9780470643822

Introduction
Descriptive Statistics
Inferential Statistics
Our Concern: Applied Statistics
Variables and Constants
Scales of Measurement
Scales of Measurement and Problems of Statistical Treatment
Do Statistics Lie?
Point of Controversy: Are Statistical Procedures Necessary?
Some Tips on Studying Statistics
Statistics and Computers
Summary
Frequency Distributions, Percentiles, and Percentile Ranks
Organizing Qualitative Data
Grouped Scores
How to Construct a Grouped Frequency Distribution
Apparent versus Real Limits
The Relative Frequency Distribution
The Cumulative Frequency Distribution
Percentiles and Percentile Ranks
Computing Percentiles from Grouped Data
Computation of Percentile Rank
Summary
Graphic Representation of Frequency Distributions
Basic Procedures
The Histogram
The Frequency Polygon
Choosing between a Histogram and a Polygon
The Bar Diagram and the Pie Chart
The Cumulative Percentage Curve
Factors Affecting the Shape of Graphs
Shape of Frequency Distributions
Summary
Central Tendency
The Mode
The Median
The Mean
Properties of the Mode
Properties of the Mean
Point of Controversy: Is It Permissible to Calculate the Mean for Tests in the Behavioral Sciences?
Properties of the Median
Measures of Central Tendency in Symmetrical and Asymmetrical Distributions
The Effects of Score Transformations
Summary
Variability and Standard (z) Scores
The Range and Semi-Interquartile Range
Deviation Scores
Deviational Measures: The Variance
Deviational Measures: The Standard Deviation
Calculation of the Variance and Standard Deviation: Raw-Score Method
Calculation of the Standard Deviation with IBM SPSS (formerly SPSS)
Point of Controversy: Calculating the Sample Variance: Should We Divide by n or (n - 1)?
Properties of the Range and Semi-Interquartile Range
Properties of the Standard Deviation
How Big Is a Standard Deviation?
Score Transformations and Measures of Variability
Standard Scores (z Scores)
A Comparison of z Scores and Percentile Ranks
Summary
Standard Scores and the Normal Curve
Historical Aspects of the Normal Curve
The Nature of the Normal Curve
Standard Scores and the Normal Curve
The Standard Normal Curve: Finding Areas When the Score Is Known
The Standard Normal Curve: Finding Scores When the Area Is Known
The Normal Curve as a Model for Real Variables
The Normal Curve as a Model for Sampling Distributions
Summary
Point of Controversy: How Normal Is the Normal Curve?
Correlation
Some History
Graphing Bivariate Distributions: The Scatter Diagram
Correlation: A Matter of Direction
Correlation: A Matter of Degree
Understanding the Meaning of Degree of Correlation
Formulas for Pearson's Coefficient of Correlation
Calculating r from Raw Scores
Calculating r with IBM SPSS
Spearman's Rank-Order Correlation Coefficient
Correlation Does Not Prove Causation
The Effects of Score Transformations
Cautions Concerning Correlation Coefficients
Summary
Prediction
The Problem of Prediction
The Criterion of Best Fit
Point of Controversy: Least-Squares Regression versus the Resistant Line
The Regression Equation: Standard-Score Form
The Regression Equation: Raw-Score Form
Error of Prediction: The Standard Error of Estimate
An Alternative (and Preferred) Formula for S_YX
Calculating the "Raw-Score" Regression Equation and Standard Error of Estimate with IBM SPSS
Error in Estimating Y from X
Cautions Concerning Estimation of Predictive Error
Prediction Does Not Prove Causation
Summary
Interpretive Aspects of Correlation and Regression
Factors Influencing r: Degree of Variability in Each Variable
Interpretation of r: The Regression Equation I
Interpretation of r: The Regression Equation II
Interpretation of r: Proportion of Variation in Y Not Associated with
Variation in X
Interpretation of r: Proportion of Variation in Y Associated with
Variation in X
Interpretation of r: Proportion of Correct Placements
Summary
Probability
Defining Probability
A Mathematical Model of Probability
Two Theorems in Probability
An Example of a Probability Distribution: The Binomial
Applying the Binomial
Probability and Odds
Are Amazing Coincidences Really That Amazing?
