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David Howell's practical approach focuses on the context of statistics in behavioral research, with an emphasis on looking at data before jumping into a test. This provides students with an understanding of the logic behind the statistics: why and how certain methods are used rather than just doing techniques by rote. Students move beyond number crunching to discover the meaning of statistical results and how they relate to the research questions being asked. FUNDAMENTAL STATISTICS FOR THE BEHAVIORAL SCIENCES contains an abundance of real data and research studies as a base and moves through an analysis of data.
1. INTRODUCTION.
The Importance of Context: An Example.
Basic Terminology.
Selection Among Statistical Procedures.
Using Computers.
Summary.
Exercises.
2. BASIC CONCEPTS.
Scales of Measurement.
Variables.
Random Sampling.
Notation.
Summary.
Exercises.
3. DISPLAYING DATA.
Plotting Data.
Stem-and-Leaf Displays.
Histograms.
Reading Graphs.
Alternative Methods of Planning Data.
Describing Distributions.
Using Computer Programs to Display Data.
Summary. Exercises.
4. MEASURES OF CENTRAL TENDENCY.
The Mode.
The Median.
The Mean.
Advantages and Disadvantages of the Mode, the Median and the Mean.
Obtaining Measures of Central Tendency Using MINITAB.
A Simple Demonstration-Seeing Statistics.
Summary.
Exercises.
5. MEASURES OF VARIABILITY.
Range.
Interquartile Range and Other Range Statistics.
The Average Deviation.
The Variance.
The Standard Deviation.
Computational Formulae for the Variance and the Standard Deviation.
The Mean and the Variance as Estimators.
Boxplots: Graphical Representations of Dispersion and Extreme Scores.
Obtaining Measures of Dispersion Using JMP.
A Final Worked Example.
Seeing Statistics.
Summary.
Exercises.
6. THE NORMAL DISTRIBUTION.
The Normal Distribution.
The Standard Normal Distribution.
Setting Probable Limits on an Observation.
Measures Related to z. Summary.
Exercises.
7. BASIC CONCEPTS OF PROBABILITY.
Probability.
Basic Terminology and Rules.
Discrete versus Continuous Variables.
Probability Distributions for Discrete Variables.
Probability Distributions for Continuous Variables.
Summary.
Exercises.
8. SAMPLING DISTRIBUTIONS AND HYPOTHESIS TESTING.
Two Simple Examples Involving Course Evaluations and Rude Motorists.
Sampling Distributions.
Hypothesis Testing.
The Null Hypothesis.
Test Statistics and Their Sampling Distributions.
Using the Normal Distribution to Test Hypotheses.
Type I and Type II Errors.
One- and Two-Tailed Tests.
Seeing Statistics.
A Final Worked Example.
Back to Course Evaluations and Rude Motorists.
Summary.
Exercises.
9. CORRELATION.
Scatter Diagrams.
The Relationship Between Speed and Accuracy.
The Covariance.
The Pearson Product-Moment Correlation Coefficient (r).
Correlations with Ranked Data.
Factors That Affect the Correlation.
If Something Looks Too Good To Be True, Perhaps It Is.
Testing the Significance of a Correlation Coefficient.
Intercorrelation Matrices.
Other Correlation Coefficients.
Using MINITAB and SPSS to Obtain Correlation Coefficients.
Seeing Statistics.
A Final Worked Example.
Summary.
Exercises.
10. REGRESSION.
The Relationship Between Stress and Health.
The Basic Data.
The Regression Line.
The Accuracy of Prediction.
The Influence of Extreme Values.
Hypothesis Testing in Regression.
Computer Solution Using SPSS.
Seeing Statistics.
A Final Worked Example.
Summary.
Exercises.
11. MULTIPLE REGRESSION.
Overview.
Course Evaluations Again.
Residuals.
The Visual Representation of Multiple Regression.
Hypothesis Testing.
Refining the Regression Equation.
A Second Example: Height and Weight.
A Third Example: Psychological Symptoms in Cancer Patients.
Summary.
Exercises.
12. HYPOTHESIS TESTS APPLIED TO MEANS: ONE SAMPLE.
Sampling Distribution of the Mean.
