Statistical methods in education and psychology /
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| Author / Creator: | Glass, Gene V, 1940- |
|---|---|
| Edition: | 2nd ed. |
| Imprint: | Englewood Cliffs, N.J. : Prentice-Hall, c1984. |
| Description: | xiii, 578 p. : ill. ; 25 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/805199 |
Table of Contents:
- Preface
- 1. Introduction
- The "Image" of Statistics
- Descriptive Statistics
- Inferential Statistics
- Statistics and Mathematics
- Case Method
- Our Targets
- 2. Measurement, Variables, and Scales
- Variables and their Measurement
- Measurement: The Observation of Variables
- Measurement Scales; Nominal Measurement
- Ordinal Measurement
- Interval Measurement
- Ratio Measurement
- Interrelationships among Measurement Scales
- Continuous and Discrete Variables
- 3. Frequency Distributions and Visual Displays of Data
- Tabulating Data
- Grouped Frequency Distributions
- Grouping and Loss of Information
- Graphing a Frequency Distribution: The Histogram
- Frequency and Percentage Polygons
- Type of Distribution
- Cumulative Distributions and the Ogive Curve
- Percentiles
- Box-and-Whisker Plots
- Stem-and-Leaf Displays
- Time-Series Graphs
- Misleading Graphs-How to Lie with Statistics
- 4. Measures of Central Tendency
- The Mode
- The Median
- Summation Notation
- The Mean
- More Summation Notation
- Adding or Subtracting a Constant
- Multiplying or Dividing by a Constant
- Sum of Deviations
- Sum of Squared Deviations
- The Mean of the Sum of Two or More Scores
- The Mean of a Difference
- Mean, Median, and Mode of Two or More Groups
- Interpretation of Mode, Median, and Mean
- Central Tendency and Skewness
- Measures of Central Tendency as Inferential Statistics
- Which Measure is Best?
- 5. Measures of Variability
- The Range
- H-Spread and the Interquartile Range
- Deviation Scores
- Sum of Squares
- More about the Summation Operator, -
- The Variance of a Population
- The Variance Estimated From a Sample
- The Standard Deviation
- The Effect of Adding or Subtracting a Constant on Measures of Variability
- The Effect of Multiplying or Dividing a Constant on Measures of Variability
- Variance of a Combined Distribution
- Inferential Properties of the Range, s2, and s
- 6. The Normal Distribution and Standard Scores
- The Importance of the Normal Distribution
- God Loves the Normal Curve
- The Standard Normal Distribution as a Standard Reference Distribution: z-Scores
- Ordinates of the Normal Distribution
- Areas Under the Normal Curve
- Other Standard Scores
- T-Scores
- Areas Under the Normal Curve in Samples
- Skewness
- Kurtosis
- Transformations
- Normalized Scores
- 7. Correlation: Measures of Relationship Between Two Variables
- The Concept of Correlation
- Scatterplots
- The Measurement of Correlation
- The Use of Correlation Coefficients
- Interpreting r as a Percent
- Linear and Curvilinear Relationships
- Calculating the Pearson Product-Moment Correlation Coefficient, r
- Scatterplots
- Correlation Expressed in Terms of z-Scores
- Linear Transformations and Correlation
- The Bivariate Normal Distribution
- Effects of Variability on Correlation
- Correcting for Restricted Variability
- Effect of Measurement Error on r and the Correction for Attenuation
- The Pearson r and Marginal Distributions
- The Effect of the Unit of Analysis on Correlation: Ecological Correlations
- The Variance of a Sum
- The Variance of a Difference
- Additional Measures of Relationship: The Spearman Rank Correlation
- The Phi Coefficient: Both X and Y are Dichotomies
- The Point Biserial Coefficient
- The Biserial Correlation
- Biserial versus Point-Biserial Correlation Coefficients
- The Tetrachoric Coefficient
- Causation and Correlation
- 8. Regression and Prediction
- Purposes of Regression Analysis
- The Regression Effect
- The Regression Equation Expressed in Standard z-Scores
- Use of Regression Equations
- Cartesian Coordinates
