Statistical inference

From Wikipedia, the free encyclopedia

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.

Contents 1 Definition 2 See also 3 Further reading 4 External links

[edit] 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

[edit] See also

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

[edit] 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.

[edit] External links

• MIT OpenCourseWare: Statistical Inference

v • d • e Statistics Descriptive statistics Continuous data Location Mean (Arithmetic, Geometric, Harmonic) · Median · Mode Dispersion Range · Standard deviation · Coefficient of variation · Percentile Moments Variance · Semivariance · Skewness · Kurtosis Categorical data Frequency · Contingency table Inferential statistics and hypothesis testing Inference Confidence interval (Frequentist inference) · Credible interval (Bayesian inference) · Significance · Meta-analysis Design of experiments Population · Sampling · Stratified sampling · Replication · Blocking · Sensitivity and specificity Sample size estimation Statistical power · Effect size · Standard error General estimation Bayesian estimator · Maximum likelihood · Method of moments · Minimum distance · Maximum spacing Specific tests Z-test (normal) · Student's t-test · F-test · Chi-square test · Pearson's chi-square test · Wald test · Mann–Whitney U · Wilcoxon signed-rank test Survival analysis Survival function · Kaplan-Meier · Logrank test · Failure rate · Proportional hazards models Correlation and regression Correlation Pearson product-moment correlation · Rank correlation (Spearman's rho, Kendall's tau) · Confounding variable Linear models General linear model · Generalized linear model · Analysis of variance · Analysis of covariance Regression analysis Linear · Nonlinear · Nonparametric · Semiparametric · Logistic Statistical graphics Bar chart · Biplot · Box plot · Control chart · Forest plot · Histogram · Q-Q plot · Run chart · Scatter plot · Stemplot Category · Portal · Topic outline · List of topics