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Fundamentals of statistical reasoning in education / Theodore Coladarci [and others].

Published:
Hoboken, NJ : John Wiley & Sons, [2011]
Copyright Date:
©2011
Edition:
3rd ed.
Physical Description:
xii, 468 pages : illustrations ; 24 cm + 1 CD-ROM (4 3/4 in.)
Additional Creators:
Coladarci, Theodore

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Series:
Contents:
Chapter 1. Introduction -- 1.1. Why Statistics? -- 1.2. Descriptive Statistics -- 1.3. Inferential Statistics -- 1.4. The Role of Statistics in Educational Research -- 1.5. Variables and Their Measurement -- 1.6. Some Tips on Studying Statistics -- Part 1. Descriptive Statistics -- Chapter 2. Frequency Distributions -- 2.1. Why Organize Data? -- 2.2. Frequency Distributions for Quantitative Variables -- 2.3. Grouped Scores -- 2.4. Some Guidelines for Forming Class Intervals -- 2.5. Constructing a Grouped-Data Frequency Distribution -- 2.6. The Relative Frequency Distribution -- 2.7. Exact Limits -- 2.8. The Cumulative Percentage Frequency Distribution -- 2.9. Percentile Ranks -- 2.10. Frequency Distributions for Qualitative Variables -- 2.11. Summary -- Chapter 3. Graphic Representation -- 3.1. Why Graph Data? -- 3.2. Graphing Qualitative Data: The Bar Chart -- 3.3. Graphing Quantitative Data: The Histogram -- 3.4. Relative Frequency and Proportional Area -- 3.5. Characteristics of Frequency Distributions -- 3.6. The Box Plot -- 3.7. Summary -- Chapter 4. Central Tendency -- 4.1. The Concept of Central Tendency -- 4.2. The Mode -- 4.3. The Median -- 4.4. The Arithmetic Mean -- 4.5. Central Tendency and Distribution Symmetry -- 4.6. Which Measure of Central Tendency to Use? -- 4.7. Summary -- Chapter 5. Variability -- 5.1. Central Tendency Is Not Enough: The Importance of Variability -- 5.2. The Range -- 5.3. Variability and Deviations From the Mean -- 5.4. The Variance -- 5.5. The Standard Deviation -- 5.6. The Predominance of the Variance and Standard Deviation -- 5.7. The Standard Deviation and the Normal Distribution -- 5.8. Comparing Means of Two Distributions: The Relevance of Variability -- 5.9. In the Denominator: n Versus n - 1 -- 5.10. Summary -- Chapter 6. Normal Distributions and Standard Scores -- 6.1. A Little History: Sir Francis Galton and the Normal Curve -- 6.2. Properties of the Normal Curve -- 6.3. More on the Standard Deviation and the Normal Distribution -- 6.4. z Scores -- 6.5. The Normal Curve Table -- 6.6. Finding Area When the Score Is Known -- 6.7. Reversing the Process: Finding Scores When the Area Is Known -- 6.8. Comparing Scores From Different Distributions -- 6.9. Interpreting Effect Size -- 6.10. Percentile Ranks and the Normal Distribution -- 6.11. Other Standard Scores -- 6.12. Standard Scores Do Not "Normalize" a Distribution -- 6.13. The Normal Curve and Probability -- 6.14. Summary -- Chapter 7. Correlation -- 7.1. The Concept of Association -- 7.2. Bivariate Distributions and Scatterplots -- 7.3. The Covariance -- 7.4. The Pearson r -- 7.5. Computation of r. The Calculating Formula -- 7.6. Correlation and Causation -- 7.7. Factors Influencing Pearson r -- 7.8. Judging the Strength of Association: r2 -- 7.9. Other Correlation Coefficients -- 7.10. Summary -- Chapter 8. Regression and Prediction -- 8.1. Correlation Versus Prediction -- 8.2. Determining the Line of Best Fit -- 8.3. The Regression Equation in Terms of Raw Scores -- 8.4. Interpreting the Raw-Score Slope -- 8.5. The Regression Equation in Terms of z Scores -- 8.6. Some Insights Regarding Correlation and Prediction -- 8.7. Regression and Sums of Squares -- 8.8. Measuring the Margin of Prediction Error: The Standard Error of Estimate -- 8.9. Correlation and Causality (Revisited) -- 8.10. Summary -- Part 2. Inferential Statistics -- Chapter 9. Probability and Probability Distributions -- 9.1. Statistical Inference: Accounting for Chance in Sample Results -- 9.2. Probability: The Study of Chance -- 9.3. Definition of Probability -- 9.4. Probability Distributions -- 9.5. The OR/addition Rule -- 9.6. The AND/Multiplication Rule -- 9.7. The Normal Curve as a Probability Distribution -- 9.8. "So What?"---Probability Distributions as the Basis for Statistical Inference -- 9.9. Summary -- Chapter 10. Sampling Distributions -- 10.1. From Coins to Means -- 10.2. Samples and Populations -- 10.3. Statistics and Parameters -- 10.4. Random Sampling Model -- 10.5. Random Sampling in Practice -- 10.6. Sampling Distributions of Means -- 10.7. Characteristics of a Sampling Distribution of Means -- 10.8. Using a Sampling Distribution of Means to Determine Probabilities -- 10.9. The Importance of Sample Size (n) -- 10.10. Generality of the Concept of a Sampling Distribution -- 10.11. Summary -- Chapter 11. Testing Statistical Hypotheses About μ When σ Is Known: The One-Sample z Test -- 11.1. Testing a Hypothesis About μ: Does "Homeschooling" Make a Difference? -- 11.2. Dr. Meyer's Problem in a Nutshell -- 11.3. The Statistical Hypotheses: Ho and H1 -- 11.4. The Test Statistic z -- 11.5. The Probability of the Test Statistic: The p Value -- 11.6. The Decision Criterion: Level of Significance (α) -- 11.7. The Level of Significance and Decision Error -- 11.8. The Nature and Role of H0 and H1 -- 11.9. Rejection Versus Retention of H0 -- 11.10. Statistical Significance Versus Importance -- 11.11. Directional and Nondirectional Alternative Hypotheses -- 11.12. The Substantive Versus the Statistical -- 11.13. Summary -- Chapter 12. Estimation -- 12.1. Hypothesis Testing Versus Estimation -- 12.2. Point Estimation Versus Interval Estimation -- 12.3. Constructing an Interval Estimate of μ -- 12.4. Interval Width and Level of Confidence -- 12.5. Interval Width and Sample Size -- 12.6. Interval Estimation and Hypothesis Testing -- 12.7. Advantages of Interval Estimation -- 12.8. Summary -- Chapter 13. Testing Statistical Hypotheses About μ When σ Is Not Known: The One-Sample t Test -- 13.1. Reality: σ Often Is Unknown -- 13.2. Estimating the Standard Error of the Mean -- 13.3. The Test Statistic t -- 13.4. Degrees of Freedom -- 13.5. The Sampling Distribution of Student's t -- 13.6. An Application of Student's t -- 13.7. Assumption of Population Normality -- 13.8. Levels of Significance Versus p Values -- 13.9. Constructing a Confidence Interval for μ When σ Is Not Known -- 13.10. Summary -- Chapter 14. Comparing the Means of Two Populations: Independent Samples -- 14.1. From One Mu (μ) to Two -- 14.2. Statistical Hypotheses -- 14.3. The Sampling Distribution of Differences Between Means -- 14.4. Estimating σx1-x2 -- 14.5. The t Test for Two Independent Samples -- 14.6. Testing Hypotheses About Two Independent Means: An Example -- 14.7. Interval Estimation of μ1 - μ2 -- 14.8. Appraising the Magnitude of a Difference: Measures of Effect Size for X1-X2 -- 14.9. How Were Groups Formed? The Role of Randomization -- 14.10. Statistical Inferences and Nonstatistical Generalizations -- 14.11. Summary -- Chapter 15. Comparing the Means of Dependent Samples -- 15.1. The Meaning of "Dependent" -- 15.2. Standard Error of the Difference Between Dependent Means -- 15.3. Degrees of Freedom -- 15.4. The t Test for Two Dependent Samples -- 15.5. Testing Hypotheses