Kernel equating is a method of equating test scores devised by P. W. Holland and D. T. Thayer (1989). It takes its name from kernel smoothing, a process of smoothing a function by replacing each discrete value with a frequency distribution. It can be used when scores on two forms of a test are to be equated directly or when they are to be equated through a common anchor. The discrete score distributions are replaced with continuous distributions, and then equating is done with the continuous distributions. This "continuization" is accomplished by replacing the frequency at each discrete score value with a continuous frequency distribution centered at that value. The distribution that replaces the discrete function is called the "kernel." Data for the examination of the procedure were taken from responses of 93,283 high school students to multiple-choice questions on the United States History Advanced Placement Examination using samples of 25, 50, 100, and 200 test takers with 50 replications for each sample size. Results support the further study of this approach and the extent to which it can be generalized to other samples. An appendix provides a formula for the root-mean squared deviation. Thirteen figures illustrate the analysis. (Contains 4 references.) (SLD)