Recent approval of HPV vaccines and their widespread provision to young women provide an interesting context to gain experience with the application of statistical methods in current research. We demonstrate how we have used data extracted from a meta-analysis examining the efficacy of HPV vaccines in clinical trials with students in applied statistics courses at both introductory and intermediate university levels. The data are suitable for various techniques in categorical data analysis including comparison of proportions, analysis of contingency tables, logistic regression and log-linear models. These data are relevant to all young people and, because of their health science context, can be used in courses in biostatistics or the health sciences as they allow for further discussion of meta analyses and randomized controlled trials. We also discuss how we have used these data to promote discussion of statistical issues such as statistical versus practical significance, independence, and a common misconception involving the interpretation of p-values.