Statistics for N = 1:A Non-Parametric Bayesian Approach

Research in education is often associated with comparing group averages and linear relations in sufficiently large samples and evidence-based practice is about using the outcomes of that research in the practice of education. However, there are questions that are important for the practice of education that cannot really be addressed by comparisons of group averages and linear relations, no matter how large the samples. Besides, different types of constraints including logistic, financial, and ethical ones may make larger-sample research unfeasible or at least questionable. What has remained less known in many fields is that there are study designs and statistical methods for research involving small samples or even individuals that allow us to address questions of importance for the practice of education. This article discusses one type of such situations and provides a simple coherent statistical approach that provides point and interval estimates of differences of interest regardless of the type of the outcome variable and that is of use in other types of studies involving large samples, small samples, and single individuals.