- Estimating Y from X: The Raw-score Regression Equation
- Error of Estimate
- Proportion of Predictable Variance
- Least-squares Criterion
- Homoscedasticity and the Standard Error of Estimate
- Regression and Pretest-Posttest Gains
- Part Correlation
- Partial Correlation
- Second-Order Partial Correlation
- Multiple Regression and Multiple Correlation
- The Standardized Regression Equation
- The Raw-Score Regression Equation
- Multiple Correlation
- Multiple Regression Equation with Three or More Independent Variables
- Stepwise Multiple Regression
- Illustration of Stepwise Multiple Regression
- Dichotomous and Categorical Variables as Predictors
- The Standard Error of Estimate in Multiple Regression
- The Multiple Correlation as an Inferential Statistic: Correction for Bias
- Assumptions
- Curvilinear Regression and Correlation
- Measuring Non-linear Relationships between Two Variables
- Transforming Non-linear Relationships into Linear Relationships
- Dichotomous Dependent Variables: Logistic Regression
- Categorical Dependent Variables more than Two Categories: Discriminant Analysis
- 9. Probability
- Probability as a Mathematical System
- First Addition Rule of Probabilities
- Second Addition Rule of Probabilities
- Multiplication Rule of Probabilities
- Conditional Probability
- Bayes's Theorem
- Permutations
- Combinations
- Binomial Probabilities
- The Binomial and Sign Test
- Intuition and Probability
- Probability as an Area
- Combining Probabilities
- Expectations and Moments
- 10. Statistical Inference: Sampling and Interval Estimation
- Overview
- Populations and Samples: Parameters and Statistics
- Infinite versus Finite Populations
- Randomness and Random Sampling
- Accidental or Convenience Samples
- Random Samples
- Independence
- Systematic Sampling
- Point and Interval Estimates
- Sampling Distributions
- The Standard Error of the Mean
- Relationship of sx to n
- Confidence Intervals
- Confidence Intervals when s is Known: An Example
- Central Limit Theorem: A Demonstration
- The Use of Sampling Distributions
- Proof that s2 = s2/n
- Properties of Estimators
- Unbiasedness
- Consistency
- Relative Efficiency
- 11. Introduction to Hypothesis Testing
- Statistical Hypotheses and Explanations
- Statistical versus Scientific Hypotheses
- Testing Hypotheses about ¿¿
- Testing H0: ¿¿ = K, a One-Sample z-Test
- Two Types of Errors in Hypothesis Testing
- Hypothesis Testing and Confidence Intervals
- Type-II Error, b, and Power
- Power
- Effect of a on Power
- Power and the Value Hypothesized in the Alternative Hypothesis
- Methods of Increasing Power
- Non-Directional and Directional Alternatives: Two-Tailed versus One- Tailed Tests
- Statistical Significance versus Practical Significance
- Confidence Limits for the Population Median
- Inference Regarding ¿¿ when s is not Known: t versus z
- The t-Distribution
- Confidence Intervals Using the t-Distribution
- Accuracy of Confidence Intervals when Sampling Non-Normal Distributions
- 12. Inferences about the Difference Between Two Means
- Testing Statistical Hypotheses Involving Two Means
- The Null Hypotheses
- The t-Test for Comparing Two Independent Means
- Computing sx1-x2
- An Illustration
- Confidence Intervals about Mean Differences
- Effect Size
- t-Test Assumptions and Robustness
- Homogeneity of Variance
- What if Sample Sizes Are Unequal and Variances Are Heterogeneous: The Welch t' Test
- Independence of Observations
- Testing H0: ¿¿1 = ¿¿2 with Paired Observations
- Direct Difference for the t-Test for Paired Observations
- Cautions Regarding the Matched-Pairs Designs in Research
- Power when Comparing Means
- Non-Parametric Alternatives: The Mann-Whitney Test and the Wilcoxon Signed-Rank Test
- 13. Statistics for Categorical Dependent Variables: Inferences about Proportions
- Overview
- The Proportion as a Mean
- The Variance of a Proportion
- The Sampling distribution of a Proportion: The Standard Error of p
