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Preface | |

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Introduction | |

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The "Image" of Statistics | |

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Descriptive Statistics | |

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Inferential Statistics | |

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Statistics and Mathematics | |

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Case Method | |

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Our Targets | |

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Measurement, Variables, and Scales | |

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Variables and their Measurement | |

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Measurement: The Observation of Variables | |

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Measurement Scales; Nominal Measurement | |

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Ordinal Measurement | |

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Interval Measurement | |

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Ratio Measurement | |

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Interrelationships among Measurement Scales | |

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Continuous and Discrete Variables | |

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Frequency Distributions and Visual Displays of Data | |

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Tabulating Data | |

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Grouped Frequency Distributions | |

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Grouping and Loss of Information | |

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Graphing a Frequency Distribution: The Histogram | |

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Frequency and Percentage Polygons | |

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Type of Distribution | |

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Cumulative Distributions and the Ogive Curve | |

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Percentiles | |

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Box-and-Whisker Plots | |

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Stem-and-Leaf Displays | |

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Time-Series Graphs | |

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Misleading Graphs-How to Lie with Statistics | |

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Measures of Central Tendency | |

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The Mode | |

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The Median | |

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Summation Notation | |

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The Mean | |

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More Summation Notation | |

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Adding or Subtracting a Constant | |

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Multiplying or Dividing by a Constant | |

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Sum of Deviations | |

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Sum of Squared Deviations | |

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The Mean of the Sum of Two or More Scores | |

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The Mean of a Difference | |

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Mean, Median, and Mode of Two or More Groups | |

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Interpretation of Mode, Median, and Mean | |

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Central Tendency and Skewness | |

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Measures of Central Tendency as Inferential Statistics | |

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Which Measure is Best? | |

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Measures of Variability | |

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The Range | |

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H-Spread and the Interquartile Range | |

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Deviation Scores | |

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Sum of Squares | |

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More about the Summation Operator, <F128>- | |

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The Variance of a Population | |

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The Variance Estimated From a Sample | |

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The Standard Deviation | |

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The Effect of Adding or Subtracting a Constant on Measures of Variability | |

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The Effect of Multiplying or Dividing a Constant on Measures of Variability | |

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Variance of a Combined Distribution | |

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Inferential Properties of the Range, s2, and s | |

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The Normal Distribution and Standard Scores | |

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The Importance of the Normal Distribution | |

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God Loves the Normal Curve | |

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The Standard Normal Distribution as a Standard Reference Distribution: z-Scores | |

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Ordinates of the Normal Distribution | |

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Areas Under the Normal Curve | |

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Other Standard Scores | |

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T-Scores | |

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Areas Under the Normal Curve in Samples | |

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Skewness | |

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Kurtosis | |

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Transformations | |

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Normalized Scores | |

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Correlation: Measures of Relationship Between Two Variables | |

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The Concept of Correlation | |

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Scatterplots | |

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The Measurement of Correlation | |

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The Use of Correlation Coefficients | |

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Interpreting r as a Percent | |

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Linear and Curvilinear Relationships | |

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Calculating the Pearson Product-Moment Correlation Coefficient, r | |

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Scatterplots | |

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Correlation Expressed in Terms of z-Scores | |

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Linear Transformations and Correlation | |

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The Bivariate Normal Distribution | |

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Effects of Variability on Correlation | |

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Correcting for Restricted Variability | |

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Effect of Measurement Error on r and the Correction for Attenuation | |

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The Pearson r and Marginal Distributions | |

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The Effect of the Unit of Analysis on Correlation: Ecological Correlations | |

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The Variance of a Sum | |

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The Variance of a Difference | |

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Additional Measures of Relationship: The Spearman Rank Correlation | |

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The Phi Coefficient: Both X and Y are Dichotomies | |

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The Point Biserial Coefficient | |

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The Biserial Correlation | |

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Biserial versus Point-Biserial Correlation Coefficients | |

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The Tetrachoric Coefficient | |

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Causation and Correlation | |

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Regression and Prediction | |

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Purposes of Regression Analysis | |

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The Regression Effect | |

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The Regression Equation Expressed in Standard z-Scores | |

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Use of Regression Equations | |

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Cartesian Coordinates | |

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Estimating Y from X: The Raw-score Regression Equation | |

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Error of Estimate | |

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Proportion of Predictable Variance | |

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Least-squares Criterion | |

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Homoscedasticity and the Standard Error of Estimate | |

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Regression and Pretest-Posttest Gains | |

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Part Correlation | |

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Partial Correlation | |

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Second-Order Partial Correlation | |

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Multiple Regression and Multiple Correlation | |

