Outline of statistics

Nature of statistics

Statistics can be described as all of the following:

Academic discipline: one with academic departments, curricula and degrees; national and international societies; and specialized journals.

Scientific field (a branch of science) – 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.

Formal science – branch of knowledge concerned with formal systems.

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 (ANOVA)

General linear model

Generalized linear model

Density estimation

Kernel density estimation

Multivariate kernel density estimation

Time series

Time series analysis

Box–Jenkins

Frequency domain

Time domain

Multivariate analysis

Principal component analysis (PCA)

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

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