Applied Statistics: Methods Using R

Table of Contents List of Overviews List of Figures List of Tables Fundamentals of Planning Scientific Work Definition and Tasks of Statistics Scientific Working Technique Data and Models Circular Processes Models in Statistics Statistics and Scientific Method Repeatable Experiences Inference: Deduction and Induction Observational Studies Hints for a Questionnaire Notes on a Survey Systematic Errors (Bias) Missing Information Descriptive Approach Characteristics and Dimensionality Data Editing Exploratory Approach Confirmatory Approach Population and Sample Open and Closed Populations Samples Random Samples Data Analysis Types of Characteristics From Observations to Data - Scaling Permissible Scale Transformations Data Structure, Data Collection and Data Recording Fundamentals of Mathematics Logical and Relational Operators Sets Concept formation Set Operations (Basic) Arithmetic Operations Sums and Products The Sum Symbol Special Sums Multiplication and Division; Factorial Powers and Roots Logarithms Rounding Calculating with Error-Prone Numbers Introduction to Matrix Algebra Definition and Notation Matrix Operations Matrix Addition and Subtraction Matrix Multiplication Determinants The Inverse Matrix Linear Dependence, Rank of a Matrix Linear Equation Systems Eigenvalues and Eigenvectors Functions Linear Functions Nonlinear Functions Polynomial Functions Periodic Functions Exponential Function and Logarithmic Function Growth Functions Area under a Function: Integral Combinatorics Permutations Binomial Coefficient Calculating with the Binomial Coefficient - Further Formulas Combinations Decomposition of a Set Bootstrap Samples The Pascal's Triangle The Multinomial Coefficient Descriptive Statistics Frequencies Absolute and Relative Frequencies Meaningful Quotients: Ratio Numbers Percentage Values Bar Plots and Pie Charts Tables Rectangle Diagram and Mosaic Plot Conditional Relative Frequencies Simpson's Paradox (Comparison of Proportional Values) Association Measures for Contingency Tables Description of Ordinal Data Median and Other Quantiles Classified Data: Calculation of Quantiles Dispersion of Ordinal Scaled Data Dot Plot and Box Plot Kendall's Correlation Coefficient Partial Rank Correlation Description of Metric Data Arithmetic Mean Standard Deviation, Variance Supplement and Combination of Means and Variances Coefficient of Variation The Dispersion Range Around the Mean Mean and Standard Deviation from Classified Measurements The Weighted Arithmetic Mean and the Weighted Variance Geometric Mean Harmonic Mean Error Calculation Errors in Measurements; Precision and Accuracy Standard Error of Multiple Determinations Error Propagation Precision of Measurements Frequency Distribution Histogram Pareto Diagram Measures of Concentration: Herfindahl Index and Gini Coefficient Measures for Correlation in Metric Data Typification of Correlative Relationships Scatter Plots Empirical Covariance Empirical Correlation Coefficient Autocorrelation Reliability Analysis Spearman Rank Correlation Coefficient Partial Correlation Coefficient Linear Regression Special Estimates of the Regression Line The Bartlett Method The Kerrich Method Orthogonal Least Squares Robust Linear Regression Nonlinear Regression Some Linearizing Transformations Nonparametric Regression Regressogram, Moving Averages and Kernel Estimators Cubic Spline Interpolation Probabilities Random Experiment - Event Concept of Probability Definition According to Laplace Relative Frequency and Probability Odds Axioms according to Kolmogorov Addition Theorem Inclusion-Exclusion Principle (Sieve Formula) Paradox of the First Digit (Benford's Law) Conditional Probabilities, Stochastic Independence Conditional Probability Multiplication Rule Risk Measures [supplemented by Section 7.7.3] Probabilities from a Mortality Table Tree Diagram and Path Rules Stochastic Independence Stochastic Independence for Three or More Events Incompatibility and Stochastic Independence Bonferroni Inequalities Conditional Probabilities and Correlation Thirteen Examples of Stochastic Independence Bayesian Theorem Bayesian Theorem and Path Rule Eight Examples of Bayes' Theorem