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The Standardized Regression Equation | |

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The Raw-Score Regression Equation | |

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Multiple Correlation | |

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Multiple Regression Equation with Three or More Independent Variables | |

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Stepwise Multiple Regression | |

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Illustration of Stepwise Multiple Regression | |

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Dichotomous and Categorical Variables as Predictors | |

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The Standard Error of Estimate in Multiple Regression | |

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The Multiple Correlation as an Inferential Statistic: Correction for Bias | |

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Assumptions | |

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Curvilinear Regression and Correlation | |

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Measuring Non-linear Relationships between Two Variables | |

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Transforming Non-linear Relationships into Linear Relationships | |

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Dichotomous Dependent Variables: Logistic Regression | |

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Categorical Dependent Variables more than Two Categories: Discriminant Analysis | |

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Probability | |

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Probability as a Mathematical System | |

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First Addition Rule of Probabilities | |

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Second Addition Rule of Probabilities | |

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Multiplication Rule of Probabilities | |

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Conditional Probability | |

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Bayes's Theorem | |

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Permutations | |

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Combinations | |

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Binomial Probabilities | |

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The Binomial and Sign Test | |

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Intuition and Probability | |

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Probability as an Area | |

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Combining Probabilities | |

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Expectations and Moments | |

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Statistical Inference: Sampling and Interval Estimation | |

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Overview | |

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Populations and Samples: Parameters and Statistics | |

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Infinite versus Finite Populations | |

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Randomness and Random Sampling | |

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Accidental or Convenience Samples | |

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Random Samples | |

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Independence | |

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Systematic Sampling | |

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Point and Interval Estimates | |

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Sampling Distributions | |

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The Standard Error of the Mean | |

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Relationship of sx to n | |

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Confidence Intervals | |

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Confidence Intervals when s is Known: An Example | |

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Central Limit Theorem: A Demonstration | |

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The Use of Sampling Distributions | |

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Proof that s2 = s2/n | |

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Properties of Estimators | |

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Unbiasedness | |

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Consistency | |

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Relative Efficiency | |

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Introduction to Hypothesis Testing | |

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Statistical Hypotheses and Explanations | |

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Statistical versus Scientific Hypotheses | |

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Testing Hypotheses about ï¿½ï¿½ | |

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Testing H0: ï¿½ï¿½ = K, a One-Sample z-Test | |

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Two Types of Errors in Hypothesis Testing | |

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Hypothesis Testing and Confidence Intervals | |

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Type-II Error, b, and Power | |

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Power | |

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Effect of a on Power | |

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Power and the Value Hypothesized in the Alternative Hypothesis | |

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Methods of Increasing Power | |

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Non-Directional and Directional Alternatives: Two-Tailed versus One- Tailed Tests | |

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Statistical Significance versus Practical Significance | |

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Confidence Limits for the Population Median | |

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Inference Regarding ï¿½ï¿½ when s is not Known: t versus z | |

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The t-Distribution | |

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Confidence Intervals Using the t-Distribution | |

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Accuracy of Confidence Intervals when Sampling Non-Normal Distributions | |

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Inferences about the Difference Between Two Means | |

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Testing Statistical Hypotheses Involving Two Means | |

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The Null Hypotheses | |

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The t-Test for Comparing Two Independent Means | |

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Computing sx1-x2 | |

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An Illustration | |

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Confidence Intervals about Mean Differences | |

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Effect Size | |

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t-Test Assumptions and Robustness | |

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Homogeneity of Variance | |

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What if Sample Sizes Are Unequal and Variances Are Heterogeneous: The Welch t' Test | |

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Independence of Observations | |

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Testing H0: ï¿½ï¿½1 = ï¿½ï¿½2 with Paired Observations | |

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Direct Difference for the t-Test for Paired Observations | |

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Cautions Regarding the Matched-Pairs Designs in Research | |

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Power when Comparing Means | |

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Non-Parametric Alternatives: The Mann-Whitney Test and the Wilcoxon Signed-Rank Test | |

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Statistics for Categorical Dependent Variables: Inferences about Proportions | |

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Overview | |

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The Proportion as a Mean | |

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The Variance of a Proportion | |

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The Sampling distribution of a Proportion: The Standard Error of p | |

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The Influence of n on sp | |

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Influence of the Sampling Fraction on sp | |

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The Influence of P on sp | |

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Confidence Intervals for P | |

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Quick Confidence Intervals for P | |

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Testing H0: P = K | |

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Testing Empirical versus Theoretical Distributions: Chi-Square Goodness of Fit Test | |

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Testing Differences among Proportions: The Chi-Square Test of Association | |

