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Preface | |

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The Statistical Imagination | |

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Introduction | |

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The Statistical Imagination | |

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Linking the Statistical Imagination to the Sociological Imagination | |

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Statistical Norms and Social Norms | |

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Statistical Ideals and Social Values | |

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Statistics and Science: Tools for Proportional Thinking | |

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Descriptive and Inferential Statistics | |

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What Is Science? | |

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Scientific Skepticism and the Statistical Imagination | |

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Conceiving of Data | |

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The Research Process | |

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Proportional Thinking: Calculating Proportions, Percentages, and Rates | |

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How to Succeed in This Course and Enjoy It | |

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Statistical Follies and Fallacies: The Problem of Small Denominators | |

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Organizing Data to Minimize Statistical Error | |

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Introduction | |

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Controlling Sampling Error | |

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Careful Statistical Estimation versus Hasty Guesstimation | |

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Sampling Error and Its Management with Probability Theory | |

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Controlling Measurement Error | |

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Levels of Measurement: Careful Selection of Statistical Procedures | |

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Measurement | |

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Nominal Variables | |

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Ordinal Variables | |

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Interval Variables | |

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Ratio Variables | |

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Improving the Level of Measurement | |

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Distinguishing Level of Measurement and Unit of Measure | |

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Coding and Counting Observations | |

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Frequency Distributions | |

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Standardizing Score Distributions | |

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Coding and Counting Interval/Ratio Data | |

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Rounding Interval/Ratio Observations | |

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The Real Limits of Rounded Scores | |

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Proportional and Percentage Frequency Distributions for Interval/Ratio Variables | |

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Cumulative Percentage Frequency Distributions | |

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Percentiles and Quartiles | |

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Grouping Interval/Ratio Data | |

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Statistical Follies and Fallacies: The Importance of Having a Representative Sample | |

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Charts and Graphs: A Picture Says a Thousand Words | |

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Introduction: Pictorial Presentation of Data | |

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Graphing and Table Construction Guidelines | |

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Graphing Nominal/Ordinal Data | |

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Pie Charts | |

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Bar Charts | |

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Graphing Interval/Ratio Variables | |

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Histograms | |

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Polygons and Line Graphs | |

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Using Graphs with Inferential Statistics and Research Applications | |

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Statistical Follies and Fallacies: Graphical Distortion | |

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Measuring Averages | |

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Introduction | |

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The Mean | |

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Proportional Thinking about the Mean | |

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Potential Weaknesses of the Mean: Situations Where Reporting It Alone May Mislead | |

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The Median | |

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Potential Weaknesses of the Median: Situations Where Reporting It Alone May Mislead | |

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The Mode | |

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Potential Weaknesses of the Mode: Situations Where Reporting It Alone May Mislead | |

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Central Tendency Statistics and the Appropriate Level of Measurement | |

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Frequency Distribution Curves: Relationships Among the Mean, Median, and Mode | |

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The Normal Distribution | |

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Skewed Distributions | |

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Using Sample Data to Estimate the Shape of a Score Distribution in a Population | |

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Organizing Data for Calculating Central Tendency Statistics | |

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Spreadsheet Format for Calculating Central Tendency Statistics | |

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Frequency Distribution Format for Calculating the Mode | |

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Statistical Follies and Fallacies: Mixing Subgroups in the Calculation of the Mean | |

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Measuring Dispersion or Spread in a Distribution of Scores | |

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Introduction | |

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The Range | |

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Limitations of the Range: Situations Where Reporting It Alone May Mislead | |

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The Standard Deviation | |

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Proportional and Linear Thinking about the Standard Deviation | |

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Limitations of the Standard Deviation | |

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The Standard Deviation as an Integral Part of Inferential Statistics | |

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Why Is It Called the "Standard" Deviation? | |

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Standardized Scores (Z-Scores) | |

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The Standard Deviation and the Normal Distribution | |

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Tabular Presentation of Results | |

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Statistical Follies and Fallacies: What Does It Indicate When the Standard Deviation Is Larger than the Mean? | |

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Probability Theory and the Normal Probability Distribution | |

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Introduction: The Human Urge to Predict the Future | |

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What Is a Probability? | |

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Basic Rules of Probability Theory | |

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Probabilities Always Range Between 0 and 1 | |

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The Addition Rule for Alternative Events | |

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Adjust for Joint Occurrences | |

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The Multiplication Rule for Compound Events | |

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Account for Replacement with Compound Events | |

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Using the Normal Curve as a Probability Distribution | |

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Proportional Thinking about a Group of Cases and Single Cases | |

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Partitioning Areas Under the Normal Curve | |

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Sample Problems Using the Normal Curve | |

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Computing Percentiles for Normally Distributed Populations | |

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The Normal Curve as a Tool for Proportional Thinking | |

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Statistical Follies and Fallacies: The Gambler's Fallacy: Independence of Probability Events | |

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Using Probability Theory to Produce Sampling Distributions | |

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Introduction: Estimating Parameters | |