The Diagnostic Test ROC - Analysis The Likelihood Quotient Decision Analysis according to A.J. Vickers Measured Values in Epidemiology Prevalence and Incidence The Vaccination Effect Standardized Rates Using the Example of Mortality Random Variables, Distributions The Random Variable Probability Function, Probability Density and Distribution Function Computational Rules for the Distribution Function Empirical Distribution Function Measures for Characterizing a Distribution Expected Value Variance Inequalities with Probabilities Moments: Skewness and Excess Calculation of Empirical Moments Power Moments Quantile Measures for Skewness and Kurtosis Discrete Distributions The Urn Model Uniform Distribution Binomial Distribution Bernoulli Trial Binomial Distribution Functions Approximation of the Binomial Distribution by the Standard Normal Distribution Approximation of the Binomial Distribution by the Poisson Distribution Multinomial Distribution (Polynomial Distribution) Poisson Distribution The Dispersion Index Approximation of the Poisson Distribution by the Standard Normal Distribution Negative Binomial Distribution Geometric Distribution Hypergeometric Distribution Approximations of the Hypergeometric Distribution Negative Hypergeometric Distribution Continuous Distributions Uniform Distribution Standard Beta Distribution Normal Distribution Central Fluctuation Intervals of the Standard Normal Distribution Hints and Examples for Normal Distribution Central Limit Theorem Half-Normal Distribution Truncated Normal Distribution Lognormal Distribution Estimation of Measures of a Lognormal Distribution Empirical Measures of a Lognormal Distribution Exponential distribution Weibull Distribution Extreme Value Distribution Type I (Gumbel Distribution) Gamma Distribution Test Distributions Student Distribution (t-distribution) Noncentral t-Distribution Chi-Squared Distribution Non-central Chi-square Distribution Fisher Distribution (F-Distribution) Interpolation of Table Values and P-values Interpolating Intermediate Values of the F-Distribution Distribution of Two-dimensional Random Variables Model Building Introductory example Distribution Function Marginal Distributions and Independence Conditional Distribution and Independence Bayes' theorem for random variables Correlation Coefficient Two-dimensional Normal Distribution Estimation Sample Survey Random Samples and Random Numbers Special Sampling Methods Estimating Parameters Preliminary Remarks The Conclusion from the Sample to the Total Population Point Estimation and Interval Estimation Estimate and Estimating Function Desirable Properties of Estimating Functions Unbiased Estimating Function for the Variance Law of Large Numbers The Mean Squared Error Estimation Methods for Parameters of a Distribution Method of Moments Maximum Likelihood Estimation (MLE) ML-Estimator for the Binomial Distribution ML-Estimator for the Negative Binomial Distribution ML Estimator for the Poisson Distribution ML estimator for the Normal Distribution ML Estimator for the Truncated Normal distribution Estimation According to Least Squared Errors (OLS) Interval Estimation - Confidence Intervals Confidence Interval for Proportions Approximation by the Normal Distribution Zero Results or Full Results Quick Estimation of Confidence Limits Based on an Observed Relative Frequency According to Clopper and Pearson Confidence Interval for the Difference of Two Proportions Confidence Interval for the Ratio of Two Proportions Minimum Sample Size for Estimating a Proportion Simultaneous Confidence Intervals for Multinomial Proportions Confidence Intervals for the Expected Value of a Poisson Distribution Central Confidence Intervals for the Expected Value Non-central Confidence Intervals According to Crow and Gardner Confidence Interval for the Ratio of Rates (Poisson distribution) Confidence intervals for Standardized Rates Confidence Intervals for the Expected Value in Normal Distribution Confidence Probability and Error Probability Confidence Interval for the Expected Value of a Normal Distribution Confidence Interval for the Difference of Two Expected Values Confidence Interval for the Expected Value From Paired Differences