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Other Formulas for the Chi-Square Test of Association | |

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The C2 Median Test | |

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Chi-Square and the Phi Coefficient | |

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Independence of Observations | |

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Inferences about H0: P1 = P2 when Observations are Paired: McNemar's Test for Correlated Proportions | |

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Inferences about Correlation Coefficient | |

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Testing Statistical Hypotheses Regarding r | |

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Testing H0: r = 0 Using the t-Test | |

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Directional Alternatives: "Two-Tailed" vs. "One- Tailed" Tests | |

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Sampling Distribution of r | |

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The Fisher Z-Transformation | |

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Setting Confidence Intervals for r | |

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Determining Confidence Intervals Graphically | |

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Testing the Difference between Independent Correlation Coefficients: H0: r1 = e2 = ...ej | |

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Averaging r's | |

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Testing Differences between Two Dependent Correlation Coefficients: H0: e31 = r32 | |

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Inferences about Other Correlation Coefficients | |

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The Point-Biserial Correlation Coefficient rpr | |

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Spearman's Rank Correlation: H0: ranks = 0 | |

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Partial Correlation: H0: r12.3 = 0 | |

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Significance of a Multiple Correlation Coefficient | |

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Statistical Significance in Stepwise Multiple Regression | |

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Significance of the Biserial Correlation Coefficient rbis | |

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Significance of the Tetrachoric Correlation Coefficient rtet | |

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Significance of the Correlation Ratio Eta | |

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Testing for Non-linearity of Regression | |

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One-Factor Analysis of Variance | |

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Why Not Several t-Tests? | |

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ANOVA Nomenclature | |

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ANOVA Computation | |

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Sum of Squares Between, SSB | |

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Sum of Squares Within, SSW | |

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ANOVA Computational Illustration | |

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ANOVA Theory | |

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Mean Square Between Groups, MSB | |

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Mean Square Within Groups, MSW | |

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The F-Test | |

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ANOVA with Equal n's | |

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A Statistical Model for the Data | |

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Estimates of the Terms in the Model | |

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Sum of Squares | |

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Restatement of the Null Hypothesis in Terms of Population Means | |

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Degrees of Freedom | |

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Mean Squares: The Expected Value of MSW | |

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The Expected Value of MSB | |

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Some Distribution Theory | |

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The F-Test of the Null Hypothesis: Rationale and Procedure | |

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Type-I versus Type-II Errors: a and b | |

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A Summary of Procedures for One-Factor ANOVA | |

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Consequences of Failure to Meet the ANOVA Assumptions: The "Robustness" of ANOVA | |

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The Welch and Brown-Forsythe Modifications of ANOVA: What Does One Do When <F128>-'s and n's Differ? | |

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The Power of the F-Test | |

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An Illustration | |

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Power When s is Unknown | |

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A Table for Estimating Power When J=2 | |

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The Non-Parametric Alternative: The Krukal-Wallis Test | |

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Inferences About Variances | |

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Chi-Square Distributions | |

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Chi-Square Distributions with u1: c 2u | |

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The Chi-Square Distribution with u Degrees of Freedom, c2u | |

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Inferences about the Population Variance: H0: s2 = K | |

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F-Distributions | |

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Inferences about Two Independent Variances: H0: s21 = s22 | |

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Testing Homogeneity of Variance: Hartley's Fmax Test | |

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Testing Homogeneity Variance from J Independent Samples: The Bartlett Test | |

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Other Tests of Homogeneity of Variance: The Levene and Brown-Forsythe Tests | |

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Inferences about H0: s21 = s22 with Paired Observations | |

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Relationships among the Normal, t, c2 and F-Distributions | |

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Multiple Comparisons and Trend Analysis | |

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Testing All Pairs of Means: The Studentized Range Statistic, q | |

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The Tukey Method of Multiple Comparisons | |

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The Effect Size of Mean Differences | |

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The Basis for Type-I Error Rate: Contrast vs. Family | |

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The Newman-Keuls Method | |

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The Tukey and Newman-Keuls Methods Compared | |

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The Definition of a Contrast | |

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Simple versus Complex Contrasts | |

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The Standard Error of a Contrast | |

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The t-Ratio for a Contrast | |

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Planned versus Post Hoc Comparisons | |

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Dunn (Bonferroni) Method of Multiple Comparisons | |

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Dunnett Method of Multiple Comparisons | |

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Scheffe Method of Multiple Comparisons | |

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Planned Orthogonal Contrasts | |

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Confidence Intervals for Contrasts | |

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Relative Power of Multiple Comparison Techniques | |

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Trend Analysis | |

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Significance of Trend Components | |

