At heart it is an applied subject, but it would be unsatisfactory if each application had to be tackled separately, devising fresh techniques for each new problem. For this reason, a body of common statistical theory has been developed so that most problems can be tackled within the same framework. Data summarization was historically the first major statistical activity.
Experimental design is of crucial importance before data are collected.
However, it is statistical inference which has seen most research and practical application in recent years, and it is inference which forms the direction of this course. There are three main types of inference, namely point estimation , interval estimation and hypothesis testing . In point estimation, for each unknown parameter of interest a single value is computed from the data, and used as an estimate of that parameter. Instead of producing a single estimate of a parameter, interval estimation provides a range of values which have a predetermined high probability of including the true, but unknown, value of the parameter. Hypothesis testing sets up specific hypotheses regarding the parameters of interest and assesses the plausibility of any specified hypothesis by seeing whether the observed data support or refute that hypothesis.