Statistics 502 Latest Verified Review 2023 Practice Questions and Answers for Exam Preparation, 100 Correct with Explanations, Highly Recommended, Download to Score A+

Statistics 502 Latest Verified Review 2023 Practice Questions and Answers for Exam Preparation, 100% Correct with Explanations, Highly Recommended, Download to Score A+ Contents 1 Principles of experimental design 1 1.1 Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Model of a process or system . . . . . . . . . . . . . . . . . . . 2 1.3 Experiments and observational studies . . . . . . . . . . . . . 2 1.4 Steps in designing an experiment . . . . . . . . . . . . . . . . 6 2 Test statistics and randomization distributions 9 2.1 Summaries of sample populations . . . . . . . . . . . . . . . . 10 2.2 Hypothesis testing via randomization . . . . . . . . . . . . . . 13 2.3 Essential nature of a hypothesis test . . . . . . . . . . . . . . 17 2.4 Sensitivity to the alternative hypothesis . . . . . . . . . . . . . 18 2.5 Basic decision theory . . . . . . . . . . . . . . . . . . . . . . . 23 3 Tests based on population models 25 3.1 Relating samples to populations . . . . . . . . . . . . . . . . . 25 3.2 The normal distribution . . . . . . . . . . . . . . . . . . . . . 29 3.3 Introduction to the t-test . . . . . . . . . . . . . . . . . . . . . 30 3.4 Two sample tests . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.5 Checking assumptions . . . . . . . . . . . . . . . . . . . . . . 42 3.5.1 Checking normality . . . . . . . . . . . . . . . . . . . . 43 3.5.2 Unequal variances . . . . . . . . . . . . . . . . . . . . . 43 4 Confidence intervals and power 47 4.1 Confidence intervals via hypothesis tests . . . . . . . . . . . . 47 4.2 Power and Sample Size Determination . . . . . . . . . . . . . 49 4.2.1 The non-central t-distribution . . . . . . . . . . . . . . 52 4.2.2 Computing the Power of a test . . . . . . . . . . . . . 54 i CONTENTS ii 5 Introduction to ANOVA 60 5.1 A model for treatment variation . . . . . . . . . . . . . . . . . 62 5.1.1 Model Fitting . . . . . . . . . . . . . . . . . . . . . . . 63 5.1.2 Testing hypothesis with MSE and MST . . . . . . . . . 66 5.2 Partitioning sums of squares . . . . . . . . . . . . . . . . . . . 70 5.2.1 The ANOVA table . . . . . . . . . . . . . . . . . . . . 72 5.2.2 Understanding Degrees of Freedom: . . . . . . . . . . . 73 5.2.3 More sums of squares geometry . . . . . . . . . . . . . 76 5.3 Unbalanced Designs . . . . . . . . . . . . . . . . . . . . . . . . 78 5.3.1 Sums of squares and degrees of freedom . . . . . . . . . 79 5.3.2 ANOVA table for unbalanced data: . . . . . . . . . . . 81 5.4 Normal sampling theory for ANOVA . . . . . . . . . . . . . . 83 5.4.1 Sampling distribution of the F-statistic . . . . . . . . . 85 5.4.2 Comparing group means . . . . . . . . . . . . . . . . . 88 5.4.3 Power calculations for the F-test . . . . . . . . . . . . 90 5.5 Model diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.5.1 Detecting violations with residuals . . . . . . . . . . . 93 5.5.2 Checking normality assumptions: . . . . . . . . . . . . 94 5.5.3 Checking variance assumptions . . . . . . . . . . . . . 96 5.5.4 Variance stabilizing transformations . . . . . . . . . . . 100 5.6 Treatment Comparisons . . . . . . . . . . . . . . . . . . . . . 106 5.6.1 Contrasts . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.6.2 Orthogonal Contrasts . . . . . . . . . . . . . . . . . . . 110 5.6.3 Multiple Comparisons . . . . . . . . . . . . . . . . . . 112 5.6.4 False Discovery Rate procedures . . . . . . . . . . . . . 115 5.6.5 Nonparametric tests . . . . . . . . . . . . . . . . . . . 115 6 Factorial Designs 116 6.1 Data analysis: . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.2 Additive effects model . . . . . . . . . . . . . . . . . . . . . . 123 6.3 Evaluating additivity: . . . . . . . . . . . . . . . . . . . . . . . 126 6.4 Inference for additive treatment effects . . . . . . . . . . . . . 130 6.5 Randomized complete block designs . . . . . . . . . . . . . . . 140 6.6 Unbalanced designs . . . . . . . . . . . . . . . . . . . . . . . . 146 6.7 Non-orthogonal sums of squares: . . . . . . . . . . . . . . . . . 153 6.8 Analysis of covariance . . . . . . . . . . . . . . . . . . . . . . 155 6.9 Types of sums of squares . . . . . . . . . . . . . . . . . . . . . 159 CONTENTS iii 7 Nested Designs 163 7.1 Mixed-effects approach . . . . . . . . . . . . . . . . . . . . . . 171 7.2 Repeated measures analysis . . . . . . . . . . . . . . . . . . . 174