ABSTRACT
This chapter gives a condensed background to error reduction and discusses estimation and hypothesis testing. The science of statistics entails two kinds of effort: reducing the error as much as possible and ameliorating its effects, that is, managing the error. There are two firmly established paradigms in statistics, frequentist and Bayesian. Bayesian analysis with a noninformative prior often reproduces the result of the (frequentist) maximum likelihood analysis that uses the same model, so the two paradigms implement essentially different approaches that lead to similar results. The frequentist paradigm requires some improvisation, such as the appeal to extra-data observations. In both paradigms, data (or a dataset) is collected according to a specified design (protocol), the purpose of which is to ensure that the data would be suitable for estimation or a similar purpose, or be (nearly) optimal, as would be appraised by a specified criterion.
