Statistical Inference: A SHORT COURSE -- Contents -- Preface -- 1 The Nature of Statistics -- 1.1 Statistics Defined -- 1.2 The Population and the Sample -- 1.3 Selecting a Sample from a Population -- 1.4 Measurement Scales -- 1.5 Let us Add -- Exercises -- 2 Analyzing Quantitative Data -- 2.1 Imposing Order -- 2.2 Tabular and Graphical Techniques: Ungrouped Data -- 2.3 Tabular and Graphical Techniques: Grouped Data -- Exercises -- Appendix 2.A Histograms with Classes of Different Lengths -- 3 Descriptive Characteristics of Quantitative Data -- 3.1 The Search for Summary Characteristics -- 3.2 The Arithmetic Mean -- 3.3 The Median -- 3.4 The Mode -- 3.5 The Range -- 3.6 The Standard Deviation -- 3.7 Relative Variation -- 3.8 Skewness -- 3.9 Quantiles -- 3.10 Kurtosis -- 3.11 Detection of Outliers -- 3.12 So What Do We Do with All This Stuff? -- Exercises -- Appendix 3.A Descriptive Characteristics of Grouped Data -- 3.A.1 The Arithmetic Mean -- 3.A.2 The Median -- 3.A.3 The Mode -- 3.A.4 The Standard Deviation -- 3.A.5 Quantiles (Quartiles, Deciles, and Percentiles) -- 4 Essentials of Probability -- 4.1 Set Notation -- 4.2 Events within the Sample Space -- 4.3 Basic Probability Calculations -- 4.4 Joint, Marginal, and Conditional Probability -- 4.5 Sources of Probabilities -- Exercises -- 5 Discrete Probability Distributions and Their Properties -- 5.1 The Discrete Probability Distribution -- 5.2 The Mean, Variance, and Standard Deviation of a Discrete Random Variable -- 5.3 The Binomial Probability Distribution -- 5.3.1 Counting Issues -- 5.3.2 The Bernoulli Probability Distribution -- 5.3.3 The Binomial Probability Distribution -- Exercises -- 6 The Normal Distribution -- 6.1 The Continuous Probability Distribution -- 6.2 The Normal Distribution -- 6.3 Probability as an Area Under the Normal Curve.

6.4 Percentiles of the Standard Normal Distribution and Percentiles of the Random Variable X -- Exercises -- Appendix 6.A The Normal Approximation to Binomial Probabilities -- 7 Simple Random Sampling and the Sampling Distribution of the Mean -- 7.1 Simple Random Sampling -- 7.2 The Sampling Distribution of the Mean -- 7.3 Comments on the Sampling Distribution of the Mean -- 7.4 A Central Limit Theorem -- Exercises -- Appendix 7.A Using a Table of Random Numbers -- Appendix 7.B Assessing Normality via the Normal Probability Plot -- Appendix 7.C Randomness, Risk, and Uncertainty -- 7.C.1 Introduction to Randomness -- 7.C.2 Types of Randomness -- 7.C.2.1 Type I Randomness -- 7.C.2.2 Type II Randomness -- 7.C.2.3 Type III Randomness -- 7.C.3 Pseudo-Random Numbers -- 7.C.4 Chaotic Behavior -- 7.C.5 Risk and Uncertainty -- 8 Confidence Interval Estimation of μ -- 8.1 The Error Bound on X as an Estimator of μ -- 8.2 A Confidence Interval for the Population Mean μ (σ Known) -- 8.3 A Sample Size Requirements Formula -- 8.4 A Confidence Interval for the Population Mean μ (σ Unknown) -- Exercises -- Appendix 8.A A Confidence Interval for the Population Median MED -- 9 The Sampling Distribution of a Proportion and its Confidence Interval Estimation -- 9.1 The Sampling Distribution of a Proportion -- 9.2 The Error Bound on ^p as an Estimator for p -- 9.3 A Confidence Interval for the Population Proportion (of Successes) p -- 9.4 A Sample Size Requirements Formula -- Exercises -- Appendix 9.A Ratio Estimation -- 10 Testing Statistical Hypotheses -- 10.1 What is a Statistical Hypothesis? -- 10.2 Errors in Testing -- 10.3 The Contextual Framework of Hypothesis Testing -- 10.3.1 Types of Errors in a Legal Context -- 10.3.2 Types of Errors in a Medical Context -- 10.3.3 Types of Errors in a Processing or Control Context -- 10.3.4 Types of Errors in a Sports Context.

