Editing Statistical theory (section)

===Interpreting data===
Besides the philosophy underlying [[statistical inference]], statistical theory has the task of considering the types of questions that [[data analyst]]s might want to ask about the problems they are studying and of providing data analytic techniques for answering them. Some of these tasks are:
*Summarising populations in the form of a fitted distribution or [[probability density function]]
*Summarising the relationship between variables using some type of [[regression analysis]]
*Providing ways of predicting the outcome of a random quantity given other related variables
*Examining the possibility of reducing the number of variables being considered within a problem (the task of [[Dimension reduction]])
When a statistical procedure has been specified in the study protocol, then statistical theory provides well-defined probability statements for the method when applied to all populations that could have arisen from the randomization used to generate the data. This provides an objective way of estimating parameters, estimating confidence intervals, testing hypotheses, and selecting the best. Even for observational data, statistical theory provides a way of calculating a value that can be used to interpret a sample of data from a population, it can provide a means of indicating how well that value is determined by the sample, and thus a means of saying corresponding values derived for different populations are as different as they might seem; however, the reliability of inferences from post-hoc observational data is often worse than for planned randomized generation of data.