A Gentle Introduction to Inference
1
The Goal
2
The Basics of Probability
2.1
Review
2.1.1
Proportions
2.1.2
The Indicator Trick
2.1.3
Percents
2.2
Chance Processes
2.2.1
The Numbered-Ticket Model
2.3
Defining Probability
2.4
Computing Probabilities
2.4.1
Counting the Equally-Likely Outcomes
2.4.2
The Probability of the Opposite
2.5
Conditional Probabilities
2.6
Multiplication Rule
2.7
Independence
2.8
Summary
2.9
Additional Exercises
3
The Numbered-Ticket Model
3.1
The Generic Form
3.2
“Is Like”
3.2.1
Key Example 1
3.2.2
Key Example 2
3.3
Summarizing the NTM Process
3.3.1
Letting a Computer Do Some Work
3.4
Expected Value and Standard Error
3.4.1
Tricks for 0-1 Boxes
3.5
The Long-Run Histogram
3.6
Summary
3.7
Additional Exercises
4
Sample Surveys
4.1
A Conceptual Framework
4.2
The Simple Random Sample
4.2.1
The Accuracy of the Simple Random Sample
4.2.2
The Importance of the Simple Random Sample
4.3
The Three Hurdles
4.4
Good Alternatives to the Simple Random Sample
4.5
Poor Alternatives to the Simple Random Samples
4.6
An Infamous Sample Survey
4.7
Modern Polling
4.8
Summary
5
Confidence Intervals
5.1
Review
5.2
The Motivating Question
5.3
Reversing the Logic
5.3.1
Replace NTM Terms with Sample Survey Terms
5.3.2
The Symmetry of Distance
5.3.3
Tense
5.4
Using the Logic
5.4.1
A Big Problem
5.4.2
A Solution
5.5
Confidence Intervals
5.5.1
Understanding a Confidence Interval
5.5.2
Interpreting a Confidence Interval
5.6
Miscellaneous
5.7
Summary
6
Hypothesis Testing
6.1
The Null Hypothesis
6.2
p
-Values
6.2.1
Focusing the Null Hypothesis
6.2.2
Computing the
p
-value for the Focused Null Hypothesis
6.3
A Summary of the Hypothesis Testing Framework
7
Extensions
7.1
Review
7.2
Sources of Randomness
7.3
Confidence Intervals in General
7.4
Hypothesis Tests in General
7.5
Statistical Significance
Appendix
A
Appendix: A Normal Table
References
Published with bookdown
A Gentle Introduction to Inference
A Gentle Introduction to Inference
Carlisle Rainey
2025-11-24
Chapter 1
The Goal
A useful, careful, and intuitive introduction to inference.