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Introduction | |

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Why Statistics? | |

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Descriptive Statistics | |

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Inferential Statistics | |

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The Role of Statistics in Educational Research | |

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Variables and Their Measurement | |

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Some Tips on Studying Statistics | |

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Descriptive Statistics | |

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Frequency Distributions | |

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Why Organize Data? | |

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Frequency Distributions for Quantitative Variables | |

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Grouped Scores | |

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Some Guidelines for Forming Class Intervals | |

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Constructing a Grouped-Data Frequency Distribution | |

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The Relative Frequency Distribution | |

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Exact Limits | |

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The Cumulative Percentage Frequency Distribution | |

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Percentile Ranks | |

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Frequency Distributions for Qualitative Variables | |

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Summary | |

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Graphic Representation | |

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Why Graph Data? | |

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Graphing Qualitative Data: The Bar Chart | |

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Graphing Quantitative Data: The Histogram | |

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The Frequency Polygon | |

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Comparing Different Distributions | |

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Relative Frequency and Proportional Area | |

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Characteristics of Frequency Distributions | |

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The Box Plot | |

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Summary | |

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Central Tendency | |

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The Concept of Central Tendency | |

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The Mode | |

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The Median | |

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The Arithmetic Mean | |

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Central Tendency and Distribution Symmetry | |

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Which Measure of Central Tendency to Use? | |

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Summary | |

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Variability | |

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Central Tendency Is Not Enough: The Importance of Variability | |

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The Range | |

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Variability and Deviations from the Mean | |

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The Variance | |

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The Standard Deviation | |

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The Predominance of the Variance and Standard Deviation | |

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The Standard Deviation and the Normal Distribution | |

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Comparing Means of Two Distributions: The Relevance of Variability | |

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In the Denominator: n vs. n - 1 | |

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Summary | |

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Normal Distributions and Standard Scores | |

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A Little History: Sir Francis Galton and the Normal Curve | |

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Properties of the Normal Curve | |

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More on the Standard Deviation and the Normal Distribution | |

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z Scores | |

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The Normal Curve Table | |

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Finding Area When the Score Is Known | |

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Reversing the Process: Finding Scores When the Area Is Known | |

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Comparing Scores from Different Distributions | |

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Interpreting Effect Size | |

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Percentile Ranks and the Normal Distribution | |

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Other Standard Scores | |

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Standard Scores Do Not "Normalize" a Distribution | |

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The Normal Curve and Probability | |

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Summary | |

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Correlation | |

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The Concept of Association | |

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Bivariate Distributions and Scatterplots | |

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The Covariance | |

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The Pearson r | |

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Computation of r: The Calculating Formula | |

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Correlation and Causation | |

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Factors Influencing Pearson r | |

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Judging the Strength of Association: r[superscript 2] | |

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Other Correlation Coefficients | |

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Summary | |

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Regression and Prediction | |

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Correlation versus Prediction | |

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Determining the Line of Best Fit | |

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The Regression Equation in Terms of Raw Scores | |

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Interpreting the Raw-Score Slope | |

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The Regression Equation in Terms of z Scores | |

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Some Insights Regarding Correlation and Prediction | |

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Regression and Sums of Squares | |

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Measuring the Margin of Prediction Error: The Standard Error of Estimate | |

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Correlation and Causality (Revisited) | |

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Summary | |

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Inferential Statistics | |

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Probability and Probability Distributions | |

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Statistical Inference: Accounting for Chance in Sample Results | |

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Probability: The Study of Chance | |

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Definition of Probability | |

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Probability Distributions | |

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The Or/addition Rule | |

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The And/multiplication Rule | |

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The Normal Curve as a Probability Distribution | |

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"So What?" Probability Distributions as the Basis for Statistical Inference | |

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Summary | |

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Sampling Distributions | |

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From Coins to Means | |

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Samples and Populations | |

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Statistics and Parameters | |

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Random Sampling Model | |

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Random Sampling in Practice | |

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Sampling Distributions of Means | |

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Characteristics of a Sampling Distribution of Means | |

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Using a Sampling Distribution of Means to Determine Probabilities | |

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The Importance of Sample Size (n) | |

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Generality of the Concept of a Sampling Distribution | |

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Summary | |

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Testing Statistical Hypotheses about [Mu] When [sigma] Is Known: The One-Sample z Test | |

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Testing a Hypothesis about [Mu]: Does "Homeschooling" Make a Difference? | |

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Dr. Meyer's Problem in a Nutshell | |

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The Statistical Hypotheses: H[subscript 0] and H[subscript 1] | |

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The Test Statistic z | |

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The Probability of the Test Statistic: The p Value | |

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The Decision Criterion: Level of Significance ([alpha]) | |

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The Level of Significance and Decision Error | |

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The Nature and Role of H[subscript 0] and H[subscript 1] | |

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Rejection versus Retention of H[subscript 0] | |

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Statistical Significance versus Importance | |

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Directional and Nondirectional Alternative Hypotheses | |

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Prologue: The Substantive versus the Statistical | |

