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Introduction | |

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About This Book | |

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Conventions Used in This Book | |

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Foolish Assumptions | |

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Icons Used in This Book | |

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Where to Go from Here | |

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Statistics in a Nutshell | |

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Designing Studies | |

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Surveys | |

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Experiments | |

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Collecting Data | |

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Selecting a good sample | |

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Avoiding bias in your data | |

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Describing Data | |

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Descriptive statistics | |

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Charts and graphs | |

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Analyzing Data | |

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Making Conclusions | |

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Descriptive Statistics | |

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Types of Data | |

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Counts and Percents | |

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Measures of Center | |

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Measures of Variability | |

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Percentiles | |

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Finding a percentile | |

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Interpreting percentiles | |

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The Five-Number Summary | |

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Charts and Graphs | |

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Pie Charts | |

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Bar Graphs | |

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Time Charts | |

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Histograms | |

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Making a histogram | |

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Interpreting a histogram | |

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The distribution of the data in a histogram | |

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Variability in the data from a histogram | |

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Center of the data from a histogram | |

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Evaluating a histogram | |

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Boxplots | |

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Making a boxplot | |

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Interpreting a boxplot | |

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Distribution of data in a boxplot | |

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Variability in a data set from a boxplot | |

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Center of the data from a boxplot | |

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The Binomial Distribution | |

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Characteristics of a Binomial | |

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Checking the binomial conditions step by step | |

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Non-binomial examples | |

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No fixed number of trials | |

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More than success or failure | |

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Probability of success (p) changes | |

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Trials are not independent | |

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Finding Binomial Probabilities Using the Formula | |

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Finding Probabilities Using the Binomial Table | |

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Finding probabilities when p ≤ 0.50 | |

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Finding probabilities when p > 0.50 | |

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Finding probabilities for X greater-than, less-than, or between two values | |

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The Expected Value and Variance of the Binomial | |

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The Normal Distribution | |

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Basics of the Normal Distribution | |

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The Standard Normal (Z) Distribution | |

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Finding Probabilities for X | |

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Finding X for a Given Probability | |

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Normal Approximation to the Binomial | |

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Sampling Distributions and the Central Limit Theorem | |

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Sampling Distributions | |

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The mean of sampling distribution | |

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The standard error of a sampling distribution | |

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Sample size and standard error | |

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Population standard deviation and standard error | |

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The shape | |

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Distribution of X is normal | |

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Distribution of X is unknown or not normal | |

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Finding Probabilities for X | |

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The Sampling Distribution of the Sample Proportion | |

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What proportion of students need math help? | |

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Finding Probabilities for p | |

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Confidence Intervals | |

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Making Your Best Guesstimate | |

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The Goal: Small Margin of Error | |

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Choosing a Confidence Level | |

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Factoring In the Sample Size | |

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Counting On Population Variability | |

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Confidence Interval for a Population Mean | |

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Confidence Interval for a Population Proportion | |

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Confidence Interval for the Difference of Two Means | |

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Confidence Interval for the Difference of Two Proportions | |

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Interpreting Confidence Intervals | |

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Spotting Misleading Confidence Intervals | |

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Hypothesis Tests | |

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Doing a Hypothesis Test | |

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Identifying what you're testing | |

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Setting up the hypotheses | |

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What's the alternative? | |

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Knowing which hypothesis is which | |

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Finding sample statistics | |

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Standardizing the evidence: the test statistic | |

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Weighing the evidence and making decisions: p-values | |

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Finding the p-value | |

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Interpreting a p-value | |

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General steps for a hypothesis test | |

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Testing One Population Mean | |

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Testing One Population Proportion | |

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Comparing Two Population Means | |

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Testing the Mean Difference: Paired Data | |

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Testing Two Population Proportions | |

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You Could Be Wrong: Errors in Hypothesis Testing | |

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A false alarm: Type-1 error | |

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A missed detection: Type-2 error | |

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The t-distribution | |

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Basics of the t-Distribution | |

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Understanding the t-Table | |

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t-distributions and Hypothesis Tests | |

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Finding critical values | |

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Finding p-values | |

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t-distributions and Confidence Intervals | |

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Correlation and Regression | |

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Picturing the Relationship with a Scatterplot | |

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Making a scatterplot | |

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Interpreting a scatterplot | |

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Measuring Relationships Using the Correlation | |

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Calculating the correlation | |

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Interpreting the correlation | |

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Properties of the correlation | |

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Finding the Regression Line | |

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Which is X and which is Y? | |

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Checking the conditions | |

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Understanding the equation | |

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Finding the slope | |

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Finding the y-intercept | |

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Interpreting the slope and y-intercept | |

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Interpreting the slope | |

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Interpreting the y-intercept | |

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The best-fitting line for the crickets | |

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Making Predictions | |

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Avoid Extrapolation! | |

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Correlation Doesn't Necessarily Mean Cause-and-Effect | |

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Two-Way Tables | |

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Organizing and Interpreting a Two-way Table | |

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Defining the outcomes | |

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Setting up the rows and columns | |

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Inserting the numbers | |

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Finding the row, column, and grand totals | |

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Finding Probabilities within a Two-Way Table | |

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Figuring joint probabilities | |

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Calculating marginal probabilities | |

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Finding conditional probabilities | |

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Checking for Independence | |

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A Checklist for Samples and Surveys | |

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The Target Population is Well Defined | |

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The Sample Matches the Target Population | |

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The Sample Is Randomly Selected | |

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The Sample Size Is Large Enough | |

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Nonresponse Is Minimized | |

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The importance of following up | |

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Anonymity versus confidentiality | |

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The Survey Is of the Right Type | |

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Questions Are Well Worded | |

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The Timing Is Appropriate | |

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Personnel Are Well Trained | |

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Proper Conclusions Are Made | |

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A Checklist for Judging Experiments | |

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Experiments versus Observational Studies | |

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Criteria for a Good Experiment | |

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Inspect the Sample Size | |

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Small samples - small conclusions | |

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Original versus final sample size | |

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Examine the Subjects | |

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Check for Random Assignments | |

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Gauge the Placebo Effect | |

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Identify Confounding Variables | |

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Assess Data Quality | |

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Check Out the Analysis | |

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Scrutinize the Conclusions | |

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Overstated results | |

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Ad-hoc explanations | |

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Generalizing beyond the scope | |

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Ten Common Statistical Mistakes | |

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Misleading Graphs | |

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Pie charts | |

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Bar graphs | |

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Time charts | |

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Histograms | |

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Biased Data | |

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No Margin of Error | |

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Nonrandom Samples | |

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Missing Sample Sizes | |

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Misinterpreted Correlations | |

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Confounding Variables | |

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Botched Numbers | |

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Selectively Reporting Results | |

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The Almighty Anecdote | |

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Appendix: Tables for Reference | |

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Index | |