In statistics, a population is a set of things from which samples may be drawn. This allows statistical inferences to be drawn, or estimates made of the total population. For example, if we were interested in crows, then we would sample the set of crows which is of interest. The population of crows is limited to crows that exist now or in the future. Probably, geography will be a limitation in practice. To fairly represent the whole population a sample needs to be random.
Population is also used to refer to a set of measurements or values, not only cases actually observed. Suppose, for example, we are interested in the set of all adult crows now alive in the county of Cambridgeshire, and we want to know the mean weight of these birds. For each bird in the population of crows there is a weight, and the set of these weights is called the population of weights.
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| Continuous data | |
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| Count data | |
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| Summary tables | |
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| Dependence | |
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| Graphics |
- Bar chart
- Biplot
- Box plot
- Control chart
- Correlogram
- Fan chart
- Forest plot
- Histogram
- Pie chart
- Q–Q plot
- Run chart
- Scatter plot
- Stem-and-leaf display
- Radar chart
- Violin plot
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| Study design |
- Population
- Statistic
- Effect size
- Statistical power
- Optimal design
- Sample size determination
- Replication
- Missing data
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| Survey methodology | |
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| Controlled experiments | |
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| Adaptive Designs |
- Adaptive clinical trial
- Up-and-Down Designs
- Stochastic approximation
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| Observational Studies |
- Cross-sectional study
- Cohort study
- Natural experiment
- Quasi-experiment
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| Statistical theory | |
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| Frequentist inference | | Point estimation |
- Estimating equations
- Unbiased estimators
- Mean-unbiased minimum-variance
- Rao–Blackwellization
- Lehmann–Scheffé theorem
- Median unbiased
- Plug-in
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| Interval estimation | |
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| Testing hypotheses |
- 1- & 2-tails
- Power
- Uniformly most powerful test
- Permutation test
- Multiple comparisons
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| Parametric tests |
- Likelihood-ratio
- Score/Lagrange multiplier
- Wald
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| Specific tests | | | Goodness of fit | |
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| Rank statistics |
- Sign
- Signed rank (Wilcoxon)
- Rank sum (Mann–Whitney)
- Nonparametric anova
- 1-way (Kruskal–Wallis)
- 2-way (Friedman)
- Ordered alternative (Jonckheere–Terpstra)
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| Bayesian inference | |
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| Correlation | |
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| Regression analysis |
- Errors and residuals
- Regression validation
- Mixed effects models
- Simultaneous equations models
- Multivariate adaptive regression splines (MARS)
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| Linear regression | |
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| Non-standard predictors |
- Nonlinear regression
- Nonparametric
- Semiparametric
- Isotonic
- Robust
- Heteroscedasticity
- Homoscedasticity
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| Generalized linear model | |
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| Partition of variance |
- Analysis of variance (ANOVA, anova)
- Analysis of covariance
- Multivariate ANOVA
- Degrees of freedom
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Categorical / Multivariate / Time-series / Survival analysis |
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| Categorical |
- Cohen's kappa
- Contingency table
- Graphical model
- Log-linear model
- McNemar's test
- Cochran-Mantel-Haenszel statistics
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| Multivariate |
- Regression
- Manova
- Principal components
- Canonical correlation
- Discriminant analysis
- Cluster analysis
- Classification
- Structural equation model
- Multivariate distributions
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| Time-series | | General |
- Decomposition
- Trend
- Stationarity
- Seasonal adjustment
- Exponential smoothing
- Cointegration
- Structural break
- Granger causality
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| Specific tests |
- Dickey–Fuller
- Johansen
- Q-statistic (Ljung–Box)
- Durbin–Watson
- Breusch–Godfrey
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| Time domain |
- Autocorrelation (ACF)
- Cross-correlation (XCF)
- ARMA model
- ARIMA model (Box–Jenkins)
- Autoregressive conditional heteroskedasticity (ARCH)
- Vector autoregression (VAR)
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| Frequency domain | |
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| Survival | | Survival function |
- Kaplan–Meier estimator (product limit)
- Proportional hazards models
- Accelerated failure time (AFT) model
- First hitting time
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| Hazard function | |
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| Test | |
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Applications |
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| Biostatistics | |
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| Engineering statistics |
- Chemometrics
- Methods engineering
- Probabilistic design
- Process / quality control
- Reliability
- System identification
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| Social statistics | |
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| Spatial statistics |
- Cartography
- Environmental statistics
- Geographic information system
- Geostatistics
- Kriging
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