- The Influence of n on sp
- Influence of the Sampling Fraction on sp
- The Influence of P on sp
- Confidence Intervals for P
- Quick Confidence Intervals for P
- Testing H0: P = K
- Testing Empirical versus Theoretical Distributions: Chi-Square Goodness of Fit Test
- Testing Differences among Proportions: The Chi-Square Test of Association
- Other Formulas for the Chi-Square Test of Association
- The C2 Median Test
- Chi-Square and the Phi Coefficient
- Independence of Observations
- Inferences about H0: P1 = P2 when Observations are Paired: McNemar's Test for Correlated Proportions
- 14. Inferences about Correlation Coefficient
- Testing Statistical Hypotheses Regarding r
- Testing H0: r = 0 Using the t-Test
- Directional Alternatives: "Two-Tailed" vs. "One- Tailed" Tests
- Sampling Distribution of r
- The Fisher Z-Transformation
- Setting Confidence Intervals for r
- Determining Confidence Intervals Graphically
- Testing the Difference between Independent Correlation Coefficients: H0: r1 = e2 = ...ej
- Averaging r's
- Testing Differences between Two Dependent Correlation Coefficients: H0: e31 = r32
- Inferences about Other Correlation Coefficients
- The Point-Biserial Correlation Coefficient rpr
- Spearman's Rank Correlation: H0: ranks = 0
- Partial Correlation: H0: r12.3 = 0
- Significance of a Multiple Correlation Coefficient
- Statistical Significance in Stepwise Multiple Regression
- Significance of the Biserial Correlation Coefficient rbis
- Significance of the Tetrachoric Correlation Coefficient rtet
- Significance of the Correlation Ratio Eta
- Testing for Non-linearity of Regression
- 15. One-Factor Analysis of Variance
- Why Not Several t-Tests?
- ANOVA Nomenclature
- ANOVA Computation
- Sum of Squares Between, SSB
- Sum of Squares Within, SSW
- ANOVA Computational Illustration
- ANOVA Theory
- Mean Square Between Groups, MSB
- Mean Square Within Groups, MSW
- The F-Test
- ANOVA with Equal n's
- A Statistical Model for the Data
- Estimates of the Terms in the Model
- Sum of Squares
- Restatement of the Null Hypothesis in Terms of Population Means
- Degrees of Freedom
- Mean Squares: The Expected Value of MSW
- The Expected Value of MSB
- Some Distribution Theory
- The F-Test of the Null Hypothesis: Rationale and Procedure
- Type-I versus Type-II Errors: a and b
- A Summary of Procedures for One-Factor ANOVA
- Consequences of Failure to Meet the ANOVA Assumptions: The "Robustness" of ANOVA
- The Welch and Brown-Forsythe Modifications of ANOVA: What Does One Do When -'s and n's Differ?
- The Power of the F-Test
- An Illustration
- Power When s is Unknown
- A Table for Estimating Power When J=2
- The Non-Parametric Alternative: The Krukal-Wallis Test
- 16. Inferences About Variances
- Chi-Square Distributions
- Chi-Square Distributions with u1: c 2u
- The Chi-Square Distribution with u Degrees of Freedom, c2u
- Inferences about the Population Variance: H0: s2 = K
- F-Distributions
- Inferences about Two Independent Variances: H0: s21 = s22
- Testing Homogeneity of Variance: Hartley's Fmax Test
- Testing Homogeneity Variance from J Independent Samples: The Bartlett Test
- Other Tests of Homogeneity of Variance: The Levene and Brown-Forsythe Tests
- Inferences about H0: s21 = s22 with Paired Observations
- Relationships among the Normal, t, c2 and F-Distributions
- 17. Multiple Comparisons and Trend Analysis
- Testing All Pairs of Means: The Studentized Range Statistic, q
- The Tukey Method of Multiple Comparisons
- The Effect Size of Mean Differences
- The Basis for Type-I Error Rate: Contrast vs. Family
- The Newman-Keuls Method
- The Tukey and Newman-Keuls Methods Compared
- The Definition of a Contrast
- Simple versus Complex Contrasts
- The Standard Error of a Contrast
- The t-Ratio for a Contrast
- Planned versus Post Hoc Comparisons
- Dunn (Bonferroni) Method of Multiple Comparisons
- Dunnett Method of Multiple Comparisons
- Scheffe Method of Multiple Comparisons
