Table of contents for Statistics : a gentle introduction / Frederick L. Coolidge.

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Table of Contents
o Chapter 1 ? A Gentle Introduction
o Don?t Panic!
o How Much Math Do I Need to Do Statistics?
o The General Purpose of Statistics: Understanding the World
o Another Purpose of Statistics: Making an Argument or a Decision
o What Is a Statistician?
* One Role: The Curious Detective
* Another Role: The Honest Attorney
* A Final Role: A Good Storyteller
o Liberal and Conservative Statisticians
o Descriptive and Inferential Statistics
o Experiments Are Designed to Test Theories and Hypotheses
o Oddball Theories
o Bad Science and Myths
o Eight Essential Questions of Any Survey or Study
* Who was surveyed or studied?
* Why did the people participate in the study?
* Was there a control group and did the control group receive a placebo?
* How many people participated in the study?
* How were the questions worded to the participants in the study?
* Was causation assumed from a correlational study?
* Who paid for the study?
* Was the study published in a peer-reviewed journal?
o On Making Samples Representative of the Population
o Experimental Design and Statistical Analysis as Controls
o The Language of Statistics
o On Conducting Scientific Experiments
o The Dependent Variable and Measurement
o Operational Definitions
o Measurement Error
o Measurement Scales: The Difference Between Continuous and Discrete Variables
o Types of Measurement Scales
o Rounding Numbers and Rounding Error
o Statistical Symbols
o History Trivia ? Achenwall to Nightingale 
o Key Terms, Symbols, and Definitions
o Chapter 1 Practice Problems
o Chapter 1 Test Questions
o Chapter 2 ? Descriptive Statistics: Understanding Distributions of Numbers
o Chapter 2 Goals
* Learn the purposes of graphs and tables
* Learn how a good graph stopped a cholera epidemic 
* Learn how bad graphs and tables contributed to the Space Shuttle Challenger explosion 
* Learn how to make graphs and tables
* Understand how to avoid chart junk 
* Learn how to make a frequency distribution
* Understand the essential characteristics of frequency distributions
o The Purpose of Graphs and Tables: Making Arguments and Decisions
o How a Good Graph Stopped a Cholera Epidemic
o How Bad Graphs and Tables Contributed to the Space Shuttle Challenger Explosion
o How a Poor PowerPoint Presentation Contributed to the Space Shuttle Columbia Disaster
o A Summary of the Purpose of Graphs and Tables
* Document the sources of statistical data and its characteristics
* Make appropriate comparisons
* Demonstrate the mechanisms of cause and effect and express the mechanisms quantitatively
* Recognize the inherent multivariate nature of analytic problems
* Inspect and evaluate alternative hypotheses
o Graphical Cautions
o Frequency Distributions
o Shapes of Frequency Distributions
o Grouping Data into Intervals
o Advice on Grouping Data into Intervals
* Choose interval widths that reduce your data to five to ten intervals
* Choose the size of your interval widths based on understandable units, for example, multiples of five or ten
* Make sure that your chosen intervals do not overlap
o The Cumulative Frequency Distribution
o Cumulative Percentages, Percentiles, and Quartiles
o Stem-and-Leaf Plot
o Non-Normal Frequency Distributions
o On the Importance of the Shapes of Distributions
o Additional Thoughts About Good Graphs Versus Bad Graphs
* Low Density Graphs
* Chart Junk
* Changing Scales Mid-Stream (or Mid-Axis)
* Labeling the Graph Badly
* The Multicolored Graph
* PowerPoint Graphs and Presentations
o History Trivia ? De Moivre to Tukey
o Key Terms and Definitions
o Chapter 2 Practice Problems
o Chapter 2 Test Questions
o Chapter 3 ? Statistical Parameters
o Measures of Central Tendency
* The Mean
* The Median
* The Mode
o Choosing Between Measures of Central Tendency
o Klinkers and Outliers
o Uncertain or Equivocal Results
o Measures of Variation
* The Range
* The Standard Deviation
o Correcting for Bias in the Sample Standard Deviation
o How the Square Root of x2 is Almost Equivalent to Taking the Absolute Value of x
o The Computational Formula for Standard Deviation
o The Variance
o The Sampling Distribution of Means, the Central Limit Theorem, and the Standard Error of the Mean
o The Use of the Standard Deviation for Prediction
o Practical Uses of the Empirical Rule: As a Definition of an Outlier
o Practical Uses of the Empirical Rule: Prediction and IQ Tests
o Some Further Comments
o History Trivia ? Fisher to Eels
o Key Terms, Symbols and Definitions
o Chapter 3 Practice Problems
o Chapter 3 Test Questions
o Chapter 4 ? Standard Scores, the Z Distribution, and Hypothesis Testing
o Standard Scores
o The Classic Standard Score: The Z Score and the Z Distribution
o Calculating Z Scores
o More Practice on Converting Raw Data into Z Scores
o Converting from Z Scores to Other Types of Standard Scores
o The Z Distribution
o Interpreting Negative Z Scores
o Testing the Predictions of the Empirical Rule with the Z Distribution
o Why is the Z Distribution So Important?
