Meaning from Data: Statistics Made Clear
Dr. Michael Starbird is Professor of Mathematics and University Distinguished Teaching Professor at The University of Texas at Austin, where he has been teaching since 1974. He received his B.A. from Pomona College in 1970 and his Ph.D. in Mathematics from the University of Wisconsin-Madison in 1974. Professor Starbird's textbook, The Heart of Mathematics: An Invitation to Effective Thinking, coauthored with Edward B. Burger, won a 2001 Robert W. Hamilton Book Award. Professors Starbird and Burger also collaborated on Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas, published in 2005. Professor Starbird has won many teaching awards, including the Mathematical Association of America's 2007 Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics, which is the association's most prestigious teaching award. It is awarded nationally to 3 people from its membership of 27,000. Professor Starbird is interested in bringing authentic understanding of significant ideas in mathematics to people who are not necessarily mathematically oriented. He has developed and taught an acclaimed class that presents higher-level mathematics to liberal arts students.
01: Describing Data and Inferring Meaning
The statistical study of data deals with two fundamental questions: How can we describe and understand a situation when we have all the pertinent data about it? How can we infer features of all the data when we know only some of the data?
02: Data and Distributions-Getting the Picture
The first three rules of statistics should be: Draw a picture, draw a picture, draw a picture. A visual representation of data reveals patterns and relationships, for example, the distribution of one variable, or an association between two variables.
03: Inference-How Close? How Confident?
The logic of statistical inference is to compare data that we collect to expectations about what the data would be if the world were random in some particular respect. Randomness and probability are the cornerstones of all methods for testing hypotheses.
04: Describing Dispersion or Measuring Spread
This lecture defines and explores standard deviation, which measures how widely data are spread from the mean. The various methods of measuring data dispersion have different properties that determine the best method to use.
05: Models of Distributions-Shapely Families
Any shaped curve can model a data set. This lecture looks at skewed and bimodal shapes, and describes other characteristically shaped classes of distributions, including exponential and Poisson. Each shape arises naturally in specific settings.
06: The Bell Curve
The most famous shape of distributions is the bell-shaped curve, also called a normal curve or a Gaussian distribution. This lecture explores its properties and why it arises so frequently-as in the central limit theorem, one of the core insights on which statistical inference is based.
07: Correlation and Regression-Moving Together
One way we attempt to understand the world is to identify cases of cause and effect. In statistics, the challenge is to describe and measure the relationship between two variables, for example, incoming SAT scores and college grade point averages.
08: Probability-Workhorse for Inference
Probability accomplishes the seemingly impossible feat of putting a useful, numerical value on the likelihood of random events. Our intuition about what to expect from randomness is often far from accurate. This lecture looks at several examples that place intuition and reality far apart.
09: Samples-The Few, The Chosen
Sampling is a technique for inferring features of a whole population from information about some of its members. A familiar example is a political poll. Interesting issues and problems arise in taking and using samples. Examples of potential pitfalls are explored.
10: Hypothesis Testing-Innocent Until
This lecture introduces a fundamental strategy of statistical inference called hypothesis testing. The method involves assessing whether observed data are consistent with a claim about the population in order to determine whether the claim might be false. Drug testing is a common application.
11: Confidence Intervals-How Close? How Sure?
Headlines at election time frequently trumpet statistics such as: "Candidate A will receive 59 percent of the vote, with a margin of error of plus or minus 3 percent." This lecture investigates what this "margin of error" statement means and why it is incomplete as written.
12: Design of Experiments-Thinking Ahead
When gathering data from which deductions can be drawn confidently, it's important to think ahead. Double-blind experiments and other strategies can help meet the goal of good experimental design.
13: Law-You're the Jury
Opening the second part of the course, which deals with applying statistics, this lecture focuses on two examples of courtroom drama: a hit-and-run accident and a gender-discrimination case. In both, the analysis of statistics aids in reaching a fair verdict.
14: Democracy and Arrow's Impossibility Theorem
An election assembles individual opinions into one societal decision. This lecture considers a surprising reality about elections: The outcome may have less to do with voters' preferences than with the voting method used, especially when three or more candidates are involved.
15: Election Problems and Engine Failure
The challenge of choosing an election winner can be thought of as taking voters' rank orderings of candidates and returning a societal rank ordering. A mathematically similar situation occurs when trying to determine what type of engine lasts longest among competing versions.
16: Sports-Who's Best of All Time?
Analyzing statistical data in sports is a sport of its own. This lecture asks, "Who is the best hitter in baseball history?" The question presents statistical challenges in comparing performances in different eras. Another mystery is also probed: "Is the 'hot hand' phenomenon real, or is it random?"
17: Risk-War and Insurance
A discussion of strategies for estimating the number of Mark V tanks produced by the Germans in World War II brings up the idea of expected value, a central concept in the risky business of buying and selling insurance.
18: Real Estate-Accounting for Value
Tax authorities often need to set valuations for every house in a tax district. The challenge is to use the data about recently sold houses to assess the values of all the houses. This classic example of statistical inference introduces the idea of multiple linear regression.
19: Misleading, Distorting, and Lying
Statistics can be used to deceive as well as enlighten. This lecture explores deceptive practices such as concealing lurking variables, using biased samples, focusing on rare events, reporting handpicked data, extrapolating trends unrealistically, and confusing correlation with causation.
20: Social Science-Parsing Personalities
This lecture addresses two topics that come up when applying statistics to social sciences: factor analysis, which seeks to identify underlying factors that explain correlation among a larger group of measured quantities, and possible limitations of hypothesis testing.
21: Quack Medicine, Good Hospitals, and Dieting
Medical treatments are commonly based on statistical studies. Aspects to consider in contemplating treatment include the characteristics of the study group and the difference between correlation and causation. Another statistical concept, regression to the mean, explains why quack medicines can appear to work.
22: Economics-"One" Way to Find Fraud
Economics relies on a wealth of statistical data, including income levels, the balance of trade, the deficit, the stock market, and the consumer price index. A surprising result of such data is that the leading digits of numbers do not occur with equal frequency, and that provides a statistical method for detecting fraud.
23: Science-Mendel's Too-Good Peas
Statistics is essential in sciences from weather forecasting to quantum physics. This lecture discusses the statistics-based research of Johannes Kepler, Edwin Hubble, and Gregor Mendel. In Mendel's case, statisticians have looked at his studies of the genetics of pea plants and discovered data that are too good to be true.
24: Statistics Everywhere
The importance of statistics will only increase as greater computer speed and capacity make dealing with ever-larger data sets possible. It has limits that need to be respected, but its potential for helping us find meaning in our data-driven world is enormous and growing.