View source for Template:Statistics

{{Navbox with collapsible groups
 | name = Statistics
 | state = {{{state|uncollapsed}}}
 | bodyclass = hlist

 | title = [[Statistics]]
 | image = <!-- [[File:Planche de Galton.jpg|thumb|100x100px|alt=Illustration of the central limit theorem|Illustration of the central limit theorem]] -->
 | selected = {{{selected|{{{expanded|{{{1|}}}}}}}}}

 | above =
* [[Outline of statistics|Outline]]
* [[List of statistics articles|Index]]

<!------------------------------- Descriptive --------------------------------->

 | abbr1 = descriptive
 | section1 = [[Descriptive statistics]]
 | list1 =
   {{Navbox |child
    | groupwidth = 12.5em <!--(should match those below)-->

    | group1 = [[Continuous probability distribution|Continuous data]]
    | list1 =
      {{Navbox |child
       | groupstyle = font-weight:normal;
       | group1 = [[Central tendency|Center]]
       | list1 =
* [[Mean]]
** [[Arithmetic mean|Arithmetic]]
** [[Arithmetic–geometric mean|Arithmetic-Geometric]]
** [[Contraharmonic mean|Contraharmonic]]
** [[Cubic mean|Cubic]]
** [[generalized mean|Generalized/power]]
** [[Geometric mean|Geometric]]
** [[Harmonic mean|Harmonic]]
** [[Heronian mean|Heronian]]
** [[Heinz mean|Heinz]]
** [[Lehmer mean|Lehmer]]
* [[Median]]
* [[Mode (statistics)|Mode]]
       | group2 = [[Statistical dispersion|Dispersion]]
       | list2 =
* [[Average absolute deviation]]
* [[Coefficient of variation]]
* [[Interquartile range]]
* [[Percentile]]
* [[Range (statistics)|Range]]
* [[Standard deviation]]
* [[Variance#Sample_variance|Variance]]
       | group3 = [[Shape of the distribution|Shape]]
       | list3 =
* [[Central limit theorem]]
* [[Moment (mathematics)|Moments]]
** [[Kurtosis]]
** [[L-moment]]s
** [[Skewness]]

      }}

    | group2 = [[Count data]]
    | list2 =
* [[Index of dispersion]]

    | group3 = Summary tables
    | list3 =
* [[Contingency table]]
* [[Frequency distribution]]
* [[Grouped data]]


    | group4 = [[Correlation and dependence|Dependence]]
    | list4 =
* [[Partial correlation]]
* [[Pearson correlation coefficient|Pearson product-moment correlation]]
* [[Rank correlation]]
** [[Kendall rank correlation coefficient|Kendall's τ]]
** [[Spearman's rank correlation coefficient|Spearman's ρ]]
* [[Scatter plot]]

    | group5 = [[Statistical graphics|Graphics]]
    | list5 =
* [[Bar chart]]
* [[Biplot]]
* [[Box plot]]
* [[Control chart]]
* [[Correlogram]]
* [[Fan chart (statistics)|Fan chart]]
* [[Forest plot]]
* [[Histogram]]
* [[Pie chart]]
* [[Q–Q plot]]
* [[Radar chart]]
* [[Run chart]]
* [[Scatter plot]]
* [[Stem-and-leaf display]]
* [[Violin plot]]
   }}


<!----------------------------- Data collection ------------------------------->

 | abbr2 = collection
 | group2 = [[Data collection]]
 | list2 =
   {{Navbox |child
    | groupwidth = 12.5em <!--(should match those above/below)-->

    | group1 = [[Design of experiments|Study design]]
    | list1 =
* [[Effect size]]
* [[Missing data]]
* [[Optimal design]]
* [[Statistical population|Population]]
* [[Replication (statistics)|Replication]]
* [[Sample size determination]]
* [[Statistic]]
* [[Statistical power]]<!-- redundant with inference, but useful -->

    | group2 = [[Survey methodology]]
    | list2 =
* [[Sampling (statistics)|Sampling]]
** [[Cluster sampling|Cluster]]
** [[Stratified sampling|Stratified]]
* [[Opinion poll]]
* [[Questionnaire]]
* [[Standard error]]

    | group3 = [[Experiment|Controlled experiments]]
    | list3 =
* [[Blocking (statistics)|Blocking]]
* [[Factorial experiment]]
* [[Interaction (statistics)|Interaction]]
* [[Random assignment]]
* [[Randomized controlled trial]]
* [[Randomized experiment]]
* [[Scientific control]]
<!-- * [[Regression discontinuity design|Regression discontinuity]] -->

    | group4 = Adaptive designs
    | list4 =
* [[Adaptive clinical trial]]
* [[Stochastic approximation]]
* [[Up-and-Down Designs|Up-and-down designs]]

    | group5 = [[Observational study|Observational studies]]
    | list5 =
* [[Cohort study]]
* [[Cross-sectional study]]
* [[Natural experiment]]
* [[Quasi-experiment]]
   }}


