Statistics: A Gentle Introduction [Kietas viršelis]

Acknowledgments		xiv
A Gentle Introduction		1	(28)
How Much Math Do I Need?		1	(1)
The Purpose of Statistics: Understanding		1	(1)
Another Purpose of Statistics: Making an Argument		1	(1)
What is a Statistician?		2	(2)
Liberal and Conservative Statisticians		4	(1)
Descriptive and Inferential Statistics		5	(1)
Experiments are Designed to Test Theories and Hypotheses		6	(1)
Oddball Theories		6	(1)
Bad Science		7	(6)
On Making Samples Representative of the Population		13	(1)
Experimental Design and Statistical Analysis as Controls		13	(2)
The Language of Statistics		15	(1)
On Conducting Scientific Experiments		15	(1)
The Dependent Variable and Measurement		16	(1)
Operational Definitions		16	(1)
Measurement Error		16	(1)
Measurement Scales: The Difference Between Continuous and Discrete Variables		17	(1)
Types of Measurement Scales		18	(2)
Rounding Numbers and Rounding Error		20	(1)
Statistical Symbols		20	(9)
History Trivia		22	(2)
Key Symbols and Terms		24	(2)
Exercises		26	(3)
Descriptive Statistics: Distributions of Numbers		29	(22)
The Purpose of Graphs and Tables: Making Arguments and Decisions		29	(3)
A Summary of the Purpose of Graphs and Tables		32	(2)
Graphical Cautions		34	(5)
Grouping Data into Intervals		39	(1)
Advice on Grouping Data into Intervals		40	(1)
The Cumulative Frequency Distribution		41	(1)
Cumulative Percentages, Percentiles, and Quartiles		42	(1)
Stem-and-Leaf Plot		43	(1)
Non-Normal Frequency Distributions		44	(1)
On the Importance of the Shapes of Distributions		45	(1)
Good Graphs versus Bad Graphs		45	(6)
History Trivia		46	(2)
Key Symbols and Terms		48	(2)
Exercises		50	(1)
Statistical Parameters		51	(18)
Measures of Central Tendency		51	(3)
Choosing Between Measures of Central Tendency		54	(1)
Klinkers and Outliers		55	(2)
Measures of Variation		57	(3)
The Computational Formula for Standard Deviation		60	(1)
The Use of the Standard Deviation for Prediction		61	(2)
Some Further Comments		63	(6)
History Trivia		64	(1)
Key Symbols and Terms		64	(2)
Exercises		66	(3)
Standard Scores, the Z Distribution, and Hypothesis Testing		69	(25)
Standard Scores		69	(1)
The Classic Standard Score: The Z Score and the Z Distribution		70	(1)
Calculating Z Scores		71	(2)
Converting From Z Scores to Other Types of Standard Scores		73	(1)
The Z Distribution		74	(1)
Interpreting Negative Z Scores		75	(1)
Testing the Predictions of the Empirical Rule with the Z Distribution		75	(1)
Where Are We Heading With All This Information?		76	(1)
How We Use the Z Distribution to Test Experimental Hypotheses		76	(2)
More Practice with the Z Distribution and T Scores		78	(11)
Summarizing Scores Through Percentiles		89	(5)
History Trivia		90	(1)
Key Symbols and Terms		91	(1)
Exercises		92	(2)
Inferential Statistics: The Archetypal Experiment, Hypothesis Testing, and the Z Distribution		94	(16)
Hypothesis Testing in the Archetypal Experiment		95	(1)
Hypothesis Testing: The Big Decision		96	(1)
How the Big Decision is Made: Back to the Z Distribution		96	(2)
The Parameter of Major Interest in Hypothesis Testing: The Mean		98	(1)
Non-Directional and Directional Alternative Hypotheses		99	(1)
A Debate: Retain the Null Hypothesis or Fail to Reject The Null Hypothesis		99	(1)
The Null Hypothesis as a Non-Conservative Beginning		100	(1)
The Four Possible Outcomes in Hypothesis Testing		101	(1)
Significance Levels		102	(1)
Significant and Non-Significant Findings		102	(1)
Trends and Does God Really Love the .05 Level of Significance More than the .06 Level?		103	(1)
Directional or Non-Directional Alternative Hypotheses: Advantages and Disadvantages		103	(1)
Did Nuclear Fusion Occur?		104	(6)
History Trivia		105	(1)
Key Symbols and Terms		106	(2)
