Elements of Statistical Reasoning, 2nd Edition

by Edward W. Minium (San Jose State Univ.); Robert C. Clarke (San Jose State Univ.); Theodore Coladarci (Univ. of Maine)

• ISBN13: 9780471192770
• ISBN10: 0471192775
• Edition: 2nd
• Format: Paperback
• Copyright: 1998-11-01
• Publisher: Wiley

Summary

This text stresses conceptual development and the logic of statistics for use in the Behavioral Sciences. It is designed for those who need to evaluate statistical findings. Coverage includes estimation procedures, independent samples t-test, Steven's scales of measurements, Pearson correlation coefficient. Updated to include Turkey's HSD test on factorial analysis of variance and Spearman's rho on assumption-free tests and all chapter have been edited to enhance clarity and flow, to simplify numbers in the worked problems, and to align all examples with the behavioral sciences.

Author Biography

About the Authors New co-author Theodore Coladarci is Professor of Educational Psychology at the University of Maine. He has published extensively, including Elementary Descriptive Statistics, which he co-authored with A.P. Coladarci. Edward W. Minium is Professor of Psychology Emeritus at San Jose State University. He is the author of the very successful text Statistical Reasoning in Psychology and Education. Through his work, Minium has gained a highly respected reputation in the field. Robert B. Clarke is also Professor of Psychology Emeritus at San Jose State University. He co-authored Statistical Reasoning and Procedures with A.P. Coladarci and J. Caffrey.

Table of Contents

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)
9.5 The OR/addition Rule	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)
12.7 Advantages of Interval Estimation	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)
17.6 Additional Factors Affecting Power	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)
18.4 Alison's Reply of Gregory	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