o How We Use the Z Distribution to Test Experimental Hypotheses
o More Practice with the Z Distribution and T Scores
o Summarizing Scores Through Percentiles
o History Trivia ? Karl Pearson to Egon Pearson
o Key Terms, Symbols, and Definitions
o Chapter 4 Practice Problems
o Chapter 4 Test Questions
o Chapter 5 ? Inferential Statistics: The Controlled Experiment, Hypothesis Testing, and the Z Distribution
o Hypothesis Testing in the Controlled Experiment
o Hypothesis Testing: The Big Decision
o How the Big Decision Is Made: Back to the Z Distribution
o The Parameter of Major Interest in Hypothesis Testing: The Mean
o Non-Directional and Directional Alternative Hypotheses
o A Debate: Retain the Null Hypothesis or Fail to Reject the Null Hypothesis
o The Null Hypothesis as a Non-Conservative Beginning
o The Four Possible Outcomes in Hypothesis Testing
* Correct Decision: Retain H0, When H0 is Actually True
* Type I Error: Reject H0, When H0 is Actually True
* Correct Decision: Reject H0, When H0 is Actually False
* Type II Error: Retain H0, When H0 is Actually False
o Significance Levels
o Significant and Non-Significant Findings
o Trends and Does God Really Love the .05 Level of Significance More Than the .06 Level?
o Directional or Non-Directional Alternative Hypotheses: Advantages and Disadvantages
o Did Nuclear Fusion Occur?
o Baloney Detection
* How reliable is the source of the claim?
* Does this source often make similar claims?
* Have the claims been verified by another source?
* How does the claim fit with known natural scientific laws?
* Can the claim be disproven or has only supportive evidence been sought?
* Do the claimant?s personal beliefs and biases drive their conclusions or vice versa?
o Conclusions about Science and Pseudoscience
o The Most Critical Elements in the Detection of Baloney in Suspicious Studies and Fraudulent Claims
o Can Statistics Solve Every Problem?
o Probability
* The Lady Tasting Tea
* The Definition of the Probability of an Event
* The Multiplication Theorem of Probability
* Combinations Theorem of Probability
* Permutations Theorem of Probability
* Gambler?s Fallacy
* Coda
o History Trivia ? Egon Pearson to Karl Pearson
o Key Terms, Symbols, and Definitions
o Chapter 5 Practice Problems
o Chapter 5 Test Questions
o Chapter 6 ? An Introduction to Correlation
o Correlation: Use and Abuse
o A Warning: Correlation Does Not Imply Causation
* Marijuana use and heroin use are positively correlated
* Milk use is positively correlated to cancer rates
* Weekly church attendance is negatively correlated with drug abuse
* Lead levels are positively correlated to antisocial behavior
* The risk of getting Alzheimer?s Dementia is negatively correlated with smoking cigarettes
* Sexual activity is negatively correlated with increases in education
* An active sex life is positively correlated with longevity
* Coffee drinking is negatively correlated with suicidal risk
o Another Warning: Chance Is Lumpy
o Correlation and Prediction
o The Four Common Types of Correlation
* Pearson?s r
* Spearman?s r
* Point-Biserial r
* Phi (í) Correlation
o The Pearson Product-Moment Correlation Coefficient
o Testing for the Significance of a Correlation Coefficient
o Obtaining the Critical Values of the t Distribution
* Choose a one-tailed or two-tailed test of significance
* Choose the level of significance