<!-------------------------------- Inference ---------------------------------->

 | abbr3 = inference
 | section3 = [[Statistical inference]]
 | list3 =
   {{Navbox |child
    | groupwidth = 12.5em <!--(should match those above/below)-->

  | group1 = [[Statistical theory]]
    | list1 =
* [[Population (statistics)|Population]]
* [[Statistic]] 
* [[Probability distribution]]
* [[Sampling distribution]]
** [[Order statistic]]
* [[Empirical distribution function|Empirical distribution]]
**[[Density estimation]]
* [[Statistical model]]
**[[Model specification]]
**[[Lp space|L<sup>''p''</sup> space]] 
* [[Statistical parameter|Parameter]]
** [[Location parameter|location]]
**[[Scale parameter|scale]]
**[[Shape parameter|shape]]
* [[Parametric statistics|Parametric family]]
** [[Likelihood function|Likelihood]]&nbsp;[[Monotone likelihood ratio|{{small|(monotone)}}]]
**[[Location–scale family]]
** [[Exponential family]]
* [[Completeness (statistics)|Completeness]]
* [[Sufficient statistic|Sufficiency]]
* [[Plug-in principle|Statistical functional]]
** [[Bootstrapping (statistics)|Bootstrap]]
** [[U-statistic|U]]
**[[V-statistic|V]] 
* [[Optimal decision]]
**[[loss function]] 
* [[Efficiency (statistics)|Efficiency]]
* [[Statistical distance]]
** [[Divergence (statistics)|divergence]] 
* [[Asymptotic theory (statistics)|Asymptotics]]
* [[Robust statistics|Robustness]]

    | group2 = [[Frequentist inference]]
    | list2 =
      {{Navbox |child
       | groupstyle=font-weight:normal;
       | evenodd = swap       
| group2 = [[Point estimation]]         
| list2 =
* [[Estimating equations]]
** [[Maximum likelihood]]
** [[Method of moments (statistics)|Method of moments]] 
** [[M-estimator]]  
** [[Minimum distance estimation|Minimum distance]]
* [[Bias of an estimator|Unbiased estimator]]s
** [[Minimum-variance unbiased estimator|Mean-unbiased minimum-variance]]
***[[Rao–Blackwell theorem|Rao–Blackwellization]]
***[[Lehmann–Scheffé theorem]]
** [[Median-unbiased estimator|Median unbiased]]
* [[Plug-in principle|Plug-in]] 
|group3=[[Interval estimation]]
|list3=
*[[Confidence interval]]
*[[Pivotal quantity|Pivot]]
*[[Likelihood interval]]
*[[Prediction interval]]
*[[Tolerance interval]]
*[[Resampling (statistics)|Resampling]]
** [[Bootstrapping (statistics)|Bootstrap]] <!-- This could also go below in the teting methods, before [[Permutation test]] --> 
**[[Jackknife resampling|Jackknife]] 
|group4=[[Statistical hypothesis testing|Testing hypotheses]]
|list4=
* [[One- and two-tailed tests|1- & 2-tails]]
* [[Power (statistics)|Power]]
** [[Uniformly most powerful test]]
<!-- *[[Bootstrapping (statistics)|Bootstrap]] appears just above as a resampling CI method --> 
* [[Permutation test]]
**[[Randomization test]]
* [[Multiple comparisons]]

       | group5 = [[Parametric statistics|Parametric tests]]
       | list5 =
* [[Likelihood-ratio test|Likelihood-ratio]]
* [[Score test|Score/Lagrange multiplier]]
* [[Wald test|Wald]]
      }}

