The material in this user-friendly text is presented as simply as possible to ensure that students will gain a solid understanding of statistical procedures and analysis. The goal of this book is to demystify and present statistics in a clear, cohesive manner. The student is presented with rules of evidence and the logic behind those rules. The book is divided into three major units: Descriptive Statistics, Inferential Statistics, and Advanced Topics in Inferential Statistics.
Each chapter has “Summary,” “Key Terms,” and “Problems.”
UNIT I: DESCRIPTIVE STATISTICS.
1. Introduction to Statistics.
Stumbling Blocks to Statistics.
A Brief Look at the History of Statistics.
Benefits of a Course in Statistics.
General Field of Statistics.
2. Graphs and Measures of Central Tendency.
Measures of Central Tendency.
Appropriate Use of the Mean, the Median, and the Mode.
Measures of Variability.
Graphs and Variability.
4. The Normal Curve and z Scores.
The Normal Curve.
Translating Raw Scores into z Scores.
z Score Translations in Practice.
Fun with Your Calculator.
5. z Scores Revisited: t Scores and Other Normal Curve Transformations.
Other Applications of the z Score.
The Percentile Table.
Normal Curve Equivalents.
Grade-Equivalent Scores: A Note of Caution.
The Importance of the z Score.
The Definition of Probability.
Probability and Percentage Areas of the Normal Curve.
Combining Probabilities for Independent Events.
A Reminder about Logic.
UNIT II: INFERENTIAL STATISTICS.
7. Statistics and Parameters.
Generalizing from the Few to the Many.
Key Concepts of the Inferential Statistics.
Techniques of Sampling.
Back to z.
Some Words of Encouragement.
8. Parameter Estimates and Hypothesis Testing.
The Standard Deviation Revisited.
Estimating the Standard Error of the Mean.
Estimating the Popular Mean: Interval Estimates and Hypothesis Testing.
The t ratio.
The Type 1 Error.
Interval Estimates: No Hypothesis Needed.
9. The Fundamentals of Research Methodology.
Independent and Dependent Variables.
The Cause-and-Effect Trap.
Theory of Measurement.
Research: Experimental versus Post-Facto.
The Experimental Method: The Case of Cause and Effect.
Creating Equivalent Groups: The True Experiment.
Designing the True Experiment.
The Hawthorne Effect.
Repeated Measure Designs with Separate Control Groups.
Requirements for the True Experiment.
Experimental Error: Failure to Use an Adequate Control Group.
Methodology as a Basis for More Sophisticated Techniques.
10. The Hypothesis of Difference.
Sampling Distribution of Differences.
Estimated Standard Error of Difference.
Two-Sample t Test for Independent Samples.
Two-Tail t Table.
Alpha and Confidence Levels.
Confidence Interval for Differences Between Two Independent Samples.
The Minimum Difference.
One-Tail t Test.
Importance of Having at Least Two Samples.
11. The Hypothesis of Association: Correlation.
Cause and Effect.
The Pearson r.
Interclass versus Intraclass.
The Spearman r.
An Important Difference between Correlation Coefficient and the t Test.
12. Analysis of Variance.
Advantages of ANOVA.
Analyzing the Variance.
Applications of ANOVA.
The Factorial ANOVA.
Eta squared and d.
Graphing the Interaction.
13. Nominal Data and the Chi Square.
Chi Square and Independent Samples.
Locating the Difference.
Chi Square and Percentages.
Chi Square and z Scores.
Chi Square and Dependent Samples.
Requirements for Using the Chi Square.
UNIT III: ADVANCED TOPICS IN INFERENTIAL STATISTICS.
14. Regression Analysis.
Regression of Y on X.
Standard Error of Estimate.
Confidence Interval Equation.
Multiple R (Linear Regression with More Than Two Variables).
Path Analysis, the Multiple R, and Causation.
15. Repeated-Measures and Matched-Subjects Designs with Interval Data.
Problem of Correlated of Dependent Samples.
Paired t Ratio.
Confidence Interval for Paired Differences.
Within-Subjects F Ration.
Within-Subjects Effect Size.
Testing Correlated and Experimental Data.
16. Nonparametrics Revisited: The Ordinal Case.
Mann-Whitney U Test for Two Ordinal Distributions with Independent Selection.
Kruskal-Wallis H Test for Three of More Ordinal Distributions with Independent Selection.
Wilcoxon T Test for Two Ordinal Distributions with Correlated Selection.
Friedman ANOVA by Ranks for Three or More Ordinal Distributions with Correlated Selection.
Advantages and Disadvantages of Nonparametric Tests.
17. Tests and Measurements.
Norm and Criterion Referencing: Relative versus Absolute Performance Measures.
The Problem of Bias.
Test Reliability, Validity, and Measurement Theory.
18. Computers and Statistical Analysis.
The Statistical Programs.
19. Research Simulations: Choosing the Correct Statistical Test.
Methodology: Research's Bottom Line.
Critical Decision Points.
Research Simulations: From A to Z.
The Research Enterprise.
A Final Thought: The Burden of Proof.
Special Unit: The Binomial Case.
Answer to Odd-Numbered Items (and Within-Chapter Exercises).