Literature Index

My primary aim in this paper is quite simple. I would like to encourage you to seek out or attempt to discern the main question of interest associated with any given set of data, expressing this question in the (usually non-statistical) terminology of the subject area from whence the data came, before you even think of analysing or modeling the data. Having done this, I would also like to encourage you to view analyses, models etc. simply as means towards the end of providing an answer to the question, where again the answer should be expressed in the terminology of the subject which characterises statistical answers. Finally, and regrettably this last point is by no means superfluous, I would then encourage you to ask yourself whether the answer you gave really did answer the question originally posed, and not some other question. A secondary aim, which I cannot hope to achieve in the time permitted to me, would be to show you how many common difficulties experienced in attempting to draw inferences from data can be resolved by carefully framing the question of interest and the form of answer sought.

Although project work involving analysis and interpretation of real data is important when<br>students are learning statistics, there is an important role for short exercises to help learn specific<br>statistical skills. Computer-based exercises can be much richer than exercises in paper-based<br>textbooks but existing resources do not make full use of the medium. The format can involve<br>multiple-choice, numerical answers, interaction with diagrams (such as sketching a histogram) or<br>a combination of these, possibly in sequence. The exercise can analyse the student response and<br>give helpful hints and feedback about different types of incorrect answer. Random generation of<br>similar questions in an exercise can allow repeated attempts until skills are mastered. Some<br>principles are given for the design of computer-based exercises and a set of nine exercises about<br>normal distributions is described.

This paper describes three spreadsheet exercises demonstrating the nature and frequency of type I errors using random number generation. The exercises are designed specifically to address issues related to testing multiple relations using correlation (Demonstration I), t tests varying in sample size (Demonstration II) and multiple comparisons using analysis of variance (Demonstration III). These demonstrations highlight the purpose and application of hypothesis testing and teach students the dangers of data dredging and a posteriori hypothesis generation.

In their article Ayton, Hunt and Wright address a number of issues that impinge on the concept of randomness. They appear to question not only the methodological soundness and general implications of research on "misconceptions" in statistics, but also the soundness of aspects of statistical inference. We concentrate here on a few key issues about which we are in disagreement (we think) with the authors.