About Two Dependent Means: An Example -- 15.6. Interval Estimation of μD -- 15.7. Summary -- Chapter 16. Comparing the Means of Three or More Independent Samples: One-Way Analysis of Variance -- 16.1. Comparing More Than Two Groups: Why Not Multiple t Tests? -- 16.2. The Statistical Hypotheses in One-Way ANOVA -- 16.3. The Logic of One-Way ANOVA: An Overview -- 16.4. Alison's Reply to Gregory -- 16.5. Partitioning the Sums of Squares -- 16.6. Within-Groups and Between-Groups Variance Estimates -- 16.7. The F Test -- 16.8. Tukey's "HSD" Test -- 16.9. Interval Estimation of μi-μj -- 16.10. One-Way ANOVA: Summarizing the Steps -- 16.11. Estimating the Strength of the Treatment Effect: Effect Size (ω2) -- 16.12. ANOVA Assumptions (and Other Considerations) -- 16.13. Summary -- Chapter 17. Inferences About the Pearson Correlation Coefficient -- 17.1. From μ to p -- 17.2. The Sampling Distribution of r When p = O -- 17.3. Testing the Statistical Hypothesis That p = 0 -- 17.4. An Example -- 17.5. In Brief: Student's t Distribution and the Regression Slope (b) -- 17.6. Table E -- 17.7. The Role of n in the Statistical Significance of r -- 17.8. Statistical Significance Versus Importance (Again) -- 17.9. Testing Hypotheses Other Than p = 0. and 17.10. Interval Estimation of p -- 17.11. Summary -- Chapter 18. Making Inferences From Frequency Data -- 18.1. Frequency Data Versus Score Data -- 18.2. A Problem Involving Frequencies: The One-Variable Case -- 18.3. X2: A Measure of Discrepancy Between Expected and Observed Frequencies -- 18.4. The Sampling Distribution of X2 -- 18.5. Completion of the Voter Survey Problem: The X2 Goodness-of-Fit Test -- 18.6. The X2 Test of a Single Proportion -- 18.7. Interval Estimate of a Single Proportion -- 18.8. When There Are Two Variables: The X2 Test of Independence -- 18.9. Finding Expected Frequencies in the Two-Variable Case -- 18.10. Calculating the Two-Variable X2 -- 18.11. The X2 Test of Independence: Summarizing the Steps -- 18.12. The 2 X 2 Contingency Table -- 18.13. Testing a Difference Between Two Proportions -- 18.14. The Independence of Observations -- 18.15. X2 and Quantitative Variables -- 18.16. Other Considerations -- 18.17. Summary -- Chapter 19. Statistical "Power" (and How to Increase It) -- 19.1. The Power of a Statistical Test -- 19.2. Power and Type II Error -- 19.3. Effect Size (Revisited) -- 19.4. Factors Affecting Power: The Effect Size -- 19.5. Factors Affecting Power: Sample Size -- 19.6. Additional Factors Affecting Power -- 19.7. Significance Versus Importance -- 19.8. Selecting an Appropriate Sample Size -- 19.9. Summary -- Epilogue: A Note on (Almost) Assumption-Free Tests -- References -- Appendix A. Review of Basic Mathematics -- A.1. Introduction -- A.2. Symbols and Their Meaning -- A.3. Arithmetic Operations Involving Positive and Negative Numbers -- A.4. Squares and Square Roots -- A.5. Fractions -- A.6. Operations Involving Parentheses -- A.7. Approximate Numbers, Computational Accuracy, and Rounding -- Appendix B. Answers to Selected End-of-Chapter Problems -- Appendix C. Statistical Tables.
Subject(s):
ISBN:
9780470574799 (paper/cd-rom)
0470574798 (paper/cd-rom)
9780470610039 (CD-ROM)
Related Titles:
PASW statistics student version 18.
Note:
Title on accompanyingCD-ROM label: PASW statistics student version 18.
Bibliography Note:
Includes bibliographical references (pages 410-411) and index.
Technical Details:
System requirements for accompanying CD-ROM: Microsoft Windows 7, Windows XP and Windows Vista or Apple Mac 10x (Leopard) and 10.6x (Snow Leopard)
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