or statistical induction
comprises the use of statistics
to make inferences
concerning some unknown aspect of a population
. It is distinguished from descriptive statistics
Two schools of inferential statistics are frequency probability and Bayesian inference.
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:
- point estimation
- interval estimation
- hypothesis testing (or statistical significance testing)
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.
- frequency probability
- Bayesian probability
- fiducial probability
The topics below are usually included in the area of statistical inference.
- Statistical assumptions
- Likelihood principle
- Estimating parameters
- Statistical hypothesis testing
- Revising opinions in statistics
- planning statistical research
- summarizing statistical data
- 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.