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Introduction | |

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What is Statistics? | |

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Introduction | |

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Why Study Statistics? | |

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Some Current Applications of Statistics | |

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What Do Statisticians Do? | |

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Quality and Process Improvement | |

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A Note to the Student | |

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Summary | |

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Supplementary Exercises | |

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Collecting the Data | |

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Using Surveys and Scientific Studies to Collect Data | |

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Introduction | |

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Surveys | |

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Scientific Studies | |

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Observational Studies | |

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Data Management: Preparing Data for Summarization and Analysis | |

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Summary | |

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Summarizing Data | |

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Data Description | |

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Introduction | |

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Describing Data on a Single Variable: Graphical Methods | |

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Describing Data on a Single Variable: Measures of Central Tendency | |

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Describing Data on a Single Variable: Measures of Variability | |

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The Box Plot | |

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Summarizing Data from More than One Variable | |

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Calculators, Computers, and Software Systems | |

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Summary | |

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Key Formulas | |

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Supplementary Exercises | |

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Tools and Concepts | |

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Probability and Probability Distributions | |

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How Probability Can Be Used in Making Inferences | |

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Finding the Probability of an Event | |

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Basic Event Relations and Probability Laws | |

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Conditional Probability and Independence | |

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Bayes's Formula | |

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Variables: Discrete and Continuous | |

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Probability Distributions for Discrete Random Variables | |

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A Useful Discrete Random Variable: The Binomial | |

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Probability Distributions for Continuous Random Variables | |

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A Useful Continuous Random Variable: The Normal Distribution | |

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Random Sampling | |

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Sampling Distributions | |

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Normal Approximation to the Binomial | |

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Summary | |

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Key Formulas | |

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Supplementary Exercises | |

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Analyzing Data: Central Values, Variances, and Proportions | |

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Inferences on a Population Central Value | |

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Introduction and Case Study | |

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Estimation of ? | |

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Choosing the Sample Size for Estimating ? | |

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A Statistical Test for ? | |

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Choosing the Sample Size for Testing ? | |

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The Level of Significance of a Statistical Test | |

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Inferences about ? for Normal Population, s Unknown | |

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Inferences About the Population Median | |

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Summary | |

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Key Formulas | |

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Supplementary Exercises | |

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Comparing Two Population Central Values | |

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Introduction and Case Study | |

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Inferences about ?1 - ?2: Independent Samples | |

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A Nonparametric Alternative: The Wilcoxon Rank Sum Test | |

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Inferences About ?1 - ?2: Paired Data | |

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A Nonparametric Alternative: The Wilcoxon Signed-Rank Test | |

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Choosing Sample Sizes for Inferences About ?1 - ?2 | |

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Summary | |

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Key Formulas | |

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Supplementary Exercises | |

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Inferences about Population Variances | |

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Introduction and Case Study | |

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Estimation and Tests for a Population Variance | |

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Estimation and Tests for Comparing Two Population Variances | |

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Tests for Comparing k>2 Population Variances | |

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Summary | |

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Key Formulas | |

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Supplementary Exercises | |

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Inferences About More Than Two Population Central Values | |

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Introduction and Case Study | |

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A Statistical Test About More Than Two Population Means | |

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Checking on the Assumptions | |

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Alternative When Assumptions are Violated: Transformations | |

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A Nonparametric Alternative: The Kruskal-Wallis test | |

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Summary | |

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Key Formulas | |

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Supplementary Exercises | |

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Mulitple Comparisons | |

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Introduction and Case Study | |

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Planned Comparisons Among Treatments: Linear Contrasts | |

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Which Error Rate is Controlled | |

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Mulitple Comparisons with the Best Treatment | |

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Comparison of Treatments to a Control | |

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Pairwise Comparison on All Treatments | |

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Summary | |

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Key Formulas | |

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Supplementary Exercises | |

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Categorical Data | |

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Introduction and Case Study | |

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Inferences About a Population Proportion p | |

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Comparing Two Population Proportions p1 - p2 | |

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Probability Distributions for Discrete Random Variables | |