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Point Estimates | |

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Predicting Sampling Error | |

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Sampling Distributions | |

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Sampling Distributions for Interval/Ratio Variables | |

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The Standard Error | |

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The Law of Large Numbers | |

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The Central Limit Theorem | |

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Sampling Distributions for Nominal Variables | |

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Rules Concerning a Sampling Distribution of Proportions | |

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Bean Counting as a Way of Grasping the Statistical Imagination | |

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Distinguishing Among Populations, Samples, and Sampling Distributions | |

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Statistical Follies and Fallacies: Treating a Point Estimate as Though It Were Absolutely True | |

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Parameter Estimation Using Confidence Intervals | |

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Introduction | |

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Confidence Interval of a Population Mean | |

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Calculating the Standard Error for a Confidence Interval of a Population Mean | |

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Choosing the Critical Z-Score, Z[subscript Alpha] | |

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Calculating the Error Term | |

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Calculating the Confidence Interval | |

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The Five Steps for Computing a Confidence Interval of a Population Mean, Mu[subscript x] | |

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Proper Interpretation of Confidence Intervals | |

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Common Misinterpretations of Confidence Intervals | |

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The Chosen Level of Confidence and the Precision of the Confidence Interval | |

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Sample Size and the Precision of the Confidence Interval | |

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Large-Sample Confidence Interval of a Population Proportion | |

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Choosing a Sample Size for Polls, Surveys, and Research Studies | |

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Sample Size for a Confidence Interval of a Population Proportion | |

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Statistical Follies and Fallacies: It Is Plus and Minus the Error Term | |

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Hypothesis Testing I: The Six Steps of Statistical Inference | |

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Introduction: Scientific Theory and the Development of Testable Hypotheses | |

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Making Empirical Predictions | |

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Statistical Inference | |

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The Importance of Sampling Distributions for Hypothesis Testing | |

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The Six Steps of Statistical Inference for a Large Single-Sample Means Test | |

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Test Preparation | |

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The Six Steps | |

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Special Note on Symbols | |

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Understanding the Place of Probability Theory in Hypothesis Testing | |

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A Focus on p-Values | |

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The Level of Significance and Critical Regions of the Sampling Distribution Curve | |

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The Level of Confidence | |

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Study Hints: Organizing Problem Solutions | |

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Solution Boxes Using the Six Steps | |

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Interpreting Results When the Null Hypothesis Is Rejected: The Hypothetical Framework of Hypothesis Testing | |

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Selecting Which Statistical Test to Use | |

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Statistical Follies and Fallacies: Informed Common Sense: Going Beyond Common Sense by Observing Data | |

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Hypothesis Testing II: Single-Sample Hypothesis Tests: Establishing the Representativeness of Samples | |

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Introduction | |

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The Small Single-Sample Means Test | |

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The "Students' t" Sampling Distribution | |

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Selecting the Critical Probability Score, t[subscript Alpha], from the t-distribution Table | |

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Special Note on Symbols | |

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What Are Degrees of Freedom? | |

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The Six Steps of Statistical Inference for a Small Single-Sample Means Test | |

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Gaining a Sense of Proportion About the Dynamics of a Means Test | |

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Relationships among Hypothesized Parameters, Observed Sample Statistics, Computed Test Statistics, p-Values, and Alpha Levels | |

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Using Single-Sample Hypothesis Tests to Establish Sample Representativeness | |

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Target Values for Hypothesis Tests of Sample Representativeness | |

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Large Single-Sample Proportions Test | |

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The Six Steps of Statistical Inference for a Large Single-Sample Proportions Test | |

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What to Do If a Sample Is Found Not to Be Representative? | |

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Presentation of Data from Single-Sample Hypothesis Tests | |

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A Confidence Interval of the Population Mean When n Is Small | |

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Statistical Follies and Fallacies: Issues of Sample Size and Sample Representativeness | |

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Bivariate Relationships: t-Test for Comparing the Means of Two Groups | |

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Introduction: Bivariate Analysis | |

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Difference of Means Tests | |

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Joint Occurrences of Attributes | |

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Correlation | |

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Two-Group Difference of Means Test (t-Test) for Independent Samples | |

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The Standard Error and Sampling Distribution for the t-Test of the Difference Between Two Means | |

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The Six Steps of Statistical Inference for the Two-Group Difference of Means Test | |

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When the Population Variances (or Standard Deviations) Appear Radically Different | |

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The Two-Group Difference of Means Test for Nonindependent or Matched-Pair Samples | |

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The Six Steps of Statistical Inference for the Two-Group Difference of Means Test for Nonindependent or Matched-Pair Samples | |

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Practical versus Statistical Significance | |

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The Four Aspects of Statistical Relationships | |

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Existence of a Relationship | |

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Direction of the Relationship | |

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Strength of the Relationship, Predictive Power, and Proportional Reduction in Error | |

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Practical Applications of the Relationship | |

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When to Apply the Various Aspects of Relationships | |

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Relevant Aspects of a Relationship for Two-Group Difference of Means Tests | |

