Using Cochran's Z Statistic to Test the Kernel-Smoothed Item Response Function Differences between Focal and Reference Groups

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. (Contains 4 tables and 1 figure.)