The

**theory of statistics**includes a number of topics:

Statistical models of the sources of data and typical problem formulation:

- Sampling from a finite population
- Measuring observational error and refining procedures
- Studying statistical relations

- Design of experiments to determine treatment effects
- Survey sampling to describe natural populations

- Choosing summary statistics to describe a sample
- Fitting probability distributions to sample data

- Common assumptions that we make
- Likelihood principle
- Estimating parameters
- Testing statistical hypotheses
- Revising opinions in statistics