Testing Hypotheses About Means When σ Is Known.
Testing a Sample Mean When σ Is Unknown (The One-Sample t Test).
Factors That Affect the Magnitude of t and the Decision About H0.
A Second Example: The Moon Illusion. How Large Is Our Effect-
Confidence Limits on the Mean.
Using JMP to Run One-Sample t Tests.
A Final Worked Example.
Seeing Statistics.
Summary.
Exercises.
13. HYPOTHESIS TESTS APPLIED TO MEANS: TWO RELATED SAMPLES.
Related Samples.
An Example: Student's t Applied to Difference Scores.
A Second Example: The Moon Illusion Again.
Advantages and Disadvantages of Using Related Samples.
How Large an Effect Have We Found-
Using SPSS for t Tests on Related Samples.
Summary.
Exercises.
14. HYPOTHESIS TESTS APPLIED TO MEANS: TWO INDEPENDENT SAMPLES.
Distribution of Differences Between Means.
Heterogeneity of Variance.
Nonnormality of Distributions.
A Second Example with Two Independent Samples.
Effect Size Again.
Confidence Limits on μ1-μ2.
Use of Computer Programs for Analysis of Two Independent Sample Means.
A Final Worked Example.
Seeing Statistics.
Summary.
Exercises.
15. POWER.
The Basic Concept.
Factors That Affect the Power of a Test.
Effect Size. Power Calculations for the One-Sample t Test.
Power Calculations for Differences Between Two Independent Means.
Power Calculations for the t Test for Related Samples.
Power Considerations in Terms of Sample Size.
You Don't Have to Do It by Hand.
Seeing Statistics.
Summary.
Exercises.
16. ONE WAY ANALYSIS OF VARIANCE.
The General Approach.
The Logic of the Analysis of Variance.
Calculations for the Analysis of Variance.
Unequal Sample Sizes.
Multiple Comparison Procedures.
Violations of Assumptions.
Magnitude of Effect.
Use of JMP for a One-Way Analysis of Variance.
A Final Worked Example.
Seeing Statistics.
Summary.
Exercises.
17. FACTORIAL ANALYSIS OF VARIANCE.
Factorial Designs.
The Extension of the Eysenck Study.
Interactions.
Simple Effects.
Unequal Sample Sizes.
Measures of Effect Size.
A Second Example: Maternal Adaptation Revisited.
Using SPSS for Factorial Analysis of Variance.
Seeing Statistics.
Summary.
Exercises.
18. REPEATED-MEASURES ANALYSIS OF VARIANCE.
An Example: The Treatment of Migraine Headaches.
Multiple Comparisons.
Effect Size.
Assumptions Involved in Repeated-Measures Designs.
Advantages and Disadvantages of Repeated-Measures Designs.
Using SPSS to Analyze Data in a Repeated-Measures Design.
A Final Worked Example.
Summary.
Exercises.
19. CHI-SQUARE.
One Classification Variable: The Chi-Square Goodness-of-Fit Test.
Two Classification Variables: Contingency Table Analysis.
Correction for Continuity.
Chi-Square for Larger Contingency Tables.
The Problem of Small Expected Frequencies.
The Use of Chi-Square as a Test on Proportions.
Non-Independent Observations.
MINITAB
Analysis of Contingency Tables.
A Final Worked Example.
Effect Size.
Seeing Statistics.
Summary.
Exercises.
20. NONPARAMETRIC AND DISTRIBUTION-VFREE STATISTICAL TESTS.
The Mann-Whitney Test.
Wilcoxon's Matched-Pairs Signed-Ranks Test.
Kruskal-Wallis One-Way Analysis of Variance.
Friedman's Rank Test for k Correlated Samples.
Summary.
Exercises.
21. CHOOSING THE APPROPRIATE ANALYSIS.
Exercises and Examples.
Appendix A: Arithmetic Review.
Appendix B: Symbols and Notation.
Appendix C: Basic Statistical Formulae.
Appendix D: Dataset.
Appendix E: Statistical Tables.
Glossary.
References.
Answers to Selected Exercises.
Index.