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Relation to Trends to Correlation Coefficients | |

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Assumptions of MC Methods | |

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Multiple Comparisons for Other Statistics | |

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Chapter Summary and Criteria for Selecting a Multiple Comparison Method | |

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Two and Three Factor ANOVA: An Introduction to Factorial Designs | |

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The Meaning of Interaction | |

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Interactions and Generalizability: Factors Do Not Interact | |

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Interactions and Generalizability: Factors Interact | |

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Interpreting when Interaction is Present | |

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Statistical Significance and Interaction | |

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Data Layout and Notation | |

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A Model for the Data | |

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Least-Squares of the Model | |

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Statement of Null Hypotheses | |

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Sums of Squares in the Two-Factor ANOVA | |

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Degrees of Freedom | |

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Mean Squares | |

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Illustration of the Computation for the Two-Factor ANOVA | |

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Expected Values of Mean Squares | |

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The Distribution of the Mean Squares | |

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Determining Power in Factorial Designs | |

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Multiple Comparisons in Factorial ANOVA Designs | |

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Confidence Intervals for Means in Two-Factor ANOVA | |

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Three-Factor ANOVA | |

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Three-Factor ANOVA: An Illustration | |

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Three-Factor ANOVA Computation | |

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The Interpretation of Three-Factor Interaction | |

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Confidence Intervals in Three-Factor ANOVA | |

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How Factorial Designs Increase Power | |

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Factorial ANOVA with Unequal n's | |

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Multi-Factor ANOVA Designs: Random, Mixed, and Fixed Effects | |

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The Random-Effects ANOVA Model | |

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Assumptions of the Random ANOVA Model | |

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An Example | |

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Mean Square, MSW | |

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Mean Square, MSB | |

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The Variance Component, sa2 | |

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Confidence Interval for sa2/se2 | |

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Summary of Random ANOVA Model | |

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The Mixed-Effects ANOVA Model | |

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Mixed-Model ANOVA Assumptions | |

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Mixed-Model ANOVA Computation | |

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Multiple Comparisons in the Two-Factor Mixed Model | |

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Crossed and Nested Factors | |

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Computation of Sums of Squares for Nested Factors | |

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Determining the Sources of Variation in the ANOVA Table | |

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Degrees of Freedom for Nested Factors | |

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Determining Expected Mean Squares | |

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Error Mean Square in Complex ANOVA Designs | |

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The Incremental Generalization Strategy: Inferential "Concentric Circles." | |

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Model Simplification and Pooling | |

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The Experimental Unit and the Observational Unit | |

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Repeated- Measures ANOVA | |

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A Simple Repeated-Measures ANOVA | |

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Repeated-Measures Assumptions | |

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Trend Analysis on Repeated-Measures Factors | |

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Estimating Reliability via Repeated-Measures ANOVA | |

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Repeated-Measures Designs with a Between-Subjects Factor | |

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Repeated-Measures ANOVA with Two Between-Subjects Factors | |

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Trend Analysis on Between-Subjects Factors | |

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Repeated-Measures ANOVA with Two Within-Subjects Factors and Two Between-Subjects Factors | |

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Repeated-Measures ANOVA vs. MANOVA | |

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An Introduction to the Analysis of Covariance | |

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The Functions of ANCOVA | |

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ANOVA Results | |

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ANCOVA Model | |

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ANCOVA Computations, SStotal | |

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The Adjusted Within Sum of Squares, SS'W | |

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The Adjusted Sum of Squares Between Groups, SS'B | |

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Degrees of Freedom in ANCOVA and the ANCOVA Table | |

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Adjusted Means, Y'j | |

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Confidence Intervals and Multiple Comparisons for Adjusted Means | |

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ANCOVA Illustrated Graphically | |

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ANCOVA Assumptions | |

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ANCOVA Precautions | |

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Covarying and Stratifying | |

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Appendix: Tables | |

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Unit-Normal (z) Distribution | |

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Random Digits | |

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t-Distribution | |

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c2-Distribution | |

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Fisher Z-Transformation | |

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F-Distribution | |

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Power Curves for the F-Test | |

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Hartley's Fmax Distribution | |

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Studentized Range Statistic: q-Distribution | |

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Critical Values of r | |

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Critical Values of rranks, Spearman's Rank Correlation | |

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Critical Values for the Dunn (Bonferroni) t-Statistic | |

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Critical Values for the Dunnett t-Statistic | |

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Coefficients (Orthogonal Polynomials) for Trend Analysis | |

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Binomial Probabilities when P = .5 | |

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Glossary of Symbols | |

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Bibliography | |

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Author Index | |

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Subject Index | |