Basic Statistical Analysis

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. Every effort has been made to keep the writing as clear as possible and always aimed at the student's life space. Computational procedures are laid out in a step-by-step, programmed format. This is a straightforward presentation of the essentials of statistical analysis emphasizing the constant interaction between statistical techniques and the resarch methodology.Preface I. DESCRIPTIVE STATISTICS 1. Introduction to Statistics Stumbling Blocks to Statistics A Brief Look at the History of Statistics Gertrude Cox (1900-1978) Benefits of a Course in Statistics General Fields of Statistics Summary Key Terms and Names Problems 2. Percentages, Graphs and Measures of Central Tendency Percentage Changes-Comparing Increases with Decreases Graphs Measures of Central Tendency Appropriate Use of the Mean the Median and the Mode Summary Key Terms Problems Computer Problems 3. Variability Measures of Variability Graphs and Variability Questionnaire Percentages Key Terms Computer Problems 4. The Normal Curve and z Scores The Normal Curve z Scores Carl Friedrich Gauss (1777-1855) Translating Raw Scores into z Scores z Score Translation in Practice Fun with your Calculator Summary Key Terms and Names Problems 5. z Scores Revisited: T Scores and Other Normal Curve Transformations Other Applications of the z Score The Percentile Table T Scores Normal Cure Equivalents Stanines Grade-Equivalent Scores: A Note of Caution The Importance of the z Score Summary Key Terms Problems 6. Probability The Definition of Probability Blaise Pascal (1623-1662) Probability and Percentage Areas of the Normal Curve Combining Probabilities for Independent Events A Reminder about Logic Summary Key Terms Problems II. INFERENTIAL STATISTICS 7. Statistics and Parameters Generalizing from the Few to the Many Key Concepts of Inferential Statistics Techniques of Sampling Sampling Distributions Infinite versus Finite Sampling Galton and the Concept of Error Back to z Some Words of Encouragement Summary Key Terms Problems 8. Parameter Estimates and Hypothesis Testing Estimating the Population Standard Deviation Estimating the Standard Error of the Mean Estimating the Population of the Mean: Interval Estimates and Hypothesis Testing The t Ratio The Type 1 Error Alpha Levels Effect Size Interval Estimates: No Hypothesis Test Needed Summary Key Terms Problems Computer Problems 9. The Fundamentals of Research Methodology Research Strategies 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-Measures Designs with Separate Control Groups Requirements for the True Experiment Post Facto-Research Combination Research Research Errors Experimental Errors Meta-Analysis Methodology as a Basis for More Sophisticated Techniques Summary Key Terms Problems 10. The Hypothesis of Difference Sampling Distribution of Differences Estimated Standard Error of Difference Two-Sample t Test for Independent Samples Significance William Sealy Gossett (1876-1937) Two-Tailed t Table Alpha Levels and Confidence Level The Minimum Difference Outliner One-Tail t Test Importance of Having at Least Two Samples Power Effect Size Summary Key Terms Problems Computer Problems 11. The Hypothesis of Association: Correlation Cause and Effect The Pearson r Interclass versus Intraclass Karl Pearon (1857-1936) Missing Data Correlation Matrix The Spearman r s' 293 An Important Difference between the Correlation Correlation Coefficient and t Test Summary Key Terms and Names Problems Computer Problems 12. Analysis of Variance Advantages of ANOVA The Bonferroni Test Ronald Aylmer, Fisher (1890-1962) Analyzing the Variance Applications of ANOVA The Factorial ANOVA Eta Square and d Graphing the Interaction Summary Key Terms and Names Problems Computer Problems 13. Nominal Data and the Chi Square Chi Square and Independent Samples Locating the Difference Chi Square Percentages Square and z Scores Chi Square and Dependent Samples Requirements for Using Chi Square Summary Key Terms Problems Computer Problems III. ADVANCED TOPICS IN INFERENTIAL STATISTICS 14. Regression Analysis Regression of Y on X Sir Francis Galton (1822-1911) Standard Error of Estimate Multiple R (Linear Regression with More Than Two Variables) Path Analysis The Multiple Rand Causation Partial Correlation Summary Key Terms and Names Computer Problems 15. Repeated-Measures and Matched-Subjects Designs With Interval Data Problem of Correlated or Dependent Samples Repeated Measures, Paired t Ratio Confidence Interval for Paired Differences Within-Subjects Effect Size Testing Correlated Experimental Data Summary Key Terms Problems Computer Problems 16. Nonparametrics Revisited: The Ordinal Case Mann-Whitney U Test for Two Ordinal Distributions with Independent Selection Kruskal-Wallis H Test for Three or More Ordinal Distributions with Independent Selection Wicoxon 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 Summary Key Terms Problems 17. Tests and Measurements Norm and Criterion Referencing: Relative Versus Absolute Performance Measure The Problem of Bias Test Reliability Validityand Measurement Theory Test Validity Item Analysis Summary Key Terms Problems Computer Problems Special Unit: The Binomial Case Special Unit: The Problem of Unequal Variance Appendix A Appendix B Glossary References Answers to Odd-Numbered Items (and Within-Chapter Exercises) Index Statistical Hall of Fame Biographies Gertrude Cox-Chapter 1 Carl Gauss-Chapter 4 Blaise Pascal-Chapter 6 William Gossett-Chapter 10 Karl Pearson-Chapter 11 Ronald Fisher-Chapter 12 Sir Francis Galton-Chapter 14 Ada Lovelace-Chapter 18