    | group3 = [[list of statistical tests|Specific tests]]
    | list3 =
      {{Navbox |child
       | groupstyle=font-weight:normal;
       | evenodd = swap
       | list1 =
* [[Z-test|''Z''-test {{smaller|(normal)}}]]
* [[Student's t-test|Student's ''t''-test]]
* [[F-test|''F''-test]]
       | group2 = [[Goodness of fit]]
       | list2 =
* [[Chi-squared test|Chi-squared]]
* [[G-test|''G''-test]]
* [[Kolmogorov–Smirnov test|Kolmogorov–Smirnov]]
* [[Anderson–Darling test|Anderson–Darling]]
* [[Lilliefors test|Lilliefors]]
* [[Jarque–Bera test|Jarque–Bera]]
* [[Shapiro–Wilk test|Normality {{smaller|(Shapiro–Wilk)}}]]
* [[Likelihood-ratio test]]
* [[Model selection]]
**[[Cross-validation (statistics)|Cross validation]]
** [[Akaike information criterion|AIC]]
** [[Bayesian information criterion|BIC]]
       | group3 = [[Rank statistics]]
       | list3 =
* [[Sign test|Sign]]
** [[Sample median]]
* [[Wilcoxon signed-rank test|Signed rank {{smaller|(Wilcoxon)}}]]
** [[Hodges–Lehmann estimator]]
* [[Mann–Whitney U test|Rank sum {{smaller|(Mann–Whitney)}}]]
* [[Nonparametric statistics|Nonparametric]] [[Analysis of variance|anova]]
** [[Kruskal–Wallis test|1-way {{smaller|(Kruskal–Wallis)}}]]
** [[Friedman test|2-way {{smaller|(Friedman)}}]]
** [[Jonckheere's trend test|Ordered alternative {{smaller|(Jonckheere–Terpstra)}}]]
* [[Van der Waerden test]]
      }}

    | group5 = [[Bayesian inference]]
    | list5 =
* [[Bayesian probability]]
** [[Prior probability|prior]]
** [[Posterior probability|posterior]]
* [[Credible interval]]
* [[Bayes factor]]
* [[Bayes estimator|Bayesian estimator]]
** [[Maximum a posteriori estimation|Maximum posterior estimator]]
   }}

<!-------------------- Correlation / Regression analysis ---------------------->

 | abbr4 = correlation
 | section4 = {{hlist|[[Correlation and dependence|Correlation]]|[[Regression analysis]]}}
 | list4 =
   {{Navbox |child
    | groupwidth = 12.5em <!--(should match those above/below)-->

    | group1 = [[Correlation and dependence|Correlation]]
    | list1 =
* [[Pearson product-moment correlation coefficient|Pearson product-moment]]
* [[Partial correlation]]
* [[Confounding|Confounding variable]]
* [[Coefficient of determination]]

    | group2 = [[Regression analysis]]
    | list2 =
* [[Errors and residuals]]
* [[Regression validation]]
* [[Mixed model|Mixed effects models]]
* [[Simultaneous equations model]]s
* [[Multivariate adaptive regression splines|Multivariate adaptive regression splines (MARS)]]

    | group3 = [[Linear regression]]
    | list3 =
* [[Simple linear regression]]
* [[Ordinary least squares]]
* [[General linear model]]
* [[Bayesian linear regression|Bayesian regression]]

    | group4 = Non-standard predictors
    | list4 =
* [[Nonlinear regression]]
* [[Nonparametric regression|Nonparametric]]
* [[Semiparametric regression|Semiparametric]]
* [[Isotonic regression|Isotonic]]
* [[Robust regression|Robust]]
* [[Homoscedasticity and heteroscedasticity|Homoscedasticity and Heteroscedasticity]]

    | group5 = [[Generalized linear model]]
    | list5 =
* [[Exponential family|Exponential families]]
* [[Logistic regression|Logistic {{smaller|(Bernoulli)}}]]{{\}}[[Binomial regression|Binomial]]{{\}}[[Poisson regression]]s

    | group6 = [[Partition of sums of squares|Partition of variance]]
    | list6 =
* [[Analysis of variance|Analysis of variance (ANOVA, anova)]]
* [[Analysis of covariance]]
* [[Multivariate analysis of variance|Multivariate ANOVA]]
* [[Degrees of freedom (statistics)|Degrees of freedom]]
   }}


<!----------- Categorical / Multivariate / Time-series / Survival ------------->

 | abbr5 = analysis
 | section5 = [[Categorical variable|Categorical]]{{\}}[[Multivariate statistics|Multivariate]]{{\}}[[Time series|Time-series]]{{\}}[[Survival analysis]]
 | list5 =
   {{Navbox |child
    | groupwidth = 12.5em <!--(should match those above/below)-->

    | group1 = [[Categorical variable|Categorical]]
    | list1 =
* [[Cohen's kappa]]
* [[Contingency table]]
* [[Graphical model]]
* [[Poisson regression|Log-linear model]]
* [[McNemar's test]]
* [[Cochran–Mantel–Haenszel statistics]]

