This is an advanced class for those students who are already familiar with some of the methods of data analysis. The focus of the class is not how, rather why. That is, we will review some of the fundamental assumptions and optimality properties of the main statistical methods. Such knowledge is necessary for the correct selection of the statistical methods to be applied and for the precise interpretation of their results. The main topics will include structure and stochastics in statistics, the link between reality and data, exploratory and confirmatory analyses, the use and interpretation of tests of hypotheses, the linear model, additive and multiplicative interaction, distance measures, least squares and maximum likelihood, asymptotic and finite sample considerations, Bayesian statistics.