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Tables of Contents for Elements of Statistical Reasoning
Chapter/Section Title
Page #
Page Count
Chapter 1 Introduction
1
16
1.1 Why Statistics?
1
1
1.2 Descriptive Statistics
2
1
1.3 Inferential Statistics
3
1
1.4 The Role of Statistics in Behavioral Research
4
1
1.5 Variables and Their Measurement
5
4
1.6 Approximate Numbers, Computational Accuracy, and Rounding
9
1
1.7 Computers, Statistical Analyses, and the Novice
10
1
1.8 Some Tips on Studying Statistics
11
6
PART I DESCRIPTIVE STATISTICS
17
142
Chapter 2 Frequency Distributions
17
18
2.1 Why Organize Data?
17
1
2.2 Frequency Distributions for Quantitative Variables
17
2
2.3 Grouped Scores
19
1
2.4 Some Guidelines for Forming Class Intervals
20
1
2.5 Constructing a Grouped-Data Frequency Distribution
21
2
2.6 The Relative Frequency Distribution
23
1
2.7 Exact Limits
24
2
2.8 The Cumulative Percentage Frequency Distribution
26
1
2.9 Percentile Scores and Percentile Ranks
27
1
2.10 Frequency Distributions for Qualitative Variables
28
1
2.11 Summary
29
6
Chapter 3 Graphic Representation
35
16
3.1 Why Graph Data?
35
1
3.2 Graphing Qualitative Data: The Bar Chart
35
1
3.3 Graphing Quantitative Data: The Histogram
36
4
3.4 The Frequency Polygon
40
1
3.5 Comparing Different Distributions
41
1
3.6 Relative Frequency and Proportional Area
42
2
3.7 Characteristics of Frequency Distributions
44
3
3.8 Summary
47
4
Chapter 4 Central Tendency
51
12
4.1 The Concept of Central Tendency
51
1
4.2 The Mode
51
1
4.3 The Median
52
1
4.4 The Arithmetic Mean
53
3
4.5 Central Tendency and Distribution Symmetry
56
2
4.6 Which Measure of Central Tendency to Use?
58
1
4.7 Summary
59
4
Chapter 5 Variability
63
16
5.1 Central Tendency Is Not Enough: The Importance of Variability
63
1
5.2 The Range
63
2
5.3 Variability and Deviations from the Mean
65
1
5.4 The Variance
66
1
5.5 The Standard Deviation
67
3
5.6 The Predominance of the Variance and Standard Deviation
70
1
5.7 The Standard Deviation and the Normal Distribution
71
1
5.8 Comparing Means of Two Distributions: The Relevance of Variability
72
3
5.9 Summary
75
4
Chapter 6 Normal Distributions and Standard Scores
79
24
6.1 A Little History: Sir Francis Galton and the Normal Curve
79
1
6.2 Properties of the Normal Curve
80
2
6.3 More on the Standard Deviation and the Normal Distribution
82
1
6.4 z Scores
83
3
6.5 The Normal Curve Table
86
1
6.6 Finding Area When the Score Is Known
87
3
6.7 Reversing the Process: Finding Scores When the Area Is Known
90
3
6.8 Comparing Scores from Different Distributions
93
1
6.9 Other Standard Scores
94
1
6.10 Interpreting Effect Size
95
2
6.11 Percentile Ranks and the Normal Distribution
97
1
6.12 The Normal Curve and Probability
98
1
6.13 Summary
98
5
Chapter 7 Correlation
103
28
7.1 The Concept of Association
103
1
7.2 Bivariate Distributions and Scatterplots
103
5
7.3 The Covariance
108
7
7.4 The Pearson r
115
3
7.5 Computation of r: The Calculating Formula
118
1
7.6 Correlation and Causation
119
1
7.7 Factors Influencing the Pearson r
120
4
7.8 Judging the Strength of Association
124
2
7.9 Other Correlation Coefficients
126
1
7.10 Summary
126
5
Chapter 8 Regression and Prediction
131
28
8.1 Correlation Versus Prediction
131
1
8.2 Determining the Line of Best Fit
132
3
8.3 The Regression Equation in Terms of Raw Scores
135
3
8.4 Interpreting the Raw-Score Slope
138
1
8.5 The Regression Equation in Terms of z Scores
139
1
8.6 Some Insights Regarding Correlation and Prediction
140
3
8.7 Regression and Sums of Squares
143
2
8.8 Measuring the Margin of Prediction Error: The Standard Error of Estimate
145
5
8.9 Correlation and Causality (Revisited)
150
1
8.10 Summary
151
8
PART 2 INFERENTIAL STATISTICS
159
266
Chapter 9 Probability and Probability Distributions
159
18
9.1 Statistical Inference: Accounting for Chance in Sample Results
159
1
9.2 Probability: The Study of Chance
160
1
9.3 Definition of Probability
161
2
9.4 Probability Distributions
163
2
165
2
9.6 The AND/multiplication Rule
167
1
9.7 The Normal Curve as a Probability Distribution
168
2
9.8 "So What?": Probability Distributions as the Basis for Statistical Inference
170
1
9.9 Summary
171
6
Chapter 10 Sampling Distributions
177
22
10.1 From Coins to Means
177
1
10.2 Samples and Populations
178
1
10.3 Statistics and Parameters
179
1
10.4 Random Sampling Model
180
1
10.5 Random Sampling in Practice
181
1
10.6 Sampling Distributions of Means
182
2
10.7 Characteristics of a Sampling Distribution of Means
184
3
10.8 Using a Sampling Distribution of Means to Determine Probabilities
187
4
10.9 The Importance of Sample Size (n)
191
1
10.10 Generality of the Concept of a Sampling Distribution
192
1
10.11 Summary
193
6
Chapter 11 Testing Statistical Hypotheses About Mu When XXX Is Known: The One-Sample z Test
