Stratford & Wilkes University DRAFT 1 Table of Contents 1 Probability ............................................................................................................................................1 1.1 Simple probabilities.......................................................................................................................1 1.2 Conditional Probability.................................................................................................................3 1.3 Bayes' theorem...............................................................................................................................3 2 Basic approaches to science and statistics ...........................................................................................5 2.1 Introduction ..................................................................................................................................5 2.2 Schools of statistical inference ......................................................................................................6 2.3 Neyman-Person and Bayesian statistics compared........................................................................9 2.4 Parameter estimation......................................................................................................................9 3 Fundamentals......................................................................................................................................10 3.1 Computing....................................................................................................................................10 3.2 Populations and samples.............................................................................................................10 3.3 Precision, Accuracy, Bias .........................................................................................................10 3.4 Significant units and rounding errors...........................................................................................11 4 Data Collection...................................................................................................................................12 4.1 Introduction.................................................................................................................................12 4.2 Types of Measurements...............................................................................................................12 4.3 Coding data..................................................................................................................................13 4.4 The data sheet .............................................................................................................................13 4.5 Sampling......................................................................................................................................14 4.6 Data management.........................................................................................................................15 5 Common Distributions.........................................................................................................................16 5.1 Histograms....................................................................................................................................16 5.2 Uniform........................................................................................................................................16 5.3 Binomial.......................................................................................................................................16 5.4 Poisson..........................................................................................................................................16 5.5 Gaussian or Normal distribution .................................................................................................17 5.6 Exponential ..................................................................................................................................18 5.7 Cauchy..........................................................................................................................................18 5.8 Gamma.........................................................................................................................................18 5.9 Beta ..............................................................................................................................................18 6 Descriptive Statistics and Exploratory Data Analysis.........................................................................19 6.1 Introduction.................................................................................................................................19 6.2 Law of large numbers...................................................................................................................19 6.3 Descriptive Statistics...................................................................................................................19 6.4 Relationships between variables ................................................................................................22 6.5 Missing values..............................................................................................................................23 6.6 Looking for curvilinear relationships ..........................................................................................23 7 Transformations..................................................................................................................................24 7.1 Introduction..................................................................................................................................24 7.2 Arcsine transformation.................................................................................................................24 7.3 Square-root arcsine transformation:.............................................................................................24 7.4 Exponential transformation..........................................................................................................24 Stratford & Wilkes University DRAFT 2 7.5 Square-root transformation...........................................................................................................24 7.6 Logarithmic transformation..........................................................................................................25 7.7 Rank transformations...................................................................................................................25 7.8 Box-Cox or power transformations..............................................................................................25 7.9 Data standardization.....................................................................................................................25 8 Introduction to Modeling.....................................................................................................................26 8.1 Introduction.................................................................................................................................26 8.2 Model Complexity and Error.......................................................................................................27 8.3 Types of models............................................................................................................................27 8.4 Fitting data to models...................................................................................................................29 8.5 Issues in Modeling .......................................................................................................................30 9 Variable and Model Selection.............................................................................................................31 9.1 Introduction..................................................................................................................................31 9.2 Stepwise........................................................................................................................................31 9.3 Likelihood ratio test......................................................................................................................31 9.4 Information Theoretic Methods....................................................................................................31 10 Generalized Linear Models (GLM)..................................................................................................34 10.1 Introduction................................................................................................................................34 11 Summary ...........................................................................................................................................35 12 Responses and Predictors are Continuous (Regression) ..................................................................36 1.2 Introduction.................................................................................................................................36 12.1 Simple linear regression.............................................................................................................36 12.2 Hypothesis testing and regression..............................................................................................38 12.3 Diagnostics.................................................................................................................................40