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The Multinomial Experiment and Chi-Square Goodness-of-Fit Test | |

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The Chi-Square Test of Homogeneity of Proportions | |

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The Chi-Square of Independence of Two Nominal Level Variables | |

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Fisher's Exact Test, a Permutation Test | |

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Measures of Association | |

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Combining Sets of Contingency Tables | |

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Summary | |

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Key Formulas | |

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Supplementary Exercises | |

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Analyzing Data: Regression Methods, Model Building | |

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Simple Linear Regression and Correlation | |

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Linear Regression and the Method of Least Squares | |

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Transformations to Linearize Data | |

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Correlation | |

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A Look Ahead: Multiple Regression | |

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Summary of Key Formulas | |

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Supplementary Exercises | |

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Inferences Related to Linear Regression and Correlation | |

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Introduction and Case Study | |

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Diagnostics for Detecting Violations of Model Conditions | |

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Inferences About the Intercept and Slope of the Regression Line | |

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Inferences About the Population Mean for a Specified Value of the Explanatory Variable | |

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Predications and Prediction Intervals | |

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Examining Lack of Fit in the Model | |

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The Inverse Regression Problem (Calibration): Predicting Values for x for a Specified Value of y | |

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Multiple Regression and the General Linear Model | |

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The General Linear Model | |

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Least Squares Estimates of Parameters in the General Linear Model | |

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Inferences About the Parameters in the General Linear Model | |

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Inferences About the Population Mean and Predictions from the General Linear Model | |

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Comparing the Slope of Several Regression Lines | |

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Logistic Regression | |

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Matrix Formulation of the General Linear Model | |

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Building Regression Models with Diagnostics | |

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Selecting the Variables (Step 1) | |

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Model Formulation (Step 2) | |

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Checking Model Conditions (Step 3) | |

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Analyzing Data: Design of Experiments and Anova | |

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Design Concepts for Experiments and Studies | |

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Experiments, Treatments, Experimental Units, Blocking, Randomization, and Measurement Units | |

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How Many Replications | |

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Studies for Comparing Means Versus Studies for Comparing Variances | |

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Analysis of Variance for Standard Designs | |

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Completely Randomized Design with Single Factor | |

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Randomized Block Design | |

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Latin Square Design | |

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Factorial Experiments in a Completely Randomized Design | |

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The Estimation of Treatment Differences and Planned Comparisons in the Treatment Means | |

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Checking Model Conditions | |

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Alternative Analyses: Transformation and Friedman's Rank Based Test | |

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Analysis of Covariance | |

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A Completely Randomized Design with One Covariate | |

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The Extrapolation Problem | |

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Multiple Covariates and More Complicated Designs | |

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Analysis of Variance for Some Unbalanced Designs | |

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A Randomized Block Design with One or More Mission Observations | |

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A Latin Square Design with Missing Data | |

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Incomplete Block Designs | |

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A Factorial Experiment with Missing Factors | |

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Analysis of Variance for Some Fixed Effects, Random Effects and Mixed Effects Models | |

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A One-Factor Experiment with Random Treatment Effects | |

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Extensions of Random-Effects Models | |

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A Mixed Model: Experiments with Both Fixed and Random Treatment Effects | |

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Models with Nested Factors | |

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Rules for Obtaining Expected Mean Squares | |

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Split-Plot Designs and Experiments with Repeated Measures | |

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Split-Plot Designs | |

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Single-Factor Experiments with Repeated Measures | |

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Two-Factor Experiments with Repeated Measures on One of the Factors | |

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Crossover Design | |

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Communicating and Documenting the Results of a Study or Experiment | |

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Communicating and Documenting the Results of a Study or Experiment | |

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Introduction | |

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The Difficulty of Good Communication | |

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Communication Hurdles: Graphical Distortions | |

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Communication Hurdles: Biased Samples | |

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Communication Hurdles | |

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Sample Size | |

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The Statistical Report | |

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Documentation and Storage of Results | |

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Summary | |

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Supplementary Exercises | |