Nature of the chi-square distribution

In this activity, students learn the true nature of the chi-square and F distributions in lecture notes (PowerPoint file) and an Excel simulation. This leads to a discussion of the properties of the two distributions. Once the sum of squares aspect is understood, it is only a short logical step to explain why a sample variance has a chi-square distribution and a ratio of two variances has an F-distribution. In a subsequent activity, instances of when the chi-square and F-distributions are related to the normal or t-distributions (e.g. Chi-square = z2, F = t2) will be illustrated. Finally, the activity will conclude with a brief overview of important applications of chi-square and F distributions, such as goodness-of-fit tests and analysis of variance.