1. Statistics and Probability Are Not Intuitive 1
We Tend to Jump to Conclusions
We Tend to be Overconfident
We See Patterns in Random Data
We Don’t Expect Variability to Depend on Sample Size
We are Fooled by Multiple Comparisons
We Tend to Ignore Alternative Explanations
We Crave Crisp Conclusions, But Statistics Offers Probabilities
2. The Complexities of Probability 6
Probability as Prediction of Long-Term Frequency Probability as Strength of Belief (Bayes)
The Distinction Between Probability and Statistics Lingo
3. From Sample to Population 11
Sampling from a Population
4. Confidence Intervals 15
Example: Survival of Premature Infants
Assumptions: Confidence Interval of a Proportion
What Does 95% Confidence Really Mean?
Are You Quantifying the Event You Really Care About?
Interpreting Confidence Intervals in Context
Confidence Intervals for Other Kinds of Data Lingo
6. Graphing Variability 32
Graphing Data to Show Scatter or Distribution
Watch Out for Preprocessed Data
7. Quantifying Variation 40
8. The Gaussian Distribution 46
How the Gaussian Distribution Arises
The Meaning of Standard Deviation in a Gaussian
What a Sample Drawn from a Gaussian Distribution Really Looks Like
Why the Gaussian Distribution is so Central to Statistical Theory
9. The Lognormal Distribution and Geometric Mean 52
Example: Relaxing Bladders
The Origin of a Lognormal Distribution
How to Analyze Lognormal Data Geometric Mean
10. Confidence Interval for a Mean 57
Interpreting a Confidence Interval for a Mean
What Values Determine the Confidence Interval for a Mean?
The Standard Error of the Mean
Assumptions: Confidence Interval for a Mean
The Appearance of Error Bars
How to Interpret Error Bars
Which Kind of Error Bar Should You Plot?
How are Standard Deviation and Standard Error
of the Mean Related to Sample Size?
12. Comparing Groups with Confidence Intervals 70
Using Confidence Intervals to Compare Groups
Examples of Confidence Intervals Used to Compare Groups
Assumuptions of Confidence Intervals
13. Comparing Groups with P Values 78
Introducing P Values via Coin Flipping
A Rule That Links Confidence Intervals and P Values Revisiting the Examples from Chapter 12
Four Things You Need to Know about P Values Lingo
| 14. Statistical Significance and Hypothesis Testing 87
Statistical Hypothesis Testing
Revisiting the Examples from Chapters 12 and 13
Analogy: Innocent Until Proven Guilty
Extremely Significant? Borderline Significant? Lingo
Choosing a Significance Level
Interpreting Results That are “Statistically Significant”
Interpreting Results That are “Not Statistically Significant” Five Explanations for “Not Statistically Significant”
16. How Common Are Type I Errors? 103
How Frequently Do Type I Errors Occur?
The Prior Probability Influences the False Discovery
Rate (A Bit of Bayes) Analogy to Clinical Testing Lingo
Why Multiple Comparisons are a Problem
A Dramatic Demonstration of the Problem with Multiple Comparisons
Multiple Comparisons in Many Contexts
How to Correct for Multiple Comparisons
18. Statistical Power and Sample Size 119
Ad Hoc Sequential Sample Size Determination Leads to Misleading Results
Interpreting a Sample Size Statement
A Calculation or a Negotiation?
An Analogy to Understand Statistical Power
Sample Size and the Margin of Error of the Confidence Interval
19. Commonly Used Statistical Tests 127
Assumptions Shared by All Standard Statistical Tests
Comparing a Continuous Variable Measured in Two Groups
Comparing a Continuous Variable Measured in Three or More Groups
Comparing a Binary Variable Assessed in Two Groups
Comparing Survival Curves
Correlation and Regression
The Problems with Normality Tests
Alternatives to Assuming a Gaussian Distribution
The Need for Outlier Tests
Five Questions to Ask Before Testing for Outliers
The Question That an Outlier Test Answers
Is It Legitimate to Remove Outliers?
Introducing the Correlation Coefficient
23. Simple Linear Regression 152
The Goals of Linear Regression
Linear Regression Results
Assumptions: Linear Regression
Comparison of Linear Regression and Correlation
24. Nonlinear, Multiple, and Logistic Regression 163
Multiple and Logistic Regression
25. Common Mistakes to Avoid When Interpreting Published Statistics 167
Mistake: Not Recognizing Publication Bias
Mistake: Testing Hypotheses Suggested by the Data
Mistake: Making a Conclusion about Causation
When the Data Only Show Correlation
Mistake: Over Interpreting Studies That Measure a Proxy or Surrogate Outcome
Mistake: Over Interpreting Data from an Observational Study
Mistake: Being Fooled by Regression to the Mean
The Fundamental Ideas of Statistics
Statistical Vocabulary by Chapter
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