Confidence Interval for the Ratio of Expected Values Confidence Interval for Ratio Numbers Confidence Interval for the Expected Value of a Lognormal Distribution Confidence Intervals for the Mean Absolute Deviation Confidence Intervals for the Median Confidence Intervals for the Difference and Ratio of Medians Distribution Independent Confidence Intervals for Arbitrary Quantiles 90%-Confidence Intervals for Reference Values Confidence Intervals Using the Bootstrap Method Confidence Intervals for the Variance or the Standard Deviation Confidence Intervals for the Coefficient of Variation Confidence Intervals for the Ratio of Variances Weibull Distribution Determination of the Parameters Confidence Interval for the Weibull Line Confidence Intervals for the Parameters of a Linear Regression The Estimation of Some Standard Deviations Confidence Intervals for the Regression Coefficient, for the Axis Intercept, and for the Residual Variance Confidence Intervals and Prediction Intervals for the Regression Line Inverse Prediction from a Linear Regression Confidence Interval for the Pearson Correlation Coefficient Agreement and Precision of Measurements Agreement of Measurement Series According to Bland-Altman Regression Method for the Agreement of Two Series of Measurements Comparison of the Precision and Accuracy of Two Measurement Series The Concordance Correlation Coefficient according to Lin Intra-class Correlation: Interrater Reliability Tolerance Limits Distribution-independent tolerance limits Prediction Intervals (Prediction Intervals) Prediction Intervals for the Mean from Future Observations Prediction Intervals for All Future Observations Prediction Intervals for the Standard Deviation from Future Observations Bayes Estimation A-priori Distributions (Prior) Parameter estimation according to Bayes Hypothesis Testing The Statistical Test Decision Principles Statistical Hypotheses and Test Decisions The Formulation of Hypotheses Alternative Hypothesis as a Contrast to the Null Hypothesis Hypotheses Suggested by Data The P-Value According to R.A. Fisher How Often is a True Null Hypothesis Rejected? Statistical Test - Step by Step The Likelihood Quotient; the Neyman-Pearson Lemma Power Function and Operating Characteristic The Operating Characteristic The OC Curve in Quality Control Test for Superiority, Equivalence, and Non-Inferiority Distribution-Independent Methods Tests of Distribution (Goodness-Of-Fit) The Quotient R/s Checking the 3rd and 4th Moments The Quantile-Quantile Plot Box-Cox Transformation The Chi-Squared Goodness-Of-Fit Test Kolmogorov-Smirnov Goodness-Of-Fit Test Fitting to a Poisson Distribution Shapiro-Wilk Test Anderson-Darling Test Outlier Problem Grubbs' Test for Outliers Dixon's Q-Test for Small Samples Standardized Extreme Deviations Single Sample Methods Hypotheses about Probabilities Binomial Test Binomial Test - Approximation by the Normal Distribution Binomial Test - Sample Size Estimation Binomial Test: Likelihood Ratio Test Hypotheses about Expected Values that Refer to an Empirical Mean One-sample t-test Sample Size Estimation for the One-sample t-Test One-sample Test for Equivalence One-Sample Median Test Comparison of an Empirical Variance with its Parameter Asymptotic Test for the Coefficient of Variation Testing the Randomness of a Sequence of Alternative Data The Successive Differences Dispersion The Iteration Test (Runs Test) Phase Frequency Test by Wallis and Moore The Sign Trend Test by Cox and Stuart Variability of Central Tendency Testing the Expectation Values of Poisson Distributions Sample Size and Power for the One-Sample Lambda Test Sample Size for Testing a Defect Rate Two-Sample Methods Comparison of Two Variances (F-Test) Variance Comparison for Small to Medium Sample Sizes Variance Comparison for Medium to Large Sample Sizes Variance Comparison for Large to Very Large Sample Sizes Sample Size and Power for the F-Test Comparison of the Dispersion of Two Small Samples According to Pillai and Buenaventura Comparison of two Coefficients of Variation Rank Dispersion Test by Siegel and Tukey Ansari-Bradley Test t-Test for Independent Samples Unknown but Equal Variances t-Test with Unknown