* Determine the degrees of freedom (df)
* Determine whether the t from the formula (called the derived t) exceeds the tabled critical values from the t distribution
o If the Null Hypothesis is Rejected
o Representing the Pearson Correlation Graphically: The Scatterplot
o Fitting the Points with a Straight Line: The Assumption of a Linear Relationship
o Interpretation of the Slope of the Best-Fitting Line
o The Assumption of Homoscedasticity
o The Coefficient of Determination: How Much One Variable Accounts for Variation in Another Variable: The Interpretation of r2
o Quirks in the Interpretation of Significant and Nonsignificant Correlation Coefficients
o Linear Regression
o Reading the Regression Line
* R
* R Square
* Adjusted R Square
o Final Thoughts About Regression Analysis
o Spearman?s Correlation
o Significance Test for Spearman?s r
o Ties in Ranks
o Point-Biserial Correlation
o Testing for the Significance of the Point-Biserial Correlation Coefficient
o Phi í Correlation
o Testing for the Significance of Phi
o History Trivia ? Galton to Fisher
o Key Terms, Symbols, and Definitions
o Chapter 6 Practice Problems
o Chapter 6 Test Questions
o Chapter 7 ?The t Test for Independent Groups
o The Statistical Analysis of the Controlled Experiment
o One t Test But Two Designs
o Assumptions of the Independent t Test
* Independent Groups
* Normality of the Dependent Variable
* Homogeneity of Variance
o The Formula for the Independent t Test
o You Must Remember This! An Overview of Hypothesis Testing with the t Test
o What Does the t Test Do?: Components of the t Test Formula
o What if the Two Variances Are Radically Different from One Another?
o A Computational Example
o Steps in the t Test Formula
o Testing the Null Hypothesis
o Steps in Determining Significance
o The Power of a Statistical Test
o Effect Size
o The Correlation Coefficient of Effect Size
o Confidence Intervals
o Estimating the Standard Error
o History Trivia ? Gosset and Guinness Brewery
o Key Terms and Definitions
o Chapter 7 Practice Problems
o Chapter 7 Test Questions
o Chapter 8 ?The t Test for Dependent Groups
o Variations on the Controlled Experiment:
o Design 1
o Design 2
o Design 3
o Assumptions of the Dependent t Test
o Why the Dependent t Test May Be More Powerful than the Independent t Test
o How to Increase the Power of a t Test
o Drawbacks of the Dependent t Test Designs
o One-Tailed or Two-Tailed Tests of Significance
o Hypothesis Testing and the Dependent t Test: Design 1 
o Design 1: Same Participants or Repeated Measures: A Computational Example
o Determination of Effect Size
o Design 2: Matched Pairs: A Computational Example
o Determination of Effect Size
o Design 3: Same Participants and Balanced Presentation: A Computational Example
o Determination of Effect Size
o History Trivia ? Fisher to Pearson
o Key Terms and Definitions 
o Chapter 8 Practice Problems
o Chapter 8 Test Questions
o Chapter 9 ? Analysis of Variance: One Factor Completely Randomized Design
o A Limitation of Multiple t Tests and a Solution
o The Equally Unacceptable Bonferroni Solution
o The Acceptable Solution: An Analysis of Variance
o The Null and Alternative Hypotheses in Analysis of Variance
o The Beauty and Elegance of the F Test Statistic
o The F Ratio
o How Can There Be Two Different Estimates of Within-Groups Variance?
