performance and Mantel-Haenszel procedure. In H. Wainer & H. I. Braun (Eds.), Test validity. Hillsdale NJ: Erlbaum.
Johnson, N.L., & Kotz, S. (1970). Continuous uni-variate distributions—2. New York: Wiley.
6.
Kendall, M., & Stuart, A. (1977). The advanced theory of statistics (Vol. 1, 4th ed.). New York: Macmillan.
7.
Lord, F.M. (1980). Applications of item response theory to practical testing problems. Hillsdale NJ: Erlbaum.
8.
Raju, N.S. (1988). The area between two item characteristic curves . Psychometrika, 53, 495-502.
9.
Raju, N.S., Bode, R.K., & Larsen, V.S. (1989). An empirical assessment of the Mantel-Haenszel statistic for studying differential item performance. Applied Measurement in Education, 2(1), 1-13.
10.
Science Research Associates, Inc. (1985). Survey of basic skills: Technical information. Chicago : Author.
11.
Thissen, D., Steinberg, L., & Wainer, H. ( 1988). Use of item response theory in the study of group differences in trace lines. In H. Wainer & H. I. Braun (Eds.), Test validity . Hillsdale NJ: Erlbaum.
12.
Wingersky, M.S., Barton, M.A., & Lord, F.M. (1983). LOGIST: A computer program for estimating examinee ability and item characteristic curve parameters. LOGIST 5, version 1. Princeton NJ: Educational Testing Service.
13.
Wright, B.D., & Stone, M.H. (1979). Best test design. Chicago: MESA Press.