10.4 Selecting a Test Statistic -- 10.5 The Classical Approach to Hypothesis Testing -- 10.6 Types of Hypothesis Tests -- 10.7 Hypothesis Tests for μ (σ Known) -- 10.8 Hypothesis Tests for μ (σ Unknown and n Small) -- 10.9 Reporting the Results of Statistical Hypothesis Tests -- 10.10 Hypothesis Tests for the Population Proportion (of Successes) p -- Exercises -- Appendix 10.A Assessing the Randomness of a Sample -- Appendix 10.B Wilcoxon Signed Rank Test (of a Median) -- Appendix 10.C Lilliefors Goodness-of-Fit Test for Normality -- 11 Comparing Two Population Means and Two Population Proportions -- 11.1 Confidence Intervals for the Difference of Means when Sampling from Two Independent Normal Populations -- 11.1.1 Sampling from Two Independent Normal Populations with Equal and Known Variances -- 11.1.2 Sampling from Two Independent Normal Populations with Unequal but Known Variances -- 11.1.3 Sampling from Two Independent Normal Populations with Equal but Unknown Variances -- 11.1.4 Sampling from Two Independent Normal Populations with Unequal and Unknown Variances -- 11.2 Confidence Intervals for the Difference of Means when Sampling from Two Dependent Populations: Paired Comparisons -- 11.3 Confidence Intervals for the Difference of Proportions when Sampling from Two Independent Binomial Populations -- 11.4 Statistical Hypothesis Tests for the Difference of Means when Sampling from Two Independent Normal Populations -- 11.4.1 Population Variances Equal and Known -- 11.4.2 Population Variances Unequal but Known -- 11.4.3 Population Variances Equal and Unknown -- 11.4.4 Population Variances Unequal and Unknown (an Approximate Test) -- 11.5 Hypothesis Tests for the Difference of Means when Sampling from Two Dependent Populations: Paired Comparisons.

11.6 Hypothesis Tests for the Difference of Proportions when Sampling from Two Independent Binomial Populations -- Exercises -- Appendix 11.A Runs Test for Two Independent Samples -- Appendix 11.B Mann-Whitney (Rank Sum) Test for Two Independent Populations -- Appendix 11.C Wilcoxon Signed Rank Test when Sampling from Two Dependent Populations: Paired Comparisons -- 12 Bivariate Regression and Correlation -- 12.1 Introducing an Additional Dimension to our Statistical Analysis -- 12.2 Linear Relationships -- 12.2.1 Exact Linear Relationships -- 12.3 Estimating the Slope and Intercept of the Population Regression Line -- 12.4 Decomposition of the Sample Variation in Y -- 12.5 Mean, Variance, and Sampling Distribution of the Least Squares Estimators β0 and β1 -- 12.6 Confidence Intervals for β0 and β1 -- 12.7 Testing Hypotheses about β0 and β1 -- 12.8 Predicting the Average Value of Y given X -- 12.9 The Prediction of a Particular Value of Y given X -- 12.10 Correlation Analysis -- 12.10.1 Case A: X and Y Random Variables -- 12.10.1.1 Estimating the Population Correlation Coefficient ρ -- 12.10.1.2 Inferences about the Population Correlation Coefficient ρ -- 12.10.2 Case B: X Values Fixed, Y a Random Variable -- Exercises -- Appendix 12.A Assessing Normality (Appendix 7.B Continued) -- Appendix 12.B On Making Causal Inferences3 -- 12.B.1 Introduction -- 12.B.2 Rudiments of Experimental Design -- 12.B.3 Truth Sets, Propositions, and Logical Implications -- 12.B.4 Necessary and Sufficient Conditions -- 12.B.5 Causality Proper -- 12.B.6 Logical Implications and Causality -- 12.B.7 Correlation and Causality -- 12.B.8 Causality from Counterfactuals -- 12.B.9 Testing Causality -- 12.B.10 Suggestions for Further Reading -- 13 An Assortment of Additional Statistical Tests -- 13.1 Distributional Hypotheses -- 13.2 The Multinomial Chi-Square Statistic.

13.3 The Chi-Square Distribution -- 13.4 Testing Goodness of Fit -- 13.5 Testing Independence -- 13.6 Testing k Proportions -- 13.7 A Measure of Strength of Association in a Contingency Table -- 13.8 A Confidence Interval for σ2 under Random Sampling from a Normal Population -- 13.9 The F Distribution -- 13.10 Applications of the F Statistic to Regression Analysis -- 13.10.1 Testing the Significance of the Regression Relationship Between X and Y -- 13.10.2 A Joint Test of the Regression Intercept and Slope -- Exercises -- Appendix A -- Table A.1 Standard Normal Areas [Z is N(0,1)] -- Table A.2 Quantiles of the t Distribution (T is tv) -- Table A.3 Quantiles of the Chi-Square Distribution (X is χ2v -- Table A.4 Quantiles of the F Distribution (F is Fv1, v2 ) -- Table A.5 Binomial Probabilities P(X -- n,p) -- Table A.6 Cumulative Binomial Probabilities -- Table A.7 Quantiles of Lilliefors' Test for Normality -- Solutions to Exercises -- References -- Index.