Statistical inference

Statistical inference or statistical induction comprises the use of statistics and random sampling to make inferences concerning some unknown aspect of a population. It is distinguished from descriptive statistics.

Two schools of statistical inference are frequency probability and Bayesian inference.

Definition

Statistical inference is inference about a population from a random sample drawn from it or, more generally, about a random process from its observed behavior during a finite period of time. It includes:

1. Point estimation
2. Interval estimation
3. Hypothesis testing (or statistical significance testing)
4. Prediction – see predictive inference

There are several distinct schools of thought about the justification of statistical inference. All are based on some idea of what real world phenomena can be reasonably modeled as probability.

1. Frequency probability
2. Bayesian probability
3. Fiducial probability

The topics below are usually included in the area of statistical inference.

1. Statistical assumptions
2. Statistical decision theory
3. Estimation theory
4. Statistical hypothesis testing
5. Revising opinions in statistics
6. Design of experiments, the analysis of variance, and regression
7. Survey sampling
8. Summarizing statistical data

See also

Statistics portal

• Descriptive statistics
• Induction (philosophy)
• Philosophy of statistics

Further reading

• Casella G. Berger RL (2001). Statistical Inference. Duxbury Press. ISBN 0534243126
• Cox, D.R. (2006). Principles of Statistical Inference, CUP. ISBN 0-521-68567-2
• Lenhard, Johannes (2006). "Models and Statistical Inference: The Controversy between Fisher and Neyman—Pearson," British Journal for the Philosophy of Science, Vol. 57 Issue 1, pp. 69-91.
• Sudderth, William D. (1994). "Coherent Inference and Prediction in Statistics," in Prawitz, Skyrms, and Westerstahl (eds.), Logic, Methodology and Philosophy of Science IX: Proceedings of the Ninth International Congress of Logic, Methodology and Philosophy of Science, Uppsala, Sweden, August 7-14, 1991, Amsterdam: Elsevier.
• Trusted, Jennifer (1979). The Logic of Scientific Inference: An Introduction, London: The Macmillan Press, Ltd.

External links

• MIT OpenCourseWare: Statistical Inference