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