    | group2 = [[Multivariate statistics|Multivariate]]
    | list2 =
* [[General linear model|Regression]]
* [[Multivariate analysis of variance|Manova]]
* [[Principal component analysis|Principal components]]
* [[Canonical correlation]]
* [[Linear discriminant analysis|Discriminant analysis]]
* [[Cluster analysis]]
* [[Statistical classification|Classification]]
* [[Structural equation modeling|Structural equation model]] 
** [[Factor analysis]]
* [[Multivariate distribution]]s 
**[[Elliptical distribution]]s
***[[Multivariate normal distribution|Normal]]

    | group3 = [[Time series|Time-series]]
    | list3 =
      {{Navbox |child
       | groupstyle = font-weight:normal;
       | group1 = General
       | list1 =
* [[Decomposition of time series|Decomposition]]
* [[Trend estimation|Trend]]
* [[Stationary process|Stationarity]]
* [[Seasonal adjustment]]
* [[Exponential smoothing]]
* [[Cointegration]]
* [[Structural break]]
* [[Granger causality]]
       | group2 = Specific tests
       | list2 =
* [[Dickey–Fuller test|Dickey–Fuller]]
* [[Johansen test|Johansen]]
* [[Ljung–Box test|Q-statistic {{smaller|(Ljung–Box)}}]]
* [[Durbin–Watson statistic|Durbin–Watson]]
* [[Breusch–Godfrey test|Breusch–Godfrey]]
       | group3 = [[Time domain]]
       | list3 =
* [[Autocorrelation|Autocorrelation (ACF)]]
** [[Partial autocorrelation function|partial (PACF)]]
* [[Cross-correlation|Cross-correlation (XCF)]]
* [[Autoregressive–moving-average model|ARMA model]]
* [[Box–Jenkins method|ARIMA model {{smaller|(Box–Jenkins)}}]]
* [[Autoregressive conditional heteroskedasticity|Autoregressive conditional heteroskedasticity (ARCH)]]
* [[Vector autoregression|Vector autoregression (VAR)]]
       | group4 = [[Frequency domain]]
       | list4 =
* [[Spectral density estimation]]
* [[Fourier analysis]]
* [[Least-squares spectral analysis]]
* [[Wavelet]]
* [[Whittle likelihood]]
      }}

    <!---group4 omitted to maintain alternating list backgrounds--->

    | group5 = [[Survival analysis|Survival]]
    | list5 ={{Navbox |child
       | groupstyle = font-weight:normal;
       | group1 = [[Survival function]]
       | list1 =
*[[Kaplan–Meier estimator|Kaplan–Meier estimator (product limit)]]
* [[Proportional hazards model]]s
* [[Accelerated failure time model|Accelerated failure time (AFT) model]]
*[[First-hitting-time model|First hitting time]]
       | group2 = [[Failure rate|Hazard function]]
       | list2 =
*[[Nelson–Aalen estimator]]
       | group3 = Test
       | list3 =
* [[Log-rank test]]
}}
   }}


<!------------------------------ Applications --------------------------------->

 | abbr6 = applications
 | section6 = [[List of fields of application of statistics|Applications]]
 | list6 =
   {{Navbox |child
    | groupwidth = 12.5em <!--(should match those above)-->

    | group1 = [[Biostatistics]]
    | list1 =
* [[Bioinformatics]]
* [[Clinical trial]]s{{\}}[[Clinical study design|studies]]
* [[Epidemiology]]
* [[Medical statistics]]

    | group2 = [[Engineering statistics]]
    | list2 =
* [[Chemometrics]]
* [[Methods engineering]]
* [[Probabilistic design]]
* [[Statistical process control|Process]]{{\}}[[quality control]]
* [[Reliability engineering|Reliability]]
* [[System identification]]

    | group3 = [[Social statistics]]
    | list3 =
* [[Actuarial science]]
* [[Census]]
* [[Crime statistics]]
* [[Demographic statistics|Demography]]
* [[Econometrics]]
* [[Jurimetrics]]
* [[National accounts]]
* [[Official statistics]]
* [[Population statistics]]
* [[Psychometrics]]

    | group4 = [[Spatial analysis|Spatial statistics]]<!--and/or in time-series/multivariate analysis-->
    | list4 =
* [[Cartography]]
* [[Environmental statistics]]
* [[Geographic information system]]
* [[Geostatistics]]
* [[Kriging]]
   }}


<!----------------------------------------------------------------------------->

 | below =
* {{icon|Category}}'''[[:Category:Statistics|Category]]'''
* '''{{Portal-inline|Mathematics}}'''
* {{Icon|commons}}'''[[commons:Category:Statistics|Commons]]'''
* {{Icon|WikiProject}} '''[[Wikipedia:WikiProject Statistics|WikiProject]]'''

}}<noinclude>{{Documentation}}</noinclude>