Summary
Random Sampling and Sampling Distributions
Random Sampling
Using a Table of Random Numbers
The Random Sampling Distribution of the Mean: An Introduction
Characteristics of the Random Sampling Distribution of the Mean
Using the Sampling Distribution of X to Determine the Probability for Different Ranges of Values of X
Random Sampling Without Replacement
Summary
Introduction to Statistical Inference: Testing Hypotheses about Single Means (z and t)
Testing a Hypothesis about a Single Mean
The Null and Alternative Hypotheses
When Do We Retain and When Do We Reject the Null Hypothesis?
Review of the Procedure for Hypothesis Testing
Dr. Brown's Problem: Conclusion
The Statistical Decision
Choice of H_A: One-Tailed and Two-Tailed Tests
Review of Assumptions in Testing Hypotheses about a Single Mean
Point of Controversy: The Single-Subject Research Design
Estimating the Standard Error of the Mean When ¿ Is Unknown
The t Distribution
Characteristics of Student's Distribution of t
Degrees of Freedom and Student's Distribution of t
An Example: Has the Violent Content of Television Programs Increased?
Calculating t from Raw Scores
Calculating t with IBM SPSS
Levels of Significance versus p-Values
Summary
Interpreting the Results of Hypothesis Testing: Effect Size, Type I and Type II Errors, and Power
A Statistically Significant Difference versus a Practically Important Difference
Point of Controversy: The Failure to Publish "Nonsignificant" Results
Effect Size
Errors in Hypothesis Testing
The Power of a Test
Factors Affecting Power: Difference between the True Population Mean and the Hypothesized Mean (Size of Effect)
Factors Affecting Power: Sample Size
Factors Affecting Power:Variability of the Measure
Factors Affecting Power: Level of Significance (¿)
Factors Affecting Power: One-Tailed versus Two-Tailed Tests
Calculating the Power of a Test
Point of Controversy: Meta-Analysis
Estimating Power and Sample Size for Tests of Hypotheses about Means
Problems in Selecting a Random Sample and in Drawing Conclusions
Summary
Testing Hypotheses about the Difference between Two Independent Groups
The Null and Alternative Hypotheses
The Random Sampling Distribution of the Difference between Two Sample Means
Properties of the Sampling Distribution of the Difference between Means
Determining a Formula for t
Testing the Hypothesis of No Difference between Two Independent Means: The Dyslexic Children Experiment
Use of a One-Tailed Test
Calculation of t with IBM SPSS
Sample Size in Inference about Two Means
Effect Size
Estimating Power and Sample Size for Tests of Hypotheses about the Difference between Two Independent Means
Assumptions Associated with Inference about the Difference between Two Independent Means
The Random-Sampling Model versus the Random-Assignment Model
Random Sampling and Random Assignment as Experimental Controls
Summary
Testing for a Difference between Two Dependent (Correlated) Groups
Determining a Formula for t
Degrees of Freedom for Tests of No Difference between Dependent Means
An Alternative Approach to the Problem of Two Dependent Means
Testing a Hypothesis about Two Dependent Means: Does Text Messaging Impair Driving?
Calculating t with IBM SPSS
Effect Size
Power
Assumptions When Testing a Hypothesis about the Difference between Two Dependent Means
Problems with Using the Dependent-Samples Design
Summary
Inference about Correlation Coefficients
The Random Sampling Distribution of r
Testing the Hypothesis that r = 0
Fisher's z' Transformation
Strength of Relationship
A Note about Assumptions
Inference When Using Spearman's r_S
Summary
An Alternative to Hypothesis Testing: Confidence Intervals
Examples of Estimation
Confidence Intervals for ¿_X
The Relation between Confidence Intervals and Hypothesis Testing
The Advantages of Confidence Intervals
Random Sampling and Generalizing Results
Evaluating a Confidence Interval
Point of Controversy: Objectivity and Subjectivity in Inferential Statistics: Bayesian Statistics
Confidence Intervals for ¿_X - ¿_Y
Sample Size Required for Confidence Intervals of ¿_X and ¿_X - ¿_Y
Confidence Intervals for ¿
Where are We in Statistical Reform?
