Foundational and Applied Statistics for Biologists Using R

Full of biological applications, exercises, and interactive graphical examples, Foundational and Applied Statistics for Biologists Using R presents comprehensive coverage of both modern analytical methods and statistical foundations. The author harnesses the inherent properties of the R environment to enable students to examine the code of complicated procedures step by step and thus better understand the process of obtaining analysis results. The graphical capabilities of R are used to provide interactive demonstrations of simple to complex statistical concepts. Assuming only familiarity with algebra and general calculus, the text offers a flexible structure for both introductory and graduate-level biostatistics courses. The first seven chapters address fundamental topics in statistics, such as the philosophy of science, probability, estimation, hypothesis testing, sampling, and experimental design. The remaining four chapters focus on applications involving correlation, regression, ANOVA, and tabular analyses. Unlike classic biometric texts, this book provides students with an understanding of the underlying statistics involved in the analysis of biological applications. In particular, it shows how a solid statistical foundation leads to the correct application of procedures, a clear understanding of analyses, and valid inferences concerning biological phenomena. Web ResourceAn R package (asbio) developed by the author is available from CRAN. Accessible to those without prior command-line interface experience, this companion library contains hundreds of functions for statistical pedagogy and biological research. The author’s website also includes an overview of R for novices.

FOUNDATIONSPhilosophical and Historical FoundationsIntroductionNature of ScienceScientific PrinciplesScientific MethodScientific HypothesesLogicVariability and Uncertainty in InvestigationsScience and StatisticsStatistics and Biology Introduction to ProbabilityIntroduction: Models for Random VariablesClassical ProbabilityConditional ProbabilityOddsCombinatorial AnalysisBayes Rule Probability Density FunctionsIntroductionIntroductory Examples of pdfsOther Important DistributionsWhich pdf to Use?Reference Tables Parameters and StatisticsIntroductionParametersStatisticsOLS and ML EstimatorsLinear TransformationsBayesian Applications Interval Estimation: Sampling Distributions, Resampling Distributions, and Simulation DistributionsIntroductionSampling DistributionsConfidence IntervalsResampling DistributionsBayesian Applications: Simulation Distributions Hypothesis TestingIntroductionParametric Frequentist Null Hypothesis TestingType I and Type II ErrorsPowerCriticisms of Frequentist Null Hypothesis TestingAlternatives to Parametric Null Hypothesis TestingAlternatives to Null Hypothesis Testing Sampling Design and Experimental DesignIntroductionSome TerminologyThe Question Is: What Is the Question?Two Important Tenets: Randomization and ReplicationSampling DesignExperimental Design APPLICATIONSCorrelationIntroductionPearson’s CorrelationRobust CorrelationComparisons of Correlation Procedures RegressionIntroductionLinear Regression ModelGeneral Linear ModelsSimple Linear RegressionMultiple RegressionFitted and Predicted ValuesConfidence and Prediction IntervalsCoefficient of Determination and Important VariantsPower, Sample Size, and Effect SizeAssumptions and Diagnostics for Linear RegressionTransformation in the Context of Linear ModelsFixing the Y-InterceptWeighted Least SquaresPolynomial RegressionComparing Model SlopesLikelihood and General Linear ModelsModel SelectionRobust RegressionModel II Regression (X Not Fixed)Generalized Linear ModelsNonlinear ModelsSmoother Approaches to Association and RegressionBayesian Approaches to Regression ANOVAIntroductionOne-Way ANOVAInferences for Factor LevelsANOVA as a General Linear ModelRandom EffectsPower, Sample Size, and Effect SizeANOVA Diagnostics and AssumptionsTwo-Way Factorial DesignRandomized Block DesignNested DesignSplit-Plot DesignRepeated Measures DesignANCOVAUnbalanced DesignsRobust ANOVABayesian Approaches to ANOVA Tabular AnalysesIntroductionProbability Distributions for Tabular AnalysesOne-Way FormatsConfidence Intervals for pContingency TablesTwo-Way TablesOrdinal VariablesPower, Sample Size, and Effect SizeThree-Way TablesGeneralized Linear Models Appendix References Index A Summary and Exercises appear at the end of each chapter.

Ken A. Aho