David Howell's practical approach focuses on the context of statistics in behavioral research, with an emphasis on looking at data before jumping into a test. This provides students with an understanding of the logic behind the statistics: why and how certain methods are used rather than just doing techniques by rote. Students move beyond number crunching to discover the meaning of statistical results and how they relate to the research questions being asked. FUNDAMENTAL STATISTICS FOR THE BEHAVIORAL SCIENCES contains an abundance of real data and research studies as a base and moves through an analysis of data.
Table of Contents
1. INTRODUCTION.
The Importance of Context: An Example.
Basic Terminology.
Selection Among Statistical Procedures.
Using Computers.
Summary.
Exercises.
2. BASIC CONCEPTS.
Scales of Measurement.
Variables.
Random Sampling.
Notation.
Summary.
Exercises.
3. DISPLAYING DATA.
Plotting Data.
Stem-and-Leaf Displays.
Histograms.
Reading Graphs.
Alternative Methods of Planning Data.
Describing Distributions.
Using Computer Programs to Display Data.
Summary. Exercises.
4. MEASURES OF CENTRAL TENDENCY.
The Mode.
The Median.
The Mean.
Advantages and Disadvantages of the Mode, the Median and the Mean.
Obtaining Measures of Central Tendency Using MINITAB.
A Simple Demonstration-Seeing Statistics.
Summary.
Exercises.
5. MEASURES OF VARIABILITY.
Range.
Interquartile Range and Other Range Statistics.
The Average Deviation.
The Variance.
The Standard Deviation.
Computational Formulae for the Variance and the Standard Deviation.
The Mean and the Variance as Estimators.
Boxplots: Graphical Representations of Dispersion and Extreme Scores.
Obtaining Measures of Dispersion Using JMP.
A Final Worked Example.
Seeing Statistics.
Summary.
Exercises.
6. THE NORMAL DISTRIBUTION.
The Normal Distribution.
The Standard Normal Distribution.
Setting Probable Limits on an Observation.
Measures Related to z. Summary.
Exercises.
7. BASIC CONCEPTS OF PROBABILITY.
Probability.
Basic Terminology and Rules.
Discrete versus Continuous Variables.
Probability Distributions for Discrete Variables.
Probability Distributions for Continuous Variables.
Summary.
Exercises.
8. SAMPLING DISTRIBUTIONS AND HYPOTHESIS TESTING.
Two Simple Examples Involving Course Evaluations and Rude Motorists.
Sampling Distributions.
Hypothesis Testing.
The Null Hypothesis.
Test Statistics and Their Sampling Distributions.
Using the Normal Distribution to Test Hypotheses.
Type I and Type II Errors.
One- and Two-Tailed Tests.
Seeing Statistics.
A Final Worked Example.
Back to Course Evaluations and Rude Motorists.
Summary.
Exercises.
9. CORRELATION.
Scatter Diagrams.
The Relationship Between Speed and Accuracy.
The Covariance.
The Pearson Product-Moment Correlation Coefficient (r).
Correlations with Ranked Data.
Factors That Affect the Correlation.
If Something Looks Too Good To Be True, Perhaps It Is.
Testing the Significance of a Correlation Coefficient.
Intercorrelation Matrices.
Other Correlation Coefficients.
Using MINITAB and SPSS to Obtain Correlation Coefficients.
Seeing Statistics.
A Final Worked Example.
Summary.
Exercises.
10. REGRESSION.
The Relationship Between Stress and Health.
The Basic Data.
The Regression Line.
The Accuracy of Prediction.
The Influence of Extreme Values.
Hypothesis Testing in Regression.
Computer Solution Using SPSS.
Seeing Statistics.
A Final Worked Example.
Summary.
Exercises.
11. MULTIPLE REGRESSION.
Overview.
Course Evaluations Again.
Residuals.
The Visual Representation of Multiple Regression.
Hypothesis Testing.
Refining the Regression Equation.
A Second Example: Height and Weight.
A Third Example: Psychological Symptoms in Cancer Patients.
Summary.
Exercises.
12. HYPOTHESIS TESTS APPLIED TO MEANS: ONE SAMPLE.
Sampling Distribution of the Mean.
