• Introduction
    • How to use this Handbook
    • Intended audience and scope
    • Suggested reading
    • Notation and symbology
    • Historical context
    • An applications-led discipline
  • Statistical data
    • The Statistical Method
    • Misuse, Misinterpretation and Bias
    • Sampling and sample size
    • Data preparation and cleaning
    • Missing data and data errors
    • Statistical error
    • Statistics in Medical Research
      • Causation
      • Conduct and reporting of medical research
        • Randomized controlled trials
        • Case-control studies
        • Cohort studies
        • Meta analysis
  • Statistical concepts
    • Probability theory
      • Odds
      • Risks
      • Frequentist probability theory
      • Bayesian probability theory
      • Probability distributions
    • Statistical modeling
    • Computational statistics
    • Inference
    • Bias
    • Confounding
    • Hypothesis testing
    • Types of error
    • Statistical significance
    • Confidence intervals
    • Power and robustness
    • Degrees of freedom
    • Non-parametric analysis
  • Descriptive statistics
    • Counts and specific values
    • Measures of central tendency
    • Measures of spread
    • Measures of distribution shape
    • Statistical indices
    • Moments
  • Key functions and expressions
    • Key functions
    • Measures of Complexity and Model selection
    • Matrices
  • Data transformation and standardization
    • Box-Cox and Power transforms
    • Freeman-Tukey (square root and arcsine) transforms
    • Log and Exponential transforms
    • Logit transform
    • Normal transform (z-transform)
  • Data exploration
    • Graphics and vizualisation
    • Exploratory Data Analysis
  • Randomness and Randomization
    • Random numbers
    • Random permutations
    • Resampling
    • Runs test
    • Random walks
    • Markov processes
    • Monte Carlo methods
      • Monte Carlo Integration
      • Monte Carlo Markov Chains (MCMC)
  • Correlation and autocorrelation
    • Pearson (Product moment) correlation
    • Rank correlation
    • Canonical correlation
    • Autocorrelation
      • Temporal autocorrelation
      • Spatial autocorrelation
  • Probability distributions
    • Discrete Distributions
      • Binomial distribution
      • Hypergeometric distribution
      • Multinomial distribution
      • Negative Binomial or Pascal and Geometric distribution
      • Poisson distribution
      • Skellam distribution
      • Zipf or Zeta distribution
    • Continuous univariate distributions
      • Beta distribution
      • Chi-Square distribution
      • Cauchy distribution
      • Erlang distribution
      • Exponential distribution
      • F distribution
      • Gamma distribution
      • Gumbel and extreme value distributions
      • Normal distribution
      • Pareto distribution
      • Student's t-distribution (Fisher's distribution)
      • Uniform distribution
      • von Mises distribution
      • Weibull distribution
    • Multivariate distributions
    • Kernel Density Estimation
  • Estimation and estimators
    • Maximum Likelihood Estimation (MLE)
    • Bayesian estimation
  • Classical tests
    • Goodness of fit tests
      • Anderson-Darling
      • Chi-square test
      • Kolmogorov-Smirnov
      • Ryan-Joiner
      • Shapiro-Wilk
      • Jarque-Bera
      • Lilliefors
    • Z-tests
      • Test of a single mean, standard deviation known
      • Test of the difference between two means, standard deviations known
      • Tests for proportions, p
    • T-tests
      • Test of a single mean, standard deviation not known
      • Test of the difference between two means, standard deviation not known
      • Test of regression coefficients
    • Variance tests
      • Chi-square test of a single variance
      • F-tests of two variances
      • Tests of homogeneity
        • Bartlett's M test
        • Levene-Brown-Forsythe test
        • Fligner-Killeen test
    • Wilcoxon rank-sum/Mann-Whitney U test
    • Sign test
  • Contingency tables
    • Chi-square contingency table test
    • G contingency table test
    • Fisher's exact test
    • Measures of association
    • McNemar's test
  • Design of experiments
    • Completely randomized designs
    • Randomized block designs
      • Latin squares
      • Graeco-Latin squares
    • Factorial designs
      • Full Factorial designs
      • Fractional Factorial designs
      • Plackett-Burman designs
    • Regression designs and response surfaces
    • Mixture designs
  • Analysis of variance and covariance
    • ANOVA
      • Single factor or one-way ANOVA
      • Two factor or two-way and higher-way ANOVA
    • MANOVA
    • ANCOVA
    • Non-Parametric ANOVA
      • Kruskal-Wallis ANOVA
      • Friedman ANOVA test
      • Mood's Median
  • Regression and smoothing
    • Least squares
    • Ridge regression
    • Simple and multiple linear regression
    • Polynomial regression
    • Generalized Linear Models (GLIM)
    • Logistic regression for proportion data
    • Poisson regression for count data
    • Non-linear regression
    • Smoothing and Generalized Additive Models (GAM)
    • Geographically weighted regression (GWR)
    • Spatial series and spatial autoregression
      • SAR models
      • CAR models
      • Spatial filtering models
  • Time series analysis and temporal autoregression
    • Moving averages
    • Trend Analysis
    • ARMA and ARIMA (Box-Jenkins) models
    • Spectral analysis
  • Resources
    • Distribution tables
    • Bibliography
    • Statistical Software
    • Test Datasets and data archives
    • Websites
    • Tests Index
      • Tests and confidence intervals for mean values
      • Tests for proportions
      • Tests and confidence intervals for the spread of datasets
      • Tests of randomness
      • Tests of fit to a given distribution
      • Tests for cross-tabulated count data
    • R Code samples
      • Scatter Plot: Inequality
      • Latin Square ANOVA
      • Log Odds Ratio Plot
      • Normal distribution plot
      • Bootstrapping