Outline of statistics

Nature of statistics

• An academic discipline: one with academic departments, curricula and degrees; national and international societies; and specialized journals.
• A scientific field - widely recognized category of specialized expertise within science, and typically embodies its own terminology and nomenclature. Such a field will usually be represented by one or more scientific journals, where peer reviewed research is published.
• A formal science - branch of knowledge concerned with formal systems.
• A mathematical science - field of science that is primarily mathematical in nature but may not be universally considered subfields of mathematics proper. Statistics, for example, is mathematical in its methods but grew out of political arithmetic which merged with inverse probability and grew through applications in the social sciences and some areas of physics and biometrics to become its own separate, though closely allied, field.

  History of statistics

• History of statistics
• Founders of statistics
• History of probability
• Timeline of probability and statistics

  Describing data

• Descriptive statistics
• Average
• *Mean
• *Median
• *Mode
• Measures of scale
• *Variance
• *Standard deviation
• *Median absolute deviation
• Correlation
• Outlier
• Statistical graphics
• *Histogram
• *Frequency distribution
• *Quantile
• *Survival function
• *Failure rate

  Experiments and surveys

• Design of experiments
• *Optimal design
• *Factorial experiment
• *Restricted randomization
• *Repeated measures design
• *Randomized block design
• Statistical survey
• Opinion poll

  Sampling

• Sampling theory
• *Sampling distribution
• *Stratified sampling
• *Quota sampling
• *Cluster sampling
• Biased sample
• *Spectrum bias
• *Survivorship bias

  Analysing data

• Regression analysis
• *Outline of regression analysis
• *Analysis of variance
• *General linear model
• *Generalized linear model
• Density estimation
• *Kernel density estimation
• *Multivariate kernel density estimation
• Time series
• *Time series analysis
• *Box–Jenkins method
• *Frequency domain
• *Time domain
• Multivariate analysis
• *Principal component analysis
• *Factor analysis
• *Cluster analysis
• Robust statistics

  Filtering data

• Recursive Bayesian estimation
• *Kalman filter
• *Particle filter
• Moving average

  Statistical inference

• Statistical inference
• Mathematical statistics
• *Likelihood function
• *Exponential family
• Bayesian inference
• *Bayes' theorem
• *Bayes estimator
• *Prior distribution
• *Posterior distribution
• *Conjugate prior
• Frequentist inference
• *Statistical hypothesis testing
• **Null hypothesis
• **Alternative hypothesis
• **P-value
• **Significance level
• **Statistical power
• *Likelihood-ratio test
• *Confidence interval
• Decision theory
• *Optimal decision
• *Type I and type II errors
• Estimation theory
• *Estimator
• *Bayes estimator
• *Maximum likelihood
• *Trimmed estimator
• *M-estimator
• Non-parametric statistics
• *Nonparametric regression
• *Kernels

  Probability distributions

• Probability distribution
• *Symmetric probability distribution
• *Unimodal probability distribution
• Conditional probability distribution
• Probability density function
• Cumulative distribution function
• Characteristic function
• List of probability distributions

  Random variables

• Random variable
• Central moment
• L-moment
• Algebra of random variables

  Probability theory

• Probability
• Conditional probability
• Law of large numbers
• Central limit theorem

  Computational statistics

• Markov chain Monte Carlo

  Statistics software

• Free statistical software
• List of statistical packages

  Statistics organizations

• List of academic statistical associations
• List of national and international statistical services

  Statistics publications

• List of statistics journals
• List of important publications in statistics
• List of scientific journals in statistics

  Persons influential in the field of statistics

• List of statisticians