Summary
Testing for Differences among Three or More Groups: One-Way Analysis of Variance (and Some Alternatives)
The Null Hypothesis
The Basis of One-Way Analysis of Variance:Variation within and between Groups
Partition of the Sums of Squares
Degrees of Freedom
Variance Estimates and the F Ratio
The Summary Table
Example: Does Playing Violent Video Games Desensitize People to Real-Life Aggression?
Comparison of t and F
Raw-Score Formulas for Analysis of Variance
Calculation of ANOVA for Independent Measures with IBM SPSS
Assumptions Associated with ANOVA
Effect Size
ANOVA and Power
Post Hoc Comparisons
Some Concerns about Post Hoc Comparisons
An Alternative to the F Test: Planned Comparisons
How to Construct Planned Comparisons
Analysis of Variance for Repeated Measures
Calculation of ANOVA for Repeated Measures with IBM SPSS
Summary
Factorial Analysis of Variance: The Two-Factor Design
Main Effects
Interaction
The Importance of Interaction
Partition of the Sums of Squares for Two-Way ANOVA
Degrees of Freedom
Variance Estimates and F Tests
Studying the Outcome of Two-Factor Analysis of Variance
Effect Size
Calculation of Two-Factor ANOVA with IBM SPSS
Planned Comparisons
Assumptions of the Two-Factor Design and the Problem of Unequal Numbers of Scores
Mixed Two-Factor Within-Subjects Design
Calculation of the Mixed Two-Factor Within-Subjects Design with IBM SPSS
Summary
Chi-Square and Inference about Frequencies
The Chi-Squre Test for Goodness of Fit
Chi-Square (¿²) as a Measure of the Difference between Observed and Expected Frequencies
The Logic of the Chi-Square Test
Interpretation of the Outcome of a Chi-Square Test
Different Hypothesized Proportions in the Test for Goodness of Fit
Effect Size for Goodness-of-Fit Problems
Assumptions in the Use of the Theoretical Distribution of Chi-Square
Chi-Square as a Test for Independence between Two Variables
Finding Expected Frequencies in a Contingency Table
Calculation of ¿² and Determination of Significance in a Contingency Table
Measures of Effect Size (Strength of Association) for Tests of Independence
Point of Controversy: Yates' Correction for Continuity
Power and the Chi-Square Test of Independence
Summary
Some (Almost) Assumption-Free Tests
The Null Hypothesis in Assumption-Freer Tests
Randomization Tests
Rank-Order Tests
The Bootstrap Method of Statistical Inference
An Assumption-Freer Alternative to the t Test of a Difference between Two Independent Groups: The Mann-Whitney U Test
Point of Controversy: A Comparison of the t Test and Mann-Whitney U Test with Real-World Distributions
An Assumption-Freer Alternative to the t Test of a Difference between Two Dependent Groups: The Sign Test
Another Assumption-Freer Alternative to the t Test of a Difference between Two Dependent Groups: The Wilcoxon Signed-Ranks Test
An Assumption-Freer Alternative to One-Way ANOVA for Independent Groups: The Kruskal-Wallis Test
An Assumption-Freer Alternative to ANOVA for Repeated Measures:
Friedman's Rank Test for Correlated Samples
Summary
Review of Basic Mathematics
List of Symbols
Answers to Problems
Statistical Tables
Areas under the Normal Curve Corresponding to Given Values of z
The Binomial Distribution
Random Numbers
Student's t Distribution
The F Distribution
The Studentized Range Statistic
Values of the Correlation Coefficient Required for Different Levels of Significance When H₀: r= 0
Values of Fisher's z' for Values of r
The ¿² Distribution
Critical One-Tail Values of SR_X for the Mann-Whitney U Test
Critical Values for the Smaller of R₊ or R_- for the Wilcoxon Signed-Ranks Test
Epilogue: The Realm of Statistics
ReferenceS
Index
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Statistical Reasoning in the Behavioral Sciences, 6th Edition

047064382X

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