This study combined the kernel smoothing procedure and a nonparametric differential item functioning statistic-Cochran’s Z-to statistically test the difference between the kernel-smoothed item response functions for reference and focal groups. Simulation studies were conducted to investigate the Type I error and power of the proposed kernel-smoothed Cochran’s Z. For the purpose of comparison, the Type I error and power rates with no correction and with regression correction were also include in the simulation. The results of this study suggest the Type I error and power performance of Cochran’s Z improved when kernel smoothing was applied.
Altman, N. ( 1992). An introduction to kernel and nearest-neighbor nonparametric regression. American Statistician, 46, 175-185.
2.
Bolt, D.M., & Gierl, M.J. ( 2006). Testing features of graphical DIF: Application of a regression correction to three nonparametric statistical tests. Journal of Educational Measurement,43, 313-333.
3.
Cohen, J. ( 1992). A power primer. Psychological Bulletin ,112, 155-159.
4.
Douglas, J.A. ( 1996). Theory and applications of nonparametric regression in item response theory. Dissertation Abstracts International: Section B. Sciences and Engineering, 57(4), 2652.
5.
Douglas, J.A. ( 1997). Joint consistency of nonparametric item characteristic curve and ability estimation. Psychometrika, 62, 7-28.
6.
Douglas, J.A., & Cohen, A. ( 2001). Nonparametric item response function estimation for assessing parametric model fit. Applied Psychological Measurement, 25, 234-243.
7.
Douglas, J.A., Stout, W., & DiBello, L.V. ( 1996). A kernel smoothed version of SIBTEST with applications to local DIF inference and function estimation. Journal of Educational and Behavioral Statistics, 21, 333-363.
8.
Fidalgo, Ferreres, D., & Muþiz J. , (2004). Utility of the Mantel-Haenszel procedure for detecting differential item functioning in small samples. Educational and Psychological Measurement, 64, 925-936.
9.
Härdle, W. ( 1990). Applied nonparametric regression. Cambridge, England: Cambridge University Press.
10.
Holland, P.W., & Thayer, D.T. ( 1988). Differential item functioning and the Mantel-Haenszel procedure. In H. Wainer & H. I. Braun (Eds.), Test validity (pp. 129-145). Hillsdale, NJ: Erlbaum.
11.
Jodoin, M.G., & Gierl, M.J. ( 2001). Evaluating Type I error and power rates using an effect size measure with logistic regression procedure for DIF detection. Applied Measurement in Education, 14, 329-349.
12.
Marascuilo, L.A., & Slaughter, R.E. (1981). Statistical procedures for identifying possible sources of item bias based on χ2 statistics . Journal of Educational Measurement,18, 229-248.
13.
Narayanan, P., & Swaminathan, H. (1994). Performance of Mantel-Haenszel and simultaneous item bias procedure for detecting differential item functioning . Applied Psychological Measurement, 18, 315-328.
Roussos, L.A., & Stout, W.F. ( 1996). Simulation studies of the effects of small sample size and studied item parameters on SIBTEST and Mantel-Haenszel type I error performance . Journal of Educational Measurement, 33, 215-230.
17.
Shealy, R.T., & Stout, W.F. ( 1993a). An item response theory model for test bias and differential test functioning. In P. W. Holland & H. Wainer (Eds.), Differential item functioning (pp. 197-239). Hillsdale, NJ: Erlbaum.
18.
Shealy, R.T., & Stout, W.F. ( 1993b). A model-based standardization approach that separates true-bias/DIF from group ability differences and detects test bias/DIF as well as item bias/ DIF. Psychometrika, 54, 159-194.
19.
Thissen, D., & Wainer, H. ( 1982). Some standard errors in item response theory. Psychometrika, 47, 397-412.
