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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 | |