Teaching Bayes' rule: A data-oriented approach

There is a current emphasis on making the introductory statistics class more data-oriented. Data distributions are used to motivate probability distributions, such as the normal, and sampling distributions. However, difficulties remain in communicating the basic tenets of traditional statistical procedures such as confidence intervals and hypothesis tests. It is shown that skills in understanding relationships between two data variables can be used to motivate basic principles of Bayesian inference. Two devices, the Bayes' box and the Bayes' scatterplot, are introduced to display the relationship between models and data. The methods are illustrated for inference problems for a proportion, and are contrasted with simulation methods for introducing traditional inference in the quantitative literacy materials.