199
22
11.1 Testing a Hypothesis About Mu: Does "Home Schooling" Make a Difference?
199
1
11.2 Dr. Meyer's Problem in a Nutshell
200
1
11.3 The Statistical Hypotheses: H(0) and H(1)
201
2
11.4 The Test Statistic: z
203
1
11.5 The Probability of the Test Statistic: The p Value
204
1
11.6 The Decision Criterion: Level of Significance (Alpha)
205
2
11.7 The Level of Significance and Decision Error
207
2
11.8 The Nature and Role of H(0) and H(1)
209
1
11.9 Rejection Versus Retention of H(0)
210
1
11.10 Statistical Significance Versus Importance
211
2
11.11 Directional and Nondirectional Alternative Hypotheses
213
2
11.12 Prologue: The Substantive Versus the Statistical
215
1
11.13 Summary
216
5
Chapter 12 Estimation
221
12
12.1 Hypothesis Testing Versus Estimation
221
1
12.2 Point Estimation Versus Interval Estimation
222
1
12.3 Constructing an Interval Estimate of Mu
223
3
12.4 Interval Width and Level of Confidence
226
1
12.5 Interval Width and Sample Size
227
1
12.6 Interval Estimation and Hypothesis Testing
227
2
229
1
12.8 Summary
230
3
Chapter 13 Testing Statistical Hypotheses About Mu When XXX Is Not Known: The One-Sample t-Test
233
18
13.1 Reality: XXX Often Is Unknown
233
1
13.2 Estimating the Standard Error of the Mean
234
2
13.3 The Test Statistic, t
236
1
13.4 Degrees of Freedom
237
1
13.5 The Sampling Distribution of Student's t
238
3
13.6 An Application of Student's t
241
2
13.7 Assumption of Population Normality
243
1
13.8 Levels of Significance Versus p Values
243
2
13.9 Constructing a Confidence Interval for Mu When XXX Is Not Known
245
1
13.10 Summary
246
5
Chapter 14 Comparing the Means of Two Populations: Independent Samples
251
24
14.1 From One Mu to Two
251
1
14.2 Statistical Hypotheses
252
1
14.3 The Sampling Distribution of Differences Between Means
253
2
14.4 Estimating XXX X(1) - X(2)
255
3
14.5 The t Test for Two Independent Samples
258
1
14.6 Testing Hypotheses About Two Independent Population Means: An Example
259
1
14.7 Interval Estimation of Mu(1) - Mu(2)
260
3
14.8 How Meaningful is the Difference? Appraising the Magnitude of X(1) - X(2)
263
3
14.9 How Were Groups Formed? The Role of Randomization
266
2
14.10 Statistical Inferences and Nonstatistical Generalizations
268
1
14.11 Summary
269
6
Chapter 15 Comparing the Means of Dependent Samples
275
18
15.1 The Meaning of "Dependent"
275
1
15.2 Standard Error of the Difference Between Dependent Means
276
2
15.3 Degrees of Freedom
278
1
15.4 The t Test for Two Dependent Samples
278
3
15.5 Testing Hypotheses About Two Dependent Means: An Example
281
4
15.6 Interval Estimation Mu(D)
285
1
15.7 Summary
286
7
Chapter 16 Inferences About the Pearson Correlation Coefficient
293
16
16.1 From Mu to p
293
1
16.2 The Sampling Distribution of r when p = 0
293
2
16.3 Testing the Statistical Hypothesis That p = 0
295
1
16.4 An Example
295
2
16.5 Table C
297
2
16.6 The Role of n in the Statistical Significance of r
299
1
16.7 Statistical Significance Versus Importance (Again)
300
1
16.8 Testing Hypotheses Other Than p = 0
301
1
16.9 Interval Estimation of p
301
3
16.10 Summary
304
5
Chapter 17 Statistical "Power" (And How to Increase It)
309
14
17.1 The Power of a Statistical Test
309
1
17.2 Power and Type 2 Error
310
1
17.3 Effect Size (Revisited)
311
1
17.4 Factors Affecting Power: The Effect Size
312
1
17.5 Factors Affecting Power: Sample Size
313
1
314
2
17.7 Significance Versus Importance
316
1
17.8 Selecting an Appropriate Sample Size
316
4
17.9 Summary
320
3
Chapter 18 Comparing the Means of Three or More Independent Samples: One-Way Analysis of Variance
