The purpose of this appendix is to show readers how the analysis of test data can help to evaluate and improve tests. Note the word ‘help’. Statistical analysis will provide the tester with useful information that may then be used in making decisions about tests and test results. But it does not take those decisions. This remains the tester's responsibility and depends not only on the information that statistical analysis provides but also on judgement and experience. The emphasis throughout will be on interpretation of statistics, not on calculation. In fact it will be assumed that readers who want to analyse their own tests statistically will have access to computer software that will do all the necessary calculation. There is no reason these days to do this calculation by hand or to write one's own programs to do it. For that reason, I have not thought it necessary to show any calculations except the most simple, and these only as part of the explanation of concepts. Where the concepts and calculation are more complex, for all but a small minority of readers the inclusion of calculations would only confuse matters. There is no pretence of full coverage of the statistical methods and issues related to testing in this chapter; that would take a book in itself. Rather, the basic notions are presented in a form which it is hoped will be recognised as both accessible and useful.