Outline of statistics

The following outline is provided as an overview and guide to the variety of topics included within the subject of statistics:

Statistics pertains to the collection, analysis, interpretation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities; it is also used and misused for making informed decisions in all areas of business and government.

Contents 1 Nature of statistics 2 History of statistics 3 Describing data 4 Experiments and surveys 4.1 Sampling 5 Analysing data 6 Filtering data 7 Statistical inference 8 Probability distributions 9 Random variables 10 Probability theory 11 Computational statistics 12 Statistics software 13 Statistics organizations 14 Statistics publications 15 Persons influential in the field of statistics 16 See also 17 External links

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 distribution
• sampling
  • Stratified sampling
  • Quota 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
• Conditional probability distribution
• Probability density function
• Cumulative distribution function
• Characteristic function

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

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

See also

• Index of statistics articles
• Glossary of probability and statistics
• Notation in probability and statistics
• Outline of probability
• Combinatorics
• Monte Carlo method
• Simulation
• List of fields of application of statistics
• List of graphical methods
• Lists of statistics topics

External links

Statistics   Descriptive statistics Continuous data Location Mean (Arithmetic, Geometric, Harmonic) Median Mode Dispersion Range Standard deviation Coefficient of variation Percentile Interquartile range Shape Variance Skewness Kurtosis Moments L-moments Count data Index of dispersion Summary tables Grouped data Frequency distribution Contingency table Dependence Pearson product-moment correlation Rank correlation (Spearman's rho, Kendall's tau) Partial correlation Scatter plot Statistical graphics Bar chart Biplot Box plot Control chart Correlogram Forest plot Histogram Q-Q plot Run chart Scatter plot Stemplot Radar chart   Data collection Designing studies Effect size Standard error Statistical power Sample size determination Survey methodology Sampling Stratified sampling Opinion poll Questionnaire Controlled experiment Design of experiments Randomized experiment Random assignment Replication Blocking Factorial experiment Optimal design Uncontrolled studies Natural experiment Quasi-experiment Observational study   Statistical inference Statistical theory Sampling distribution Sufficient statistic Meta-analysis Bayesian inference Bayesian probability Prior Posterior Credible interval Bayes factor Bayesian estimator Maximum posterior estimator Frequentist inference Confidence interval Hypothesis testing Likelihood-ratio Specific tests Z-test (normal) Student's t-test F-test Pearson's chi-squared test Wald test Mann–Whitney U Shapiro–Wilk Signed-rank Kolmogorov–Smirnov test General estimation Bias Robustness Efficiency Maximum likelihood Method of moments Minimum distance Density estimation   Correlation and regression analysis Correlation Pearson product-moment correlation Partial correlation Confounding variable Coefficient of determination Regression analysis Errors and residuals Regression model validation Mixed effects models Simultaneous equations models Linear regression Simple linear regression Ordinary least squares General linear model Bayesian regression Non-standard predictors Nonlinear regression Nonparametric Semiparametric Isotonic Robust Generalized linear model Exponential families Logistic (Bernoulli) Binomial Poisson Partition of variance Analysis of variance (ANOVA) Analysis of covariance Multivariate ANOVA Degrees of freedom   Categorical, multivariate, time-series, or survival analysis Categorical data Cohen's kappa Contingency table Graphical model Log-linear model McNemar's test Multivariate statistics Multivariate regression Principal components Factor analysis Cluster analysis Copulas Time series analysis Decomposition (Trend, Stationary process) ARMA model ARIMA model Vector autoregression Spectral density estimation Survival analysis Survival function Kaplan–Meier Logrank test Failure rate Proportional hazards models Accelerated failure time model   Applications Biostatistics Bioinformatics Biometrics Clinical trials & studies Epidemiology Medical statistics Engineering statistics Chemometrics Methods engineering Probabilistic design Process & Quality control Reliability System identification Social statistics Actuarial science Census Crime statistics Demography Econometrics National accounts Official statistics Population Psychometrics Spatial statistics Cartography Environmental statistics Geographic information system Geostatistics Kriging Category Portal Outline Index

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