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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 �� | |
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| Testing H0: �� = 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 �� 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: ��1 = ��2 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 | |