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What is included with this book?
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 H_{0}: 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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