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Statistical Follies and Fallacies: Fixating on Differences of Means While Ignoring Differences in Variances | |

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Analysis of Variance: Differences Among Means of Three or More Groups | |

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Introduction | |

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Calculating Main Effects | |

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The General Linear Model: Testing the Statistical Significance of Main Effects | |

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Determining the Statistical Significance of Main Effects Using ANOVA | |

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The F-Ratio Test Statistic | |

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How the F-Ratio Turns Out When Group Means Are Not Significantly Different | |

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The F-Ratio as a Sampling Distribution | |

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Relevant Aspects of a Relationship for ANOVA | |

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Existence of the Relationship | |

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Direction of the Relationship | |

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Strength of the Relationship | |

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Practical Applications of the Relationship | |

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The Six Steps of Statistical Inference for One-Way ANOVA | |

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Tabular Presentation of Results | |

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Multivariate Applications of the General Linear Model | |

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Similarities Between the t-Test and the F-Ratio Test | |

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Statistical Follies and Fallacies: Individualizing Group Findings | |

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Nominal Variables: The Chi-Square and Binomial Distributions | |

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Introduction: Proportional Thinking About Social Status | |

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Crosstab Tables: Comparing the Frequencies of Two Nominal/Ordinal Variables | |

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The Chi-Square Test: Focusing on the Frequencies of Joint Occurrences | |

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Calculating Expected Frequencies | |

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Differences Between Observed and Expected Cell Frequencies | |

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Degrees of Freedom for the Chi-Square Test | |

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The Chi-Square Sampling Distribution and Its Critical Regions | |

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The Six Steps of Statistical Inference for the Chi-Square Test | |

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Relevant Aspects of a Relationship for the Chi-Square Test | |

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Using Chi-Square as a Difference of Proportions Test | |

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Tabular Presentation of Data | |

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Small Single-Sample Proportions Test: The Binomial Distribution | |

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The Binomial Distribution Equation | |

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Shortcut Formula for Expanding the Binomial Equation | |

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The Six Steps of Statistical Inference for a Small Single-Sample Proportions Test: The Binomial Distribution Test | |

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Statistical Follies and Fallacies: Low Statistical Power When the Sample Size Is Small | |

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Bivariate Correlation and Regression: Part 1: Concepts and Calculations | |

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Introduction: Improving Best Estimates of a Dependent Variable | |

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A Correlation Between Two Interval/Ratio Variables | |

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Identifying a Linear Relationship | |

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Drawing the Scatterplot | |

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Identifying a Linear Pattern | |

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Using the Linear Regression Equation to Measure the Effects of X on Y | |

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Pearson's r Bivariate Correlation Coefficient | |

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Computational Spreadsheet for Calculating Bivariate Correlation and Regression Statistics | |

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Characteristics of the Pearson's r Bivariate Correlation Coefficient | |

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Understanding the Pearson's r Formulation | |

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Regression Statistics | |

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The Regression Coefficient or Slope, b | |

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The Y-intercept, a | |

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Calculating the Terms of the Regression Line Formula | |

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For the Especially Inquisitive: The Mathematical Relationship Between Pearson's r Correlation Coefficient and the Regression Coefficient, b | |

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Statistical Follies and Fallacies The Failure to Observe a Scatterplot Before Calculating Pearson's r | |

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Linear Equations Work Only with a Linear Pattern in the Scatterplot | |

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Outlier Coordinates and the Attenuation and Inflation of Correlation Coefficients | |

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Bivariate Correlation and Regression: Part 2: Hypothesis Testing and Aspects of a Relationship | |

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Introduction: Hypothesis Test and Aspects of a Relationship Between Two Interval/Ratio Variables | |

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Organizing Data for the Hypothesis Test | |

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The Six Steps of Statistical Inference and the Four Aspects of a Relationship | |

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Existence of a Relationship | |

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Direction of the Relationship | |

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Strength of the Relationship | |

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Practical Applications of the Relationship | |

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Careful Interpretation of Correlation and Regression Statistics | |

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Correlations Apply to a Population, Not to an Individual | |

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Careful Interpretation of the Slope, b | |

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Distinguishing Statistical Significance from Practical Significance | |

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Tabular Presentation: Correlation Tables | |

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Statistical Follies and Fallacies: Correlation Does Not Always Indicate Causation | |

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Review of Basic Mathematical Operations | |

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Statistical Probability Tables | |

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Statistical Table A-Random Number Table | |

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Statistical Table B-Normal Distribution Table | |

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Statistical Table C-t-Distribution Table | |

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Statistical Table D-Critical Values of the F-Ratio Distribution at the .05 Level of Significance | |

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Statistical Table E-Critical Values of the F-Ratio Distribution at the .01 Level of Significance | |

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Statistical Table F-q-Values of Range Tests at the .05 and .01 Levels of Significance | |

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Statistical Table G-Critical Values of the Chi-Square Distribution | |

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Answers to Selected Chapter Exercises | |

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Guide to SPSS for Windows | |

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References | |

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Index | |