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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

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