Statistical Reasoning
1
The Benefits and Risks of Using Statistics
1.1
Introductory Activity
1.2
Chapter One “The Benefits and Risks of Using Statistics”
1.3
The Physicians’ Aspirin Study
1.4
The Physicians’ Aspirin Study (continued)
1.5
Questions about the Aspirin Study
1.6
Current Population Survey, Incomes by Education
2
Reading The News
2.1
Statistics In The Media
2.2
Bad News Article
2.3
How To Defend Yourself Against Misleading Statistics In The News
2.4
A Good Looking Graph
3
Measurements, Mistakes and Misunderstandings
3.1
Types of Data
3.2
Levels of Measurement
3.3
Is Thirty-Nine Degrees Hot?
3.4
Levels of Measurement at a restaurant
3.5
Reliability and Validity
3.6
Seven Pitfalls
4
How To Get a Good Sample
4.1
Collecting a Sample of Teachers or a Sample of Voters
4.2
Non-Probability Sampling
4.3
Selection Bias
4.4
Sampling Mistakes
4.5
Probability Sampling
4.6
Simple Random Sampling
4.7
Systematic Sampling
4.8
Stratified Sampling
4.9
Why Use Stratified Sampling?
4.10
Cluster Sampling
4.11
Why Use Cluster Sampling?
4.12
Multistage Sampling
5
Experiments & Observational Studies
5.1
Video
5.2
Association
5.3
Osteoarthritis Study
5.4
Designed Experiments: Single Group Design
5.5
Observational Study
5.6
Experiemental Study
5.7
Single Factor Design
5.8
Types of Randomzied Experiments
5.9
Factorial Design
5.10
Randomized Block Design
5.11
Single-Blind Study
5.12
Double-Blind Study
5.13
Single- and Double-Blindness
6
Getting The Big Picture
7
Summarizing and Displaing Measurement Data
7.1
Class Data
7.2
Stemplot
7.3
Histogram
7.4
Measures of Central Tendency
7.5
Sample Mean
7.6
Population Mean
7.7
Median and Mode
7.8
Computing Mean, Median, Mode
7.9
Measures of Variability
7.10
Range and Five-Number Summary
7.11
Five-Number Summary
7.12
Range and Five-Number Summary
7.13
Tukey’s Rule for Outliers
7.14
Tukey’s Boxplot
7.15
Variance and Standard Deviation
7.16
Symmetric Distribution
7.17
Right-Skewed Distribution
7.18
Left-Skewed Distribution
7.19
Comparing Distributions
7.20
Comparing Groups
7.21
Effect of Linear Transformations
7.22
More on Comparing Distributions
7.23
Add/Subtract a constant
7.24
Multiply/Divide by a constant
7.25
Linear Transformation
8
Normal Distribution
8.1
Normal probability density function
8.2
Properties
8.3
Standardization
8.4
Empirical Rule
8.5
Normal Probabilities With a Table
8.6
Inverse Normal Problem
8.7
Use the
\(z\)
-score formula
8.8
Middle
\(100(1-\alpha)\)
% of the Normal Distribution
9
Chapter 9: Graphs, Good and (mostly) Bad
9.1
Characteristics of a Good Graph
9.2
Graphs for Categorical Data
9.3
Graphs for Measurement Data
9.4
Time Series Graphs
9.5
The “Best” Graph Ever (you may not agree)
9.6
The “Worst” Graphs Ever
10
Correlation
10.1
Univariate Statistics vs Bivariate Statistics
10.2
Scatterplot
10.3
The Correlation Coefficient
10.4
Correlation does not imply causation
10.5
Calculating the correlation coefficient
11
Linear Regression
11.1
Guessing the Line of Best Fit
11.2
Finding the Line of Best Fit
11.3
Interpreting the Regression Model
11.4
Dangers of Extrapolation
12
Relationships Between Categorical Variables
12.1
Probability vs Odds
12.2
A
\(2 \times 2\)
Contingency Table
12.3
Relative Risk,
\(RR\)
12.4
Odds Ratio,
\(OR\)
12.5
A Typical Medical Journal
12.6
Relative Risk vs Odds Ratio
12.7
A Larger Contingency Table
13
Statistical Significance for 2 x 2 Tables
14
Understanding Probablity
14.1
Definitions
14.2
Personal (Subjective) Probability
14.3
Objective Probability
14.4
Law of Large Numbers
14.5
Classical Probability
14.6
The Deck of Cards
14.7
Probabilities from Cards
14.8
Blood Type Problem
14.9
Addition Rule
14.10
Complement Rule
14.11
Multiplication Rule
14.12
Coin Flipping (independent)
14.13
Expected Value
14.14
Expected Value of a Casino Game
14.15
Expected Value of Insurance
14.16
Let’s Make a Deal
15
Chapter 15
16
Chapter 16
17
Chapter 17
18
Chapter 18
19
Sampling Distributions
19.1
Rule For Sample Proportions
19.2
Central Limit Theorem
20
Confidence Intervals For Proportions
20.1
Format and Formula for CIs
20.2
Polling Example
20.3
Correct Interpretations of CIs
21
Confidence Intervals for Means
21.1
Confidence Interval Based On the
\(z\)
distribution
21.2
What if We Don’t Know
\(\sigma\)
?
21.3
The
\(t\)
-distribution
21.4
Confidence Interval Based On the
\(t\)
distribution
21.5
Some example of confidence intervals from the scientific literature
22
Hypothesis Testing
22.1
One-Proportion
\(Z\)
-test
22.2
Six Step Method for Hypothesis Testing
22.3
Relationship Between a Two-Sided Test and a CI
22.4
What if We Have a One-Sided Test?
22.5
The Concept of Hypothesis Testing
22.6
Type I and II Error
22.7
Statistical & Practical Significance
22.8
Are P-Values Broken??
23
Hypothesis Tests About One Mean
23.1
Confidence Interval Based On the
\(t\)
distribution (Review)
23.2
The
\(z\)
-test for a Single Mean
23.3
The
\(t\)
-test for a Single Mean
24
Hypothesis Tests About Two Means
24.1
Paired Samples
\(t\)
-test
24.2
Example of Paired Samples
24.3
Independent Samples
\(t\)
-test
24.4
Unequal Variances
25
Meta-analysis
25.1
Defintion
25.2
What To Include
25.3
Combining Results
25.4
The ‘Pygmalion’ Study example and the Forest Plot
25.5
Wine and Beer Consumption example
25.6
Marital Quality example
25.7
Poll Aggregators
26
Ethics In Statistics
26.1
The Milgram Experiment
26.2
Informed Consent
26.3
Data Snooping/Fishing and
\(p\)
-hacking
26.4
Deception at Duke
26.5
The Ronald Fisher Controversy
26.6
David Blackwell’s Experience with Racism
Published with bookdown
STA 125 Notes (Statistical Reasoning)
Chapter 13
Statistical Significance for 2 x 2 Tables