Statistical theory

The theory of statistics includes a number of topics:

Statistical models of the sources of data and typical problem formulation:
 * 1) Sampling from a finite population
 * 2) Measuring observational error and refining procedures
 * 3) Studying statistical relations

Planning statistical research to measure and control observational error:


 * 1) Design of experiments to determine treatment effects
 * 2) Survey sampling to describe natural populations

Summarizing statistical data in conventional forms (also known as descriptive statistics)


 * 1) Choosing summary statistics to describe a sample
 * 2) Fitting probability distributions to sample data

Interpreting statistical data is the final objective of all research:


 * 1) Common assumptions that we make
 * 2) Likelihood principle
 * 3) Estimating parameters
 * 4) Testing statistical hypotheses
 * 5) Revising opinions in statistics