Introduction to Statistical Reasoning

Syllabus and Description

David Madigan

Department of Statistics

Columbia University

madigan-at-stat.columbia.eeedddduuu

The inexorable rise of computing and large-scale data storage has impacted all our lives, sometimes in profound ways. Medicine, for example, has become an information science where the tools of data analysis are as commonplace as the microscope. In the Business arena, financial markets generate rivers of intensely scrutinized data and all major global-scale retailers store and analyze vast quantities of customer and transaction data. The trend is universal and unstoppable.

Statistics as a discipline exists to develop tools for analyzing data. As such, Statistics is an engineering discipline and methodology is its core. This class aims to teach you how to tell good statistical methodology from bad. We will focus quite a bit on statistics in the media, but the lessons you learn should serve you well in many if not all professional walks of life.

Outline of Course Structure

The syllabus below describes in outline the material we hope to cover. This may change as we go, depending on time constraints and the interests of the students in the class.

Part I: FINDING DATA IN LIFE.

01. The Benefits and Risks of Using Statistics.
02. Reading the News.
03. Measurements, Mistakes and Misunderstandings.
04. How to Get a Good Sample.
05. Experiments and Observational Studies.
06. Getting the Big Picture.

Part II: FINDING LIFE IN DATA.
07. Summarizing and Displaying Measurement Data.
08. Bell-Shaped Curves and Other Shapes.
09. Plots, Graphs and Pictures.
10. Relationships Between Measurement Variables.
11. Relationships Can be Deceiving.
12. Relationships Between Categorical Variables.
13. Reading the Economic News.
14. Understanding and Reporting Trends Over Time.

Part III: UNDERSTANDING UNCERTAINTY IN LIFE.
15. Understanding Probability and Long-Term Expectations.
16. Psychological Influences on Personal Probability.
17. When Intuition Differs from Relative Frequency.

Part IV: MAKING JUDGEMENTS FROM SURVEYS AND EXPERIMENTS.
18. The Diversity of Samples from the Same Population.
19. Estimating Proportions with Confidence.
20. The Role of Confidence Intervals in Research.
21. Rejecting Chance--Testing Hypothesis in Research.
22. Hypothesis Testing--Examples and Case Studies.
23. Significance, Importance and Undetected Differences.
24. Meta-Analysis: Resolving Inconsistencies Across Studies.
25. Putting What You Have Learned to the Test.

Textbook

Jessica Utts (2005) Seeing through statistics (third edition). Brooks Cole.
This will be the primary text for the course.