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Statistical Methods in Education and Psychology

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ISBN-10: 0138449449

ISBN-13: 9780138449445

Edition: 2nd 1984

Authors: Gene V. Glass, Kenneth D. Hopkins

List price: $62.00
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The approach of SMEP-III is conceptual rather than mathematical. The authors stress the understanding, applications, and interpretation of concepts rather than derivation and proof or hand-computation. Copyright � Libri GmbH. All rights reserved.
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Book details

List price: $62.00
Edition: 2nd
Copyright year: 1984
Publisher: Prentice Hall PTR
Binding: Hardcover
Pages: 608
Language: English

The "Image" of Statistics
Descriptive Statistics
Inferential Statistics
Statistics and Mathematics
Case Method
Our Targets
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
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
Box-and-Whisker Plots
Stem-and-Leaf Displays
Time-Series Graphs
Misleading Graphs-How to Lie with Statistics
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?
Measures of Variability
The Range
H-Spread and the Interquartile Range
Deviation Scores
Sum of Squares
More about the Summation Operator, <F128>-
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
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
Areas Under the Normal Curve in Samples
Normalized Scores
Correlation: Measures of Relationship Between Two Variables
The Concept of Correlation
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
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
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
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
Probability as a Mathematical System
First Addition Rule of Probabilities
Second Addition Rule of Probabilities
Multiplication Rule of Probabilities
Conditional Probability
Bayes's Theorem
Binomial Probabilities
The Binomial and Sign Test
Intuition and Probability
Probability as an Area
Combining Probabilities
Expectations and Moments
Statistical Inference: Sampling and Interval Estimation
Populations and Samples: Parameters and Statistics
Infinite versus Finite Populations
Randomness and Random Sampling
Accidental or Convenience Samples
Random Samples
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
Relative Efficiency
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
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
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
Statistics for Categorical Dependent Variables: Inferences about Proportions
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
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
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 <F128>-'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
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
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
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
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
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
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
An Introduction to the Analysis of Covariance
The Functions of ANCOVA
ANOVA Results
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
Unit-Normal (z) Distribution
Random Digits
Fisher Z-Transformation
Power Curves for the F-Test
Hartley's Fmax Distribution
Studentized Range Statistic: q-Distribution
Critical Values of r
Critical Values of rranks, Spearman's Rank Correlation
Critical Values for the Dunn (Bonferroni) t-Statistic
Critical Values for the Dunnett t-Statistic
Coefficients (Orthogonal Polynomials) for Trend Analysis
Binomial Probabilities when P = .5
Glossary of Symbols
Author Index
Subject Index