Variances, Which May be Unequal Sample Size for the t-Test: Two Independent Samples Bootstrap: t-Test Variant Multivariate t-Test: Hotelling's T2 t-Test for Paired Differences Paired Observations Absolute or Percentage Changes t-Test for Pairwise Arranged Measurements Testing the Equality of Two Variances of Paired Samples Wilcoxon Rank Sum Test for Two Independent Samples (U-Test) The U-Test with Rank Division (Ties) Effect Size in Comparison of Independent Samples Sample Size Estimation for the U-Test Wilcoxon Matched Paired Difference Test Confidence Interval for the Median of Paired Differences The Maximum Test for Paired Differences The Sign Test by Dixon and Mood Sample Size for the Sign Test / Wilcoxon Test for Paired Differences Comparison of Two Expected Values from Poisson Distributions Comparison of Two Independent Samples According to Kolmogorov/Smirnoff Cramér-von Mises Test Some Further Distribution Independent Methods for Comparing Independent Samples The Two-Sample Dispersion Test: Count Five Rosenbaum's Quick Tests Permutation Test, Randomization Test The Comparison of Two Independent Samples: Quick Test According to Tukey The Median Test Two-Sample Test for Equivalence Test for Bioequivalence Multiple Hypothesis Testing Multiple Testing Problem Adjustment of P-values Combination of P-Values from Unidirectional One-Sided Tests Testing Multiple Samples - Analysis of Variance Methods Testing the Equality of Variances from Normally Distributed Populations Testing the Equality of Variances According to Hartley Testing the Equality of Variances According to Cochran Testing the Equality of Variances According to Bartlett Robust Test for Homogeneity of Variance According to Levene Transformation for Variance Stabilization Simple Analysis of Variance (ANOVA, Analysis Of Variance) Permutation Test for Analysis of Variance Sample Size and Power for Analysis of Variance Multiple Pairwise Comparisons and Further Mean Comparisons Multiple Comparisons According to Tukey-Kramer Multiple Comparisons According to Games-Howell Multiple Comparisons with a Control According to Dunnett Multiple Comparisons: Selection of the Best According to Hsu Estimation of the Range for max and Selection of the "Best" "7016xi Multiple Comparison of Means with the Overall Mean: Maximum-Modulus Approach Assessment of Linear Contrasts According to Scheffé Formation of Homogeneous Groups of Averages Using the Hayter Modified LSD Test, a Gap Test for Ordered i H-Test by Kruskal and Wallis Multiple Pairwise Comparisons of Mean Ranks H-Test with Sample Subgroups H-Test Variant: Comparison of a Standard with Multiple Treatments Trend Test According to Jonckheere: Comparison of Several Ordered Distribution Functions, also a Trend Test for Medians Analysis of Variance for Repeated Measurements (Block Analysis of Variance) Friedman Test Multiple Pairwise Comparisons with a Control Multiple Pairwise Comparisons According to Wilcoxon and Wilcox Page Test for Ordered Alternatives Quade's Range Rank Test Two-Way Analysis of Variance Analysis of Repeated Measurements Typing of Repeated Measurements ANOVA for Repeated Measurements (Mixed Models) Principles of Experimental Design The Analysis of Frequencies Comparison of Two Relative Frequencies Analysis of Fourfold Tables Sample Size and Power for the Fourfold Test Minimum n for the Fourfold Test Beware of Fallacies in the Fourfold Test Special Risk and Effect Measures Odds Ratio and Relative Risk Confidence Intervals for the Relative Risk and for the Odds Ratio Sample Sizes for Estimating Odds Ratio and Relative Risk The Proportion of Disease Attributable to Exposure: Population Attributable Risk Number Needed to Treat (NNT) Exact Test According to R.A. Fisher Equivalence of Two Binomial Probabilities The McNemar Modified Sign Test Mantel-Haenszel Test Breslow-Day Test The Combination of Fourfold Tables The kx2-field Chi-squared Test According to Brandt and Snedecor Multiple Comparison of Proportions (Marascuilo Procedure) Homogeneity Test According to Ryan (gap test) Power and Sample Size Estimation for the k2-field Test Cochran-Armitage Test for Linear Trend Comparison of Several Proportions with a Given Proportion Value (Standard) The Analysis of Contingency Tables Contingency Coefficient - Strength of the Relationship Sample Size and Power for the Analysis of Contingency Tables Localization of Stochastic Dependency According to Hommel Simultaneous Pair Comparisons According to Royen Bowker Test for Symmetry in Squared Multi-field Tables Lehmacher's Marginal Homogeneity Test Stuart-Maxwell Test for Homogeneity of Marginal Distributions Q-Test by Cochran Simultaneous Confidence Intervals for Pairwise Differences of Success Proportions Cohen's Kappa Coefficient The Weighted Kappa The Kappa for Multiple Ratings (Multi-Rater) Krippendorff's Alpha Kendall's Concordance Coefficient W Hypothesis Tests for Correlation and Regression Hypothesis Test for the Correlation Coefficient (Pearson) "705Fz-Transformation According to R.A. Fisher Correlation in Multiple Measurements Sample Size and Power for the Correlation Coefficient The Comparison of Several Correlation Coefficients Testing the Spearman Rank Correlation Coefficient (Rho-S) Testing the Rank Correlation Coefficient According to Kendall (Tau) Hypothesis Tests for the Parameters of a Regression Testing the Linearity of a Regression Chow Test: Structural Break in a Linear Regression Durbin-Watson Test: Autocorrelation in the Residuals Testing the Regression Coefficient Against Zero Testing the Difference Between an Estimated and a Hypothetical Regression Coefficient. Testing the Difference Between an Estimated and a Hypothetical Axis Intercept. Comparison of two Regression Coefficients Comparison of Two Axis Intercepts Statistical Model Building Introduction Linear Regression Models Simple Linear Regression Multiple Linear Regression Overcoming Multicollinearity in Regression Models. Analysis of Residuals in the Linear Model Heteroscedasticity in the Linear Model Hypothesis Testing and Confidence Intervals for the Linear Model Variable Selection Method Nominal Scaled Influencing Variables Analysis of Variance in the Linear Model Single Factor Analysis of Variance Expectation Value Parameterization Effect Parameterization: Dummy Coding Effect Parameterization: Effect Coding Variance Components - ANOVA Classification of Continuous Influencing Variables Two-factor Analysis of Variance Logistic Regression Hypothesis Test in the Logistic Regression Model Multiple Logistic Regression Interpretation of Regression Coefficients Variable Selection in the Context of Model Building Residual Analysis Pseudo Coefficients of Determination (Pseudo-R2) Quality of Classification: ROC/AUC Analysis Propensity Score Matching Poisson Regression and Loglinear Models Poisson Regression Dispersion Index and Poisson Regression Poisson Regression for Relative Risk from Rates Analysis of Contingency Tables Loglinear Model Using 2 Factors as an Example Three-dimensional Contingency Tables Modeling Under Various Restrictions Model Selection in the Loglinear Approach Five Restrictions and Notes on the Loglinear Model Models for Repeated Measurements Analysis of Variance for Repeated Measurements Linear Mixed Models Analysis of Clustered Data Generalized Estimating Equations Analysis of Survival Times Kaplan-Meier Estimation of the Survival Function The Logrank Test Parametric Regression Models for Survival Times Exponential Regression Model Gompertz Regression Model Weibull Regression Model Log-logistic Regression Model Model Selection and Goodness of Fit AFT Models (Accelerated Failure Time) The Proportional Hazards Model by Cox Parameter Estimation for the Cox Model Interpretation of the Parameters Selection and Evaluation of Influencing Variables Residual Analysis - Quality of Model Fit Introduction to R The Console Window Getting Help in R Objects in R Vectors Generating Vectors and Data Entry Factors in R, Class Formation Generating Matrices and Contingency Tables Calculating with Matrices in R using an Example of Deriving a Covariance Matrix Table Structure: Data in Frames Missing Data Selection and Sorting of Data Flow Control: Logical Conditions and Functions in R Some Mathematical and Statistical Functions Model Building in R Simple Graphical Functions and Tools References Author Index Subject Index Examples Index R Functions Index