Probability and statistics are two related but separate academic disciplines. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is mostly of mathematical interest and not directly relevant to statistics. Moreover, many topics in statistics are independent of probability theory.
See also
- List of probability topics
- List of statistical topics
- Notation in probability and statistics
External links
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Descriptive statistics |
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| Continuous data |
| Location | |
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| | Dispersion | |
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| | Shape |
Variance
Skewness
Kurtosis
Moments
L-moments |
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| | Count data |
Index of dispersion |
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| | Summary tables |
Grouped data
Frequency distribution
Contingency table |
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| | Dependence | |
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| | Statistical graphics |
Bar chart
Biplot
Box plot
Control chart
Correlogram
Fan chart
Forest plot
Histogram
Pie chart
Q–Q plot
Run chart
Scatter plot
Stemplot
Radar chart |
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Data collection |
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| Designing studies |
- Effect size
- Standard error
- Statistical power
- Sample size determination
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| | Survey methodology |
Sampling
Stratified sampling
Cluster sampling
Opinion poll
Questionnaire |
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| | Controlled experiment |
Design of experiments
Randomized experiment
Random assignment
Replication
Blocking
Factorial experiment
Optimal design |
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| | Uncontrolled studies |
Natural experiment
Quasi-experiment
Observational study |
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| Statistical theory |
- Sampling distribution
- Order statistic
- Scan statistic
- Record value
- Sufficiency
- Completeness
- Exponential family
- Permutation test (Randomization test)
- Empirical distribution
- Bootstrap
- U statistic
- Efficiency
- Asymptotics
- Robustness
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| | Frequentist inference |
Unbiased estimator (Mean unbiased minimum variance, Median unbiased)
Biased estimators (Maximum likelihood, Method of moments, Minimum distance, Density estimation)
Confidence interval
Testing hypotheses
Power
Parametric tests (Likelihood-ratio, Wald, Score) |
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| | Specific tests |
Z (normal)
Student's t-test
F
Goodness of fit (Chi-squared, G, Sample source, sample normality, Skewness & kurtosis Normality, Model comparison, Model quality)
Signed-rank (1-sample, 2-sample, 1-way anova)
Shapiro–Wilk
Kolmogorov–Smirnov
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| | Bayesian inference |
Bayesian probability
Prior
Posterior
Credible interval
Bayes factor
Bayesian estimator
Maximum posterior estimator |
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Correlation and regression analysis |
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| Correlation | |
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| | Regression analysis |
Errors and residuals
Regression model validation
Mixed effects models
Simultaneous equations models
MARS |
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| | Linear regression |
Simple linear regression
Ordinary least squares
General linear model
Bayesian regression |
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| | Non-standard predictors |
Nonlinear regression
Nonparametric
Semiparametric
Isotonic
Robust
Heteroscedasticity
Homoscedasticity |
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| | Generalized linear model |
Exponential families
Logistic (Bernoulli)
Binomial
Poisson |
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| | Partition of variance |
Analysis of variance (ANOVA)
Analysis of covariance
Multivariate ANOVA
Degrees of freedom |
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Categorical, multivariate, time-series, or survival analysis |
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| Categorical data |
- Cohen's kappa
- Contingency table
- Graphical model
- Log-linear model
- McNemar's test
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| | Multivariate statistics |
Multivariate regression
Principal components
Factor analysis
Cluster analysis
Classification
Copulas |
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| | Time series analysis |
| General |
- Decomposition
- Trend
- Stationarity
- Seasonal adjustment
- Exponential smoothing
- Cointegration
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| | Specific tests |
Granger causality
Q-Statistic
Durbin–Watson |
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| | Time domain |
ACF
PACF
XCF
ARMA model
ARIMA model
ARCH
Vector autoregression |
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| | Frequency domain |
Spectral density estimation
Fourier analysis
Wavelet |
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| | Survival analysis |
Survival function
Kaplan–Meier
Logrank test
Failure rate
Proportional hazards models
Accelerated failure time model |
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Applications |
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| Biostatistics |
- Bioinformatics
- Clinical trials & studies
- Epidemiology
- Medical statistics
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| | Engineering statistics |
Chemometrics
Methods engineering
Probabilistic design
Process & Quality control
Reliability
System identification |
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| | Social statistics |
Actuarial science
Census
Crime statistics
Demography
Econometrics
National accounts
Official statistics
Population
Psychometrics |
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| | Spatial statistics |
Cartography
Environmental statistics
Geographic information system
Geostatistics
Kriging |
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