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Meaning from Data: Statistics Made Clear

Meaning from Data: Statistics Made Clear

Professor Michael Starbird Ph.D.
The University of Texas at Austin

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Meaning from Data: Statistics Made Clear

Meaning from Data: Statistics Made Clear

Professor Michael Starbird Ph.D.
The University of Texas at Austin
Course No.  1487
Course No.  1487
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Course Overview

About This Course

24 lectures  |  30 minutes per lecture

Who was the greatest baseball hitter of all time? How likely is it that a poll is correct? Is it smart to buy last year's highest-performing stock? Which hospital has the best outcome for a given procedure? When is it a good idea to buy a product's extended warranty?

These questions all involve the interpretation of statistics, as do a surprising number of other mysteries, including: Is the "hot hand" among sports players real? How can you tell if Shakespeare is the probable author of a newly discovered poem? What is a guilt-free way to get someone to admit to cheating? And, how does a tax assessor calculate the market value of a house?

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Who was the greatest baseball hitter of all time? How likely is it that a poll is correct? Is it smart to buy last year's highest-performing stock? Which hospital has the best outcome for a given procedure? When is it a good idea to buy a product's extended warranty?

These questions all involve the interpretation of statistics, as do a surprising number of other mysteries, including: Is the "hot hand" among sports players real? How can you tell if Shakespeare is the probable author of a newly discovered poem? What is a guilt-free way to get someone to admit to cheating? And, how does a tax assessor calculate the market value of a house?

Meaning from Data: Statistics Made Clear is your introduction to a vitally important subject in today's data-driven society. In 24 half-hour lectures, you will explore the principles and methods that underlie the study of statistics. You have probably heard such terms as mean, median, percentile, quartile, statistically significant, and bell curve, and you may have a rough idea of what they mean