This article explores the uses of a simulation model (the two bucket story)?implemented by a stand-alone computer program, or an Excel workbook (both on the web)?that can be used for deriving bootstrap confidence intervals, and simulating various probability distributions. The strengths of the model are its generality, the fact that it provides a powerful approach that can be fully understood with very little technical background, and the fact that it encourages an active approach to statistics?the user can see the method being acted out either physically, or in imagination, or by a computer. The article argues that this model and other similar models provide an alternative to conventional approaches to deriving probabilities and making statistical inferences. These simulation approaches have a number of advantages compared with conventional approaches: their generality and robustness; the amount of technical background knowledge is much reduced; and, because the methods are essentially sequences of physical actions, it is likely to be easier to understand their interpretation and limitations.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education