Fundamentals of statistical reasoning in education / 2nd ed.

Introduction p. 1
Why Statistics? p. 1
Descriptive Statistics p. 2
Inferential Statistics p. 3
The Role of Statistics in Educational Research p. 4
Variables and Their Measurement p. 5
Some Tips on Studying Statistics p. 9
Descriptive Statistics p. 13
Frequency Distributions p. 15
Why Organize Data? p. 15
Frequency Distributions for Quantitative Variables p. 15
Grouped Scores p. 17
Some Guidelines for Forming Class Intervals p. 18
Constructing a Grouped-Data Frequency Distribution p. 19
The Relative Frequency Distribution p. 21
Exact Limits p. 22
The Cumulative Percentage Frequency Distribution p. 24
Percentile Ranks p. 25
Frequency Distributions for Qualitative Variables p. 27
Summary p. 28
Graphic Representation p. 37
Why Graph Data? p. 37
Graphing Qualitative Data: The Bar Chart p. 37
Graphing Quantitative Data: The Histogram p. 38
The Frequency Polygon p. 42
Comparing Different Distributions p. 43
Relative Frequency and Proportional Area p. 44
Characteristics of Frequency Distributions p. 46
The Box Plot p. 49
Summary p. 51
Central Tendency p. 59
The Concept of Central Tendency p. 59
The Mode p. 59
The Median p. 60
The Arithmetic Mean p. 62
Central Tendency and Distribution Symmetry p. 64
Which Measure of Central Tendency to Use? p. 66
Summary p. 67
Variability p. 75
Central Tendency Is Not Enough: The Importance of Variability p. 75
The Range p. 76
Variability and Deviations from the Mean p. 77
The Variance p. 78
The Standard Deviation p. 79
The Predominance of the Variance and Standard Deviation p. 81
The Standard Deviation and the Normal Distribution p. 81
Comparing Means of Two Distributions: The Relevance of Variability p. 82
In the Denominator: n vs. n - 1 p. 85
Summary p. 85
Normal Distributions and Standard Scores p. 91
A Little History: Sir Francis Galton and the Normal Curve p. 91
Properties of the Normal Curve p. 92
More on the Standard Deviation and the Normal Distribution p. 93
z Scores p. 95
The Normal Curve Table p. 97
Finding Area When the Score Is Known p. 99
Reversing the Process: Finding Scores When the Area Is Known p. 102
Comparing Scores from Different Distributions p. 104
Interpreting Effect Size p. 105
Percentile Ranks and the Normal Distribution p. 107
Other Standard Scores p. 108
Standard Scores Do Not "Normalize" a Distribution p. 110
The Normal Curve and Probability p. 110
Summary p. 111
Correlation p. 119
The Concept of Association p. 119
Bivariate Distributions and Scatterplots p. 119
The Covariance p. 124
The Pearson r p. 130
Computation of r: The Calculating Formula p. 133
Correlation and Causation p. 135
Factors Influencing Pearson r p. 136
Judging the Strength of Association: r[superscript 2] p. 139
Other Correlation Coefficients p. 141
Summary p. 142
Regression and Prediction p. 149
Correlation versus Prediction p. 149
Determining the Line of Best Fit p. 150
The Regression Equation in Terms of Raw Scores p. 153
Interpreting the Raw-Score Slope p. 156
The Regression Equation in Terms of z Scores p. 157
Some Insights Regarding Correlation and Prediction p. 158
Regression and Sums of Squares p. 161
Measuring the Margin of Prediction Error: The Standard Error of Estimate p. 163
Correlation and Causality (Revisited) p. 168
Summary p. 169
Inferential Statistics p. 179
Probability and Probability Distributions p. 181
Statistical Inference: Accounting for Chance in Sample Results p. 181
Probability: The Study of Chance p. 182
Definition of Probability p. 183
Probability Distributions p. 185
The Or/addition Rule p. 187
The And/multiplication Rule p. 188
The Normal Curve as a Probability Distribution p. 189
"So What?" Probability Distributions as the Basis for Statistical Inference p. 192
Summary p. 192
Sampling Distributions p. 197
From Coins to Means p. 197
Samples and Populations p. 198
Statistics and Parameters p. 199
Random Sampling Model p. 200
Random Sampling in Practice p. 202
Sampling Distributions of Means p. 202
Characteristics of a Sampling Distribution of Means p. 204
Using a Sampling Distribution of Means to Determine Probabilities p. 207
The Importance of Sample Size (n) p. 211
Generality of the Concept of a Sampling Distribution p. 212
Summary p. 213
Testing Statistical Hypotheses about [Mu] When [sigma] Is Known: The One-Sample z Test p. 221
Testing a Hypothesis about [Mu]: Does "Homeschooling" Make a Difference? p. 221
Dr. Meyer's Problem in a Nutshell p. 222
The Statistical Hypotheses: H[subscript 0] and H[subscript 1] p. 223
The Test Statistic z p. 225
The Probability of the Test Statistic: The p Value p. 226
The Decision Criterion: Level of Significance ([alpha]) p. 227
The Level of Significance and Decision Error p. 229
The Nature and Role of H[subscript 0] and H[subscript 1] p. 231
Rejection versus Retention of H[subscript 0] p. 232
Statistical Significance versus Importance p. 233