323
30
18.1 Comparing More Than Two Groups: Way Not Multiple t Tests?
323
1
18.2 The Statistical Hypotheses in One-Way ANOVA
324
1
18.3 The Logic of One-Way ANOVA: An Overview
325
3
328
1
18.5 Partition of Sums of Squares
329
4
18.6 Within-Groups and Between-Groups Variance Estimates
333
1
18.7 The F Test
334
2
18.8 Raw Score Formulas for One-Way ANOVA
336
3
18.9 Tukey's "HSD" Test
339
3
18.10 Interval Estimation of Mu(i) - Mu(j)
342
1
18.11 One-Way ANOVA: Summarizing the Steps
343
2
18.12 ANOVA Assumptions (and Other Considerations)
345
1
18.13 Summary
346
7
Chapter 19 Factorial Analysis of Variance: Two-Way ANOVA
353
30
19.1 "Factorial" Designs
353
1
19.2 The Logic of Two-Way ANOVA: An Overview
354
1
19.3 An Example of a "2 X 3" Design
355
2
19.4 Main Effects
357
1
19.5 Interaction
358
3
19.6 The Importance of Interaction
361
1
19.7 Assumptions (and Other Considerations)
362
1
19.8 Partitioning the Total Sum of Squares and Degrees of Freedom
363
5
19.9 Variance Estimates and F Tests
368
2
19.10 Two-Way ANOVA: Summarizing the Steps
370
3
19.11 Summary
373
10
Chapter 20 Chi-Square and Frequency Data
383
24
20.1 Frequency Data Versus Score Data
383
1
20.2 A Problem Involving Frequencies: The One-Variable Case
384
1
20.3 X(2): A Measure of Discrepancy Between Expected and Observed Frequencies
385
2
20.4 The Sampling Distribution of X(2)
387
1
20.5 Completion of the Voter Survey Problem: The X(2) Test
388
1
20.6 The Case of Two Categories: The X(2) Test of a Single Proportion
389
2
20.7 The Two-Variable Case and the Test of Independence: Contingency Tables
391
1
20.8 The Null Hypothesis of Independence
392
2
20.9 Finding Expected Frequencies in a Contingency Table and Calculating X(2)
394
2
20.10 The X(2) Test of Independence: Summarizing the Steps
396
1
20.11 The 2 X 2 Contingency Table
397
2
20.12 The Independence of Observations
399
1
20.13 X(2) and Quantitative Variables
399
1
20.14 Other Considerations
400
1
20.15 Summary
401
6
Chapter 21 Some (Almost) Assumption-Free Tests
407
18
21.1 Parametric Versus Nonparametric Tests
407
1
21.2 Placing Scores in Rank Order
408
1
21.3 Test of Location for Two Independent Groups: The Mann-Whitney Test
409
3
21.4 Test of Location Among Several Independent Groups: The Kruskal-Wallis Test
412
3
21.5 Test of Location for Two Dependent Groups: The Sign Test
415
2
21.6 Test of Association: The Spearman Rank Correlation
417
2
21.7 Summary
419
6
References
425
2
Appendices
427
50
Appendix A Review of Basic Mathematics
427
6
Appendix B Answers to Selected End-of-Chapter Problems
433
26
Appendix C Statistical Tables
459
1
Table A Areas Under the Normal Curve
460
4
Table B Student's t Distribution
464
2
Table C Critical Values of r
466
1
Table D The F Distribution
467
3
Table E The Studentized Range Statistic
470
2
Table F The X(2) Statistic
472
2
Table G Critical Values of SigmaR(1) for the Mann-Whitney Test
474
2
Table H Critical Values for the Spearman Rank Correlation
476
1
Index
477