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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 | |