o ANOVA Designs
o ANOVA Assumptions
o Pragmatic Overview
o What a Significant ANOVA Indicates
o A Computational Example
o Determining Effect Size in ANOVA 
o History Trivia ? Gosset to Fisher
o Key Terms and Definitions
o Chapter 9 Practice Problems
o Chapter 9 Test Questions
o Chapter 10 ? After a Significant Analysis of Variance: Multiple Comparison Tests
o Multiple Comparison Tests
o Conceptual Overview of Tukey?s Test
o Computation of Tukey?s HSD Test
o What to Do if the Error Degrees of Freedom Are Not Listed in the Table of Tukey?s q Values
o Determining What It All Means
o On the Importance of Nonsignificant Mean Differences
o Final Results of ANOVA
o Tukey?s with Unequal Ns
o History Trivia
o Key Terms, Symbols and Definitions
o Chapter 10 Practice Problems
o Chapter 10 Test Questions
o Chapter 11 ? Analysis of Variance: One Factor Repeated Measures Design
o The Repeated Measures ANOVA
o Assumptions of the One Factor Repeated Measures ANOVA 
o Computational Example
o Determining Effect Size in ANOVA 
o Key Terms and Definitions
o Chapter 11 Practice Problems
o Chapter 11 Test Questions
o Chapter 12 ? Analysis of Variance: Two Factor Completely Randomized Design
o Factorial Designs
o The Most Important Feature of a Factorial Design: The Interaction
o Fixed and Random Effects and In Situ Designs
o The Null Hypothesis in a Two Factor ANOVA 
o Assumptions and Unequal Numbers of Participants
o Computational Example
* Computation of the First Main Effect
* Computation of the Second Main Effect
* Computation of the Interaction Between the Two Main Effects
o Interpretation of the Results
o Key Terms and Definitions
o Chapter 12 Practice Problems
o Chapter 12 Test Questions
o Chapter 13 ? Post Hoc Analysis of Factorial ANOVA
o Main Effect Interpretation: Gender
o Why a Multiple Comparison Test is Unnecessary for a Two-Level Main Effect, and When is a Multiple Comparison Test Necessary
o Main Effect: Age Levels
o Multiple Comparison Test for the Main Effect for Age
o When Is a Multiple Comparison Test Necessary for a Significant Main Effect?
o Warning: Limit Your Main Effect Conclusions when the Interaction is Significant
o Multiple Comparison Tests
o Interpretation of Interaction Effect
o Final Summary
o Writing Up the Results Journal Style
o Language to Avoid
o Exploring the Possible Outcomes in a Two Factor ANOVA 
o Determining Effect Size in a Two Factor ANOVA 
o History Trivia ? Fisher and Smoking
o Key Terms, Symbols, and Definitions
o Chapter 13 Practice Problems
o Chapter 13 Test Questions
o Chapter 14 ? Factorial Analysis of Variance: Additional Designs
o The Split-Plot Design
o Overview of the Split-Plot ANOVA
o Computational Example
* Main Effect: Social Facilitation
* Main Effect: Trials
* Interaction Effect: Social Facilitation x Trials
o Two Factor ANOVA: Repeated Measures on Both Factors Design
o Overview of the Repeated Measures ANOVA 
o Computational Example
o History Trivia
o Key Terms and Definitions
o Chapter 14 Practice Problems
o Chapter 14 Test Questions
o Chapter 15 ? Nonparametric Statistics ? The Chi Square Test
o Overview of the Purpose of Chi Square
o Overview of Chi Square Designs
o Chi Square Designs
o Chi Square Test: Two-Cell Design (Equal Probabilities Type)
* Computation of the Two-Cell Design
o The Chi Square Distribution
o Assumptions of the Chi Square Test
o Chi Square Test: Two-Cell Design (Different Probabilities Type)
* Computation of the Two-Cell Design
o Interpreting a Significant Chi Square Test for a Newspaper
o Chi Square Test: Three-Cell Experiment (Equal Probabilities Type))
* Computation of the Three Cell Design
o Chi Square Test: Two by Two Design
* Computation of the Chi Square Test: Two by Two Design
o What to Do After a Chi Square Test Is Significant
o When Cell Frequencies Are Less Than Five Revisited
o History Trivia ? Pearson and Biometrika
o Key Terms, Symbols, and Definitions
o Chapter 15 Practice Problems
o Chapter 15 Test Questions
o Chapter 16 ? Other Statistical Parameters and Tests
o Health Science Statistics
o Test Characteristics
o Risk Assessment
o Parameters of Mortality and Morbidity
o Multivariate Statistics
o Analysis of Covariance
o Multivariate Analysis of Variance
o Multivariate Analysis of Covariance
o Factor Analysis
o Multiple Regression
o Canonical Correlation
o Linear Discriminant Function Analysis
o Cluster Analysis
o A Summary of Multivariate Statistics 
o Coda
o Key Terms and Definitions
o Chapter 16 Practice Problems
o Chapter 16 Test Questions
o Appendix A: Z Distribution
o Appendix B: The t Distribution
o Appendix C: Spearman?s Correlation
o Appendix D: The Chi Square Distribution
o Appendix E: The F Distribution
o Appendix F: Tukey?s Table
o References
o Index

Library of Congress Subject Headings for this publication:

Mathematical statistics -- Textbooks.