- Planned Orthogonal Contrasts
- Confidence Intervals for Contrasts
- Relative Power of Multiple Comparison Techniques
- Trend Analysis
- Significance of Trend Components
- Relation to Trends to Correlation Coefficients
- Assumptions of MC Methods
- Multiple Comparisons for Other Statistics
- Chapter Summary and Criteria for Selecting a Multiple Comparison Method
- 18. Two and Three Factor ANOVA: An Introduction to Factorial Designs
- The Meaning of Interaction
- Interactions and Generalizability: Factors Do Not Interact
- Interactions and Generalizability: Factors Interact
- Interpreting when Interaction is Present
- Statistical Significance and Interaction
- Data Layout and Notation
- A Model for the Data
- Least-Squares of the Model
- Statement of Null Hypotheses
- Sums of Squares in the Two-Factor ANOVA
- Degrees of Freedom
- Mean Squares
- Illustration of the Computation for the Two-Factor ANOVA
- Expected Values of Mean Squares
- The Distribution of the Mean Squares
- Determining Power in Factorial Designs
- Multiple Comparisons in Factorial ANOVA Designs
- Confidence Intervals for Means in Two-Factor ANOVA
- Three-Factor ANOVA
- Three-Factor ANOVA: An Illustration
- Three-Factor ANOVA Computation
- The Interpretation of Three-Factor Interaction
- Confidence Intervals in Three-Factor ANOVA
- How Factorial Designs Increase Power
- Factorial ANOVA with Unequal n's
- 19. Multi-Factor ANOVA Designs: Random, Mixed, and Fixed Effects
- The Random-Effects ANOVA Model
- Assumptions of the Random ANOVA Model
- An Example
- Mean Square, MSW
- Mean Square, MSB
- The Variance Component, sa2
- Confidence Interval for sa2/se2
- Summary of Random ANOVA Model
- The Mixed-Effects ANOVA Model
- Mixed-Model ANOVA Assumptions
- Mixed-Model ANOVA Computation
- Multiple Comparisons in the Two-Factor Mixed Model
- Crossed and Nested Factors
- Computation of Sums of Squares for Nested Factors
- Determining the Sources of Variation in the ANOVA Table
- Degrees of Freedom for Nested Factors
- Determining Expected Mean Squares
- Error Mean Square in Complex ANOVA Designs
- The Incremental Generalization Strategy: Inferential "Concentric Circles."
- Model Simplification and Pooling
- The Experimental Unit and the Observational Unit
- 20. Repeated- Measures ANOVA
- A Simple Repeated-Measures ANOVA
- Repeated-Measures Assumptions
- Trend Analysis on Repeated-Measures Factors
- Estimating Reliability via Repeated-Measures ANOVA
- Repeated-Measures Designs with a Between-Subjects Factor
- Repeated-Measures ANOVA with Two Between-Subjects Factors
- Trend Analysis on Between-Subjects Factors
- Repeated-Measures ANOVA with Two Within-Subjects Factors and Two Between-Subjects Factors
- Repeated-Measures ANOVA vs. MANOVA
- 21. An Introduction to the Analysis of Covariance
- The Functions of ANCOVA
- ANOVA Results
- ANCOVA Model
- ANCOVA Computations, SStotal
- The Adjusted Within Sum of Squares, SS'W
- The Adjusted Sum of Squares Between Groups, SS'B
- Degrees of Freedom in ANCOVA and the ANCOVA Table
- Adjusted Means, Y'j
- Confidence Intervals and Multiple Comparisons for Adjusted Means
- ANCOVA Illustrated Graphically
- ANCOVA Assumptions
- ANCOVA Precautions
- Covarying and Stratifying
- Appendix: Tables
- Table A. Unit-Normal (z) Distribution
- Table B. Random Digits
- Table C. t-Distribution
- Table D. c2-Distribution
- Table E. Fisher Z-Transformation
- Table F. F-Distribution
- Table G. Power Curves for the F-Test
- Table H. Hartley's Fmax Distribution
- Table I. Studentized Range Statistic: q-Distribution
- Table J. Critical Values of r
- Table K. Critical Values of rranks, Spearman's Rank Correlation
- Table L. Critical Values for the Dunn (Bonferroni) t-Statistic
- Table M. Critical Values for the Dunnett t-Statistic
- Table N. Coefficients (Orthogonal Polynomials) for Trend Analysis
- Table O. Binomial Probabilities when P = .5
- Glossary of Symbols
- Bibliography
- Author Index
- Subject Index