Testing Hypotheses About Means When σ Is Known.
Testing a Sample Mean When σ Is Unknown (The One-Sample t Test).
Factors That Affect the Magnitude of t and the Decision About H0.
A Second Example: The Moon Illusion. How Large Is Our Effect-
Confidence Limits on the Mean.
Using JMP to Run One-Sample t Tests.
A Final Worked Example.
Seeing Statistics.
Summary.
Exercises.
13. HYPOTHESIS TESTS APPLIED TO MEANS: TWO RELATED SAMPLES.
Related Samples.
An Example: Student's t Applied to Difference Scores.
A Second Example: The Moon Illusion Again.
Advantages and Disadvantages of Using Related Samples.
How Large an Effect Have We Found-
Using SPSS for t Tests on Related Samples.
Summary.
Exercises.
14. HYPOTHESIS TESTS APPLIED TO MEANS: TWO INDEPENDENT SAMPLES.
Distribution of Differences Between Means.
Heterogeneity of Variance.
Nonnormality of Distributions.
A Second Example with Two Independent Samples.
Effect Size Again.
Confidence Limits on μ1-μ2.
Use of Computer Programs for Analysis of Two Independent Sample Means.
A Final Worked Example.
Seeing Statistics.
Summary.
Exercises.
15. POWER.
The Basic Concept.
Factors That Affect the Power of a Test.
Effect Size. Power Calculations for the One-Sample t Test.
Power Calculations for Differences Between Two Independent Means.
Power Calculations for the t Test for Related Samples.
Power Considerations in Terms of Sample Size.
You Don't Have to Do It by Hand.
Seeing Statistics.
Summary.
Exercises.
16. ONE WAY ANALYSIS OF VARIANCE.
The General Approach.
The Logic of the Analysis of Variance.
Calculations for the Analysis of Variance.
Unequal Sample Sizes.
Multiple Comparison Procedures.
Violations of Assumptions.
Magnitude of Effect.
Use of JMP for a One-Way Analysis of Variance.
A Final Worked Example.
Seeing Statistics.
Summary.
Exercises.
17. FACTORIAL ANALYSIS OF VARIANCE.
Factorial Designs.
The Extension of the Eysenck Study.
Interactions.
Simple Effects.
Unequal Sample Sizes.
Measures of Effect Size.
A Second Example: Maternal Adaptation Revisited.
Using SPSS for Factorial Analysis of Variance.
Seeing Statistics.
Summary.
Exercises.
18. REPEATED-MEASURES ANALYSIS OF VARIANCE.
An Example: The Treatment of Migraine Headaches.
Multiple Comparisons.
Effect Size.
Assumptions Involved in Repeated-Measures Designs.
Advantages and Disadvantages of Repeated-Measures Designs.
Using SPSS to Analyze Data in a Repeated-Measures Design.
A Final Worked Example.
Summary.
Exercises.
19. CHI-SQUARE.
One Classification Variable: The Chi-Square Goodness-of-Fit Test.
Two Classification Variables: Contingency Table Analysis.
Correction for Continuity.
Chi-Square for Larger Contingency Tables.
The Problem of Small Expected Frequencies.
The Use of Chi-Square as a Test on Proportions.
Non-Independent Observations.
MINITAB
Analysis of Contingency Tables.
A Final Worked Example.
Effect Size.
Seeing Statistics.
Summary.
Exercises.
20. NONPARAMETRIC AND DISTRIBUTION-VFREE STATISTICAL TESTS.
The Mann-Whitney Test.
Wilcoxon's Matched-Pairs Signed-Ranks Test.
Kruskal-Wallis One-Way Analysis of Variance.
Friedman's Rank Test for k Correlated Samples.
Summary.
Exercises.
21. CHOOSING THE APPROPRIATE ANALYSIS.
Exercises and Examples.
Appendix A: Arithmetic Review.
Appendix B: Symbols and Notation.
Appendix C: Basic Statistical Formulae.
Appendix D: Dataset.
Appendix E: Statistical Tables.
Glossary.
References.
Answers to Selected Exercises.
Index.