Statistical Analysis Handbook - StatsRef

1 Dr M J de SmithStatistical AnalysisHandbookA comprehensive Handbook ofstatistical concepts, techniques andsoftware toolsStatistical Analysis HandbookA comprehensive Handbook of Statistical concepts, techniques andsoftware toolsby Dr M J de SmithAll rights reserved. No parts of this work may be reproduced in any form or by any means - graphic, electronic, ormechanical, including photocopying, recording, taping, or information storage and retrieval systems - without the writtenpermission of the that are referred to in this document may be either trademarks and/or registered trademarks of the respectiveowners.

2 The publisher and the author make no claim to these every precaution has been taken in the preparation of this document, the publisher and the author assume noresponsibility for errors or omissions, or for damages resulting from the use of information contained in this document orfrom the use of programs and source code that may accompany it. In no event shall the publisher and the author be liablefor any loss of profit or any other commercial damage caused or alleged to have been caused directly or indirectly by Analysis Handbook 2014 Dr M J de Smith : cover image: Polar bubble plot (source: MatPlotLib library, Python)Rear cover image: Florence Nightingale's polar diagram of causes of mortality, by date (source: Wikipedia)Citation: de Smith M J (2015) StatsRef : Statistical Analysis Handbook - a web-based statisticsresource.

3 The Winchelsea Press, Winchelsea, UK 2014 Dr M J de Smith : of ContentsPart 1-4 How to use this 1-5 Intended audience and 1-6 Suggested 1-11 Notation and 1-14 Historical 1-20An applications-led disciplinePart IIStatistical 2-17 The Statistical 2-25 Misuse, Misinterpretation and 2-36 Sampling and sample 2-46 Data preparation and 2-48 Missing data and data 2-53 Statistical 2-54 Statistics in Medical 2-57 Causation .. 2-61 Conduct and reporting of medical research .. 2-64 Randomized controlled 2-67 Case-control 2-69 Cohort 2-71 Meta analysisPart IIIS tatistical 3-3 Probability 3-5 Odds.

4 3-6 Risks .. 3-8 Frequentist probability theory .. 3-12 Bayesian probability theory .. 3-17 Probability distributions .. 3-19 Statistical 3-22 Computational 3-28 Hypothesis 3-31 Types of 3-33 Statistical significance 2014 Dr M J de Smith : 3-36 Confidence 3-40 Power and 3-41 Degrees of 3-42 Non-parametric analysisPart IVDescriptive 4-3 Counts and specific 4-5 Measures of central 4-12 Measures of 4-22 Measures of distribution 4-26 Statistical 4-28 MomentsPart VKey functions and 5-3 Key 5-10 Measures of Complexity and Model 5-14 MatricesPart VIData transformation and 6-3 Box-Cox and Power 6-5 Freeman-Tukey (square root and arcsine) 6-8 Log and Exponential 6-11 Logit 6-13 Normal transform (z-transform)

5 Part VIIData 7-3 Graphics and 7-19 Exploratory Data AnalysisPart VIIIR andomness and 8-4 Random 8-12 Random 8-18 Runs 8-19 Random 8-28 Markov 8-34 Monte Carlo 8-35 Monte Carlo Integration .. 8-39 Monte Carlo Markov Chains (MCMC) Part IXCorrelation and autocorrelation9-2 2014 Dr M J de Smith : 9-3 Pearson (Product moment) 9-12 Rank 9-16 Canonical 9-20 Temporal autocorrelation .. 9-26 Spatial autocorrelation Part XProbability 10-6 Discrete 10-7 Binomial distribution .. 10-11 Hypergeometric distribution .. 10-14 Multinomial distribution .. 10-16 Negative Binomial or Pascal and Geometric distribution.

6 10-18 Poisson distribution .. 10-24 Skellam distribution .. 10-25 Zipf or Zeta distribution .. 10-26 Continuous univariate 10-27 Beta distribution .. 10-29 Chi-Square distribution .. 10-32 Cauchy distribution .. 10-34 Erlang distribution .. 10-36 Exponential distribution .. 10-39F distribution .. 10-41 Gamma distribution .. 10-43 Gumbel and extreme value distributions .. 10-47 Normal distribution .. 10-52 Pareto distribution .. 10-54 Student's t-distribution (Fisher's distribution) .. 10-58 Uniform distribution .. 10-60von Mises distribution .. 10-65 Weibull distribution .. 10-67 Multivariate 10-71 Kernel Density EstimationPart XIEstimation and 11-4 Maximum Likelihood Estimation (MLE).

7 11-9 Bayesian estimationPart XIIC lassical 12-3 Goodness of fit 12-5 Anderson-Darling .. 12-7 Chi-square test .. 12-10 Kolmogorov-Smirnov .. 12-13 Ryan-Joiner .. 12-14 Shapiro-Wilk .. 12-16 Jarque-Bera .. 12-17 Lilliefors .. 12-18Z-tests 2014 Dr M J de Smith : 12-19 Test of a single mean, standard deviation known .. 12-22 Test of the difference between two means, standard deviations known .. 12-23 Tests for proportions, p .. 12-26 Test of a single mean, standard deviation not known .. 12-28 Test of the difference between two means, standard deviation not known .. 12-30 Test of regression coefficients.

8 12-32 Variance 12-33 Chi-square test of a single variance .. 12-35F-tests of two variances .. 12-37 Tests of homogeneity .. 12-38 Bartlett's M 12-40 Levene-Brown-Forsythe 12-41 Fligner-Killeen 12-42 Wilcoxon rank-sum/Mann-Whitney U 12-46 Sign testPart XIIIC ontingency 13-4 Chi-square contingency table 13-6G contingency table 13-7 Fisher's exact 13-10 Measures of 13-11 McNemar's testPart XIVD esign of 14-9 Completely randomized 14-10 Randomized block 14-12 Latin squares .. 14-15 Graeco-Latin squares .. 14-16 Factorial 14-17 Full Factorial designs .. 14-19 Fractional Factorial designs.

9 14-21 Plackett-Burman designs .. 14-23 regression designs and response 14-25 Mixture designsPart XVAnalysis of variance and 15-10 Single factor or one-way ANOVA .. 15-15 Two factor or two-way and higher-way ANOVA .. 15-21 Non-Parametric 15-22 Kruskal-Wallis ANOVA .. 15-25 Friedman ANOVA test .. 15-27 Mood's Median 2014 Dr M J de Smith : XVIR egression and 16-7 Least 16-12 Ridge 16-13 Simple and multiple linear 16-27 Polynomial 16-29 Generalized Linear Models (GLIM).. 16-31 logistic regression for proportion 16-34 Poisson regression for count 16-39 Non-linear 16-43 Smoothing and Generalized Additive Models (GAM).

10 16-45 Geographically weighted regression (GWR).. 16-50 Spatial series and spatial 16-57 SAR models .. 16-64 CAR models .. 16-70 Spatial filtering models Part XVIITime series Analysis and 17-7 Moving 17-12 Trend 17-18 ARMA and ARIMA (Box-Jenkins) 17-27 Spectral analysisPart 18-3 Distribution 18-25 Statistical 18-27 Test Datasets and data 18-39 Tests 18-40 Tests and confidence intervals for mean values .. 18-41 Tests for proportions .. 18-42 Tests and confidence intervals for the spread of datasets .. 18-43 Tests of randomness .. 18-44 Tests of fit to a given distribution.