By Peter Freeman (Carnegie Mellon University)
Information
The chi-square goodness-of-fit test is ubiquitous in the field of statistics. When students encounter this test, they typically learn details such as the statistic, the statistic's assumed sampling distribution, and the test's limitations (namely that the expected number of counts in each bin must be five or larger). What students typically do not learn, however, is that in the age of computers they need not use the goodness-of-fit test at all: it is extremely simple to quickly estimate accurate and precise p-values by simulating multinomial data under an assumed null hypothesis. The approximately 160 students each year who take the mathematical statistics for majors class at our R1 research university routinely implement such simulations when completing, e.g., homework assignments, and they observe how the results can substantially differ from those that arise from goodness-of-fit tests, particularly in the low-sample-size limit.
In this presentation, our goals are (1) to demonstrate how simple it is for instructors to incorporate multinomial-based hypothesis testing into their classes, and (2) to provide pointers to materials that they can adopt/adapt when presenting it to their students.