Directional and Nondirectional Alternative Hypotheses p. 235
Prologue: The Substantive versus the Statistical p. 237
Summary p. 239
Estimation p. 247
Hypothesis Testing versus Estimation p. 247
Point Estimation versus Interval Estimation p. 248
Constructing an Interval Estimate of [Mu] p. 249
Interval Width and Level of Confidence p. 252
Interval Width and Sample Size p. 253
Interval Estimation and Hypothesis Testing p. 253
Advantages of Interval Estimation p. 255
Summary p. 256
Testing Statistical Hypotheses about [Mu] When [sigma] Is Not Known: The One-Sample t Test p. 263
Reality: [sigma] Often Is Unknown p. 263
Estimating the Standard Error of the Mean p. 264
The Test Statistic t p. 266
Degrees of Freedom p. 267
The Sampling Distribution of Student's t p. 268
An Application of Student's t p. 270
Assumption of Population Normality p. 272
Levels of Significance versus p Values p. 273
Constructing a Confidence Interval for [Mu] When [sigma] Is Not Known p. 275
Summary p. 275
Comparing the Means of Two Populations: Independent Samples p. 283
From One Mu to Two p. 283
Statistical Hypotheses p. 284
The Sampling Distribution of Differences Between Means p. 285
Estimating [Characters not reproducible] p. 288
The t Test for Two Independent Samples p. 289
Testing Hypotheses about Two Independent Means: An Example p. 290
Interval Estimation of [Mu subscript 1] - [Mu subscript 2] p. 293
Appraising the Magnitude of a Difference: Measures of Effect Size for X[subscript 1]-X[subscript 2] p. 295
How Were Groups Formed? The Role of Randomization p. 299
Statistical Inferences and Nonstatistical Generalizations p. 300
Summary p. 301
Comparing the Means of Dependent Samples p. 309
The Meaning of "Dependent" p. 309
Standard Error of the Difference Between Dependent Means p. 310
Degrees of Freedom p. 312
The t Test for Two Dependent Samples p. 312
Testing Hypotheses about Two Dependent Means: An Example p. 315
Interval Estimation of [Mu subscript D] p. 317
Summary p. 318
Comparing the Means of Three or More Independent Samples: One-Way Analysis of Variance p. 327
Comparing More Than Two Groups: Why Not Multiple t Tests? p. 327
The Statistical Hypotheses in One-Way ANOVA p. 328
The Logic of One-Way ANOVA: An Overview p. 329
Alison's Reply to Gregory p. 332
Partitioning the Sums of Squares p. 333
Within-Groups and Between-Groups Variance Estimates p. 337
The F Test p. 337
Tukey's "HSD" Test p. 339
Interval Estimation of [Mu subscript i] - [Mu subscript j] p. 342
One-Way ANOVA: Summarizing the Steps p. 343
Estimating the Strength of the Treatment Effect: Effect Size ([Omega superscript 2]) p. 345
ANOVA Assumptions (and Other Considerations) p. 346
Summary p. 347
Inferences about the Pearson Correlation Coefficient p. 357
From [Mu] to [rho] p. 357
The Sampling Distribution of r When [rho] = 0 p. 357
Testing the Statistical Hypothesis That [rho] = 0 p. 359
An Example p. 359
Table E p. 361
The Role of n in the Statistical Significance of r p. 363
Statistical Significance versus Importance (Again) p. 364
Testing Hypotheses Other Than [rho] = 0 p. 364
Interval Estimation of [rho] p. 365
Summary p. 367
Making Inferences from Frequency Data p. 375
Frequency Data versus Score Data p. 375
A Problem Involving Frequencies: The One-Variable Case p. 376
X[superscript 2]: A Measure of Discrepancy Between Expected and Observed Frequencies p. 377
The Sampling Distribution of X[superscript 2] p. 379
Completion of the Voter Survey Problem: The X[superscript 2] Goodness-of-Fit Test p. 380
The X[superscript 2] Test of a Single Proportion p. 381
Interval Estimate of a Single Proportion p. 383
When There Are Two Variables: The X[superscript 2] Test of Independence p. 385
Finding Expected Frequencies in the Two-Variable Case p. 386
Calculating the Two-Variable X[superscript 2] p. 387
The X[superscript 2] Test of Independence: Summarizing the Steps p. 389
The 2 x 2 Contingency Table p. 390
Testing a Difference Between Two Proportions p. 391
The Independence of Observations p. 391
X[superscript 2] and Quantitative Variables p. 392
Other Considerations p. 393
Summary p. 393
Statistical "Power" (and How to Increase It) p. 403
The Power of a Statistical Test p. 403
Power and Type II Error p. 404
Effect Size (Revisited) p. 405
Factors Affected Power: The Effect Size p. 406
Factors Affecting Power: Sample Size p. 407
Additional Factors Affecting Power p. 408
Significance versus Importance p. 410
Selecting an Appropriate Sample Size p. 410
Summary p. 414
References p. 419
Review of Basic Mathematics p. 421
Introduction p. 421
Symbols and Their Meaning p. 421
Arithmetic Operations Involving Positive and Negative Numbers p. 422
Squares and Square Roots p. 422
Fractions p. 423
Operations Involving Parentheses p. 424
Approximate Numbers, Computational Accuracy, and Rounding p. 425
Answers to Selected End-of-Chapter Problems p. 426
Statistical Tables p. 448
Index p. 461
Useful Formulas p. 479