The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The modules also introduce students to real world math concepts and problems that property and casualty actuaries come across in their work. They are designed to be used by teachers and…

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…

The extent to which log-linear smoothing could improve the accuracy of common-item equating by the chained equipercentile method in small samples of examinees was investigated with responses from a 100-item test and 93,283 examinees. Smoothing reduced the sample size required for a given degree of accuracy. (SLD)