# Statistical theory

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**Statistics:**
Scientific method ·
Research methods ·
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Undergraduate statistics courses ·
Statistical tests ·
Game theory ·
Decision theory

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

Planning statistical research to measure and control observational error:

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

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

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

Interpreting statistical data is the final objective of all research:

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