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Summary | |

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Estimation | |

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Hypothesis Testing versus Estimation | |

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Point Estimation versus Interval Estimation | |

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Constructing an Interval Estimate of [Mu] | |

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Interval Width and Level of Confidence | |

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Interval Width and Sample Size | |

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Interval Estimation and Hypothesis Testing | |

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Advantages of Interval Estimation | |

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Summary | |

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Testing Statistical Hypotheses about [Mu] When [sigma] Is Not Known: The One-Sample t Test | |

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Reality: [sigma] Often Is Unknown | |

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Estimating the Standard Error of the Mean | |

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The Test Statistic t | |

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Degrees of Freedom | |

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The Sampling Distribution of Student's t | |

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An Application of Student's t | |

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Assumption of Population Normality | |

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Levels of Significance versus p Values | |

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Constructing a Confidence Interval for [Mu] When [sigma] Is Not Known | |

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Summary | |

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Comparing the Means of Two Populations: Independent Samples | |

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From One Mu to Two | |

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Statistical Hypotheses | |

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The Sampling Distribution of Differences Between Means | |

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Estimating [Characters not reproducible] | |

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The t Test for Two Independent Samples | |

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Testing Hypotheses about Two Independent Means: An Example | |

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Interval Estimation of [Mu subscript 1] - [Mu subscript 2] | |

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Appraising the Magnitude of a Difference: Measures of Effect Size for X[subscript 1]-X[subscript 2] | |

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How Were Groups Formed? The Role of Randomization | |

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Statistical Inferences and Nonstatistical Generalizations | |

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Summary | |

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Comparing the Means of Dependent Samples | |

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The Meaning of "Dependent" | |

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Standard Error of the Difference Between Dependent Means | |

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Degrees of Freedom | |

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The t Test for Two Dependent Samples | |

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Testing Hypotheses about Two Dependent Means: An Example | |

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Interval Estimation of [Mu subscript D] | |

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Summary | |

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Comparing the Means of Three or More Independent Samples: One-Way Analysis of Variance | |

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Comparing More Than Two Groups: Why Not Multiple t Tests? | |

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The Statistical Hypotheses in One-Way ANOVA | |

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The Logic of One-Way ANOVA: An Overview | |

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Alison's Reply to Gregory | |

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Partitioning the Sums of Squares | |

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Within-Groups and Between-Groups Variance Estimates | |

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The F Test | |

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Tukey's "HSD" Test | |

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Interval Estimation of [Mu subscript i] - [Mu subscript j] | |

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One-Way ANOVA: Summarizing the Steps | |

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Estimating the Strength of the Treatment Effect: Effect Size ([Omega superscript 2]) | |

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ANOVA Assumptions (and Other Considerations) | |

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Summary | |

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Inferences about the Pearson Correlation Coefficient | |

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From [Mu] to [rho] | |

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The Sampling Distribution of r When [rho] = 0 | |

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Testing the Statistical Hypothesis That [rho] = 0 | |

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An Example | |

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Table E | |

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The Role of n in the Statistical Significance of r | |

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Statistical Significance versus Importance (Again) | |

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Testing Hypotheses Other Than [rho] = 0 | |

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Interval Estimation of [rho] | |

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Summary | |

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Making Inferences from Frequency Data | |

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Frequency Data versus Score Data | |

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A Problem Involving Frequencies: The One-Variable Case | |

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X[superscript 2]: A Measure of Discrepancy Between Expected and Observed Frequencies | |

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The Sampling Distribution of X[superscript 2] | |

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Completion of the Voter Survey Problem: The X[superscript 2] Goodness-of-Fit Test | |

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The X[superscript 2] Test of a Single Proportion | |

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Interval Estimate of a Single Proportion | |

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When There Are Two Variables: The X[superscript 2] Test of Independence | |

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Finding Expected Frequencies in the Two-Variable Case | |

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Calculating the Two-Variable X[superscript 2] | |

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The X[superscript 2] Test of Independence: Summarizing the Steps | |

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The 2 x 2 Contingency Table | |

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Testing a Difference Between Two Proportions | |

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The Independence of Observations | |

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X[superscript 2] and Quantitative Variables | |

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Other Considerations | |

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Summary | |

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Statistical "Power" (and How to Increase It) | |

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The Power of a Statistical Test | |

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Power and Type II Error | |

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Effect Size (Revisited) | |

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Factors Affected Power: The Effect Size | |

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Factors Affecting Power: Sample Size | |

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Additional Factors Affecting Power | |

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Significance versus Importance | |

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Selecting an Appropriate Sample Size | |

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Summary | |

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References | |

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Review of Basic Mathematics | |

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Introduction | |

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Symbols and Their Meaning | |

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Arithmetic Operations Involving Positive and Negative Numbers | |

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Squares and Square Roots | |

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Fractions | |

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Operations Involving Parentheses | |

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Approximate Numbers, Computational Accuracy, and Rounding | |

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Answers to Selected End-of-Chapter Problems | |

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Statistical Tables | |

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Index | |

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Useful Formulas | |