<P> Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution . Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates . It is assumed that the observed data set is sampled from a larger population . </P> <P> Inferential statistics can be contrasted with descriptive statistics . Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population . </P> <P> Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling . Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model . </P> <P> Konishi & Kitagawa state, "The majority of the problems in statistical inference can be considered to be problems related to statistical modeling". Relatedly, Sir David Cox has said, "How (the) translation from subject - matter problem to statistical model is done is often the most critical part of an analysis". </P>

In doing statistical inference data are gathered by the process of