Teaching Statistics through Resampling KEYWORDS: Computer; Randomization test, Bootstrap ;Simulation

MANY students of statistics, especially those who are not studying mathematics, have difficulty with the mathematical formulation of statistical methods. The theory of statistics is largely based upon the theory of probability distributions and sampling distributions of parameters such as the mean or test statistics such as chi-squared. Because each approach uses a different formula, many students have difficulty in choosing the right formula to use. We have recently investigated the use of a computer-intensive approach to teaching statistics that is not formula-based. Computers have had a tremendous impact on the teaching of statistics, especially at post-16 level. Statistics packages are used to carry out the relatively tedious calculations required in many estimation and testing procedures. However, this is doing no more than using the computer package as a very fast calculator. The computer-intensive approach, in contrast, uses the computer to mimic the real-life sampling (and repetitive re-sampling) which gives rise to such things as the Central Limit Theorem, confidence limits and hypothesis testing. There are no formulae involved these are replaced by a sampling algorithm that reflects the underlying statistical and probabilistic process. The only understanding that is required is to be able to interpret a histogram and to be able to generate a sampling process. Computer-intensive methods are becoming increasingly popular as computers become faster and cheaper. The commonly used methods are randomization testing and bootstrap estimation. There are few packages available and one of the drawbacks of using these methods to teach probability and statistics is that programming is required. However, the recent development of a new package Resampling Stats in the USA and its competitive pricing policy now makes this approach feasible for most schools and colleges. This package has been developed by The Resampling Project led by Julian L. Simon, a professor of business administration at the University of Maryland. For a review of the work of the Project see Peterson (1991) and Simon and Bruce (1991). In this paper we report on the use of this approach to a mixed experience class in Higher Education, many of whom had not previously studied statistics. It is important to note, however, that the approach can be used either as a substitute for traditional theory or as an aid to understanding it, and is relevant to all levels of probability and statistics teaching, from the National Curriculum to Higher Education.