Exercises		108	(2)
An Introduction to Correlation		110	(31)
Correlation: Use and Abuse		111	(1)
A Warning: Correlation Does Not Imply Causation		112	(2)
Another Warning: Chance is Lumpy		114	(1)
Correlation and Prediction		115	(1)
The Four Common Types of Correlation		115	(1)
The Pearson Product-Moment Correlation Coefficient		115	(3)
Testing for the Significance of a Correlation Coefficient		118	(1)
Obtaining the Critical Values of the t Distribution		119	(1)
Representing the Pearson Correlation Graphically: The Scatterplot		120	(1)
Fitting the Points with a Straight Line: The Assumption of a Linear Relationship		121	(1)
Interpretation of the Slope of the Best-Fitting Line		122	(3)
The Assumption of Homoscedasticity		125	(1)
The Coefficient of Determination: How Much One Variable Accounts for Variation in Another Variable: The Interpretation of r2		125	(1)
Quirks in the Interpretation of Significant and Non-Significant Correlation Coefficients		126	(1)
Spearman's Correlation		127	(1)
Significance Test for Spearman's r		128	(1)
Ties in Ranks		128	(2)
Point-Biserial Correlation		130	(1)
Testing for the Significance of the Point-Biserial Correlation Coefficient		131	(1)
Phi ϕ Correlation		132	(1)
Testing for the Significance of Phi		133	(8)
History Trivia		134	(1)
Key Symbols and Terms		135	(2)
Exercises		137	(4)
The Statistical Analysis of the Archetypal Experiment: The t Test for Independent Groups		141	(15)
One t test But Two Designs		142	(1)
Assumptions of the Independent t Test		143	(1)
The Formula for the Independent t Test		144	(1)
You Must Remember This!: An Overview of Hypothesis Testing with the t Test		144	(1)
What does the t Test do?: Components of the t Test Formula		144	(1)
What if Variances are Radically Different From One Another?		145	(1)
A Computational Example		146	(2)
Testing the Null Hypothesis		148	(2)
The Power of a Statistical Test		150	(1)
Effect Size		151	(1)
The Correlation Coefficient of Effect Size		151	(5)
History Trivia		152	(2)
Key Symbols and Terms		154	(1)
Exercises		155	(1)
Variations on the Archetypal Experiment: The t test for Dependent Groups		156	(16)
Design 1		156	(1)
Design 2		157	(1)
Design 3		157	(1)
Assumptions of the Dependent t Test		158	(1)
Why the Dependment t Test May Be More Powerful Than the Independent t Test		158	(1)
How to Increase the Power of a t Test		158	(1)
Drawbacks of the Dependent t Test Designs		159	(1)
One-Tailed or Two-Tailed Tests of Significance		159	(1)
Hypothesis Testing and the Dependent t Test: Design 1		160	(12)
Glossary of Key Symbols and Terms		170	(1)
Exercises		171	(1)
Analysis of Variance: One Factor Completely Randomized Design		172	(17)
A Limitation of t Tests and a Solution		172	(1)
The Equally Unacceptable Bonferroni Solution		172	(1)
The Acceptable Solution: An Analysis of Variance		173	(1)
The Null and Alternative Hypotheses in Analysis of Variance		173	(1)
The Beauty and Elegance of the F Test Statistic		174	(1)
The F Ratio		175	(1)
How Can There Be Two Different Estimates of Within-Groups Variance?		175	(2)
ANOVA Designs		177	(1)
ANOVA Assumptions		177	(1)
Pragmatic Overview		178	(1)
What a Significant ANOVA Indicates		179	(1)
A Computational Example		179	(3)
Determining Effect Size in ANOVA		182	(7)
History Trivia		183	(2)
Key Symbols and Terms		185	(2)
Exercises		187	(2)
After a Significant Analysis of Variance: Multiple Comparison Tests		189	(8)
Conceptual Overview of Tukey's Test		189	(1)
Computation of Tukey's HSD Test		190	(2)
Determining What It All Means		192	(1)
On the Importance of Non-Significant Mean Differences		193	(1)
Tukey's with Unequal Ns		193	(4)
Key Symbols and Terms		194	(1)
Exercises		195	(2)
Analysis of Variance: One Factor Repeated Measures Design		197	(8)
The Repeated Measures Design		197	(1)
Assumptions of the One Factor Repeated Measures ANOVA		198	(1)
Computational Example		198	(4)
Determining Effect Size in ANOVA		202	(3)
Key Symbols and Terms		203
Exercises		00	(205)
Analysis of Variance: Two Factor Completely Randomized Design		205	(16)
Factorial Designs		205	(1)
The Most Important Feature of a Factorial Design: The Interaction		205	(1)
Fixed and Random Effects and In Situ Designs		206	(1)
The Null Hypotheses in a Two Factor ANOVA		206	(1)
Assumptions and Unequal Numbers of Participants		207	(1)
Computational Example		207	(6)
Warning: Limit Your Main Effect Conclusions When the Interaction is Significant		213	(1)
Multiple Comparison Tests		213	(1)
Writing Up the Results Journal Style		214	(1)
Language to Avoid		214	(1)
Exploring the Possible Outcomes in a Two Factor ANOVA		215	(1)
Determining Effect Size in a Two Factor ANOVA		216	(5)
Key Symbols and Terms		217	(2)
Exercises		219	(2)
Factorial Analysis of Variance: Additional Designs		221	(18)
The Split-Plot Design		221	(1)
Overview of the Split-Plot ANOVA		221	(1)
Computational Example		222	(6)
Two Factor ANOVA: Repeated Measures on Both Factors Design		228	(1)
Overview of the Repeated Measures ANOVA		229	(1)
Computational Example		229	(10)
Key Symbols and Terms		237	(1)
Exercises		238	(1)
Nonparametric Statistics: Chi Square		239	(17)
Overview of the Purpose of Chi Square		239	(1)
Overview of Chi Square Designs		240	(1)
Chi Square Designs		240	(2)
The Chi Square Distribution		242	(1)
Power in Chi Square Analyses		242	(1)
Assumptions of the Chi Square Test		243	(2)
Interpreting a Significant Chi Square Test for a Newspaper		245	(3)
Chi Square Test: Two by Two Design		248	(2)
What To Do After a Chi Square Test is Significant		250	(1)
When Cell Frequencies are Less Than 5 Revisited		251	(5)
History Trivia		252	(1)
Key Symbols and Terms		252	(2)
Exercises		254	(2)
Other Statistical Parameters and Tests		256	(17)
Health Science Statistics		256	(4)
Risk Assessment		260	(1)
Parameters of Mortality and Morbidity		261	(2)
Multivariate Statistics		263	(1)
Analysis of Covariance		263	(1)
Multivariate Analysis of Variance		264	(1)
Multivariate Analysis of Covariance		265	(1)
Factor Analysis		265	(1)
Multiple Regression		266	(1)
Canonical Correlation		267	(1)
Linear Discriminant Function Analysis		267	(1)
Cluster Analysis		267	(6)
A Summary of Multivariate Statistics		268	(1)
Key Symbols and Terms		269	(4)
Appendix A: Z Distribution		273	(3)
Appendix B: The t Distribution		276	(1)
Appendix C: Spearman's Correlation		277	(1)
Appendix D: The Chi Square Distribution		278	(1)
Appendix E: The F Distribution		279	(4)
Appendix F: Tukey's Table		283	(2)
References		285	(2)
Index		287

Frederick L. Coolidge (Ph.D.) received his B.A., M.A., and Ph.D. in Psychology at the University of Florida. He completed a two-year postdoctoral fellowship in clinical neuropsychology at Shands Teaching Hospital in Gainesville, Florida. He has been awarded three Fulbright Fellowships to India (1987, 1992, and 2005). He has also won three teaching awards at the University of Colorado (1984, 1987, and 1992), including the lifetime title of University of Colorado Presidential Teaching Scholar. In 2005, he received the University of Colorado at Colorado Springs College of Letters, Arts, and Sciences Outstanding Research and Creative Works award. Dr. Coolidge conducts research in behavioral genetics and has established the strong heritability of gender identity and gender identity disorder. He also conducts research in lifespan personality assessment and has established the reliability of posthumous personality evaluations, and also applies cognitive models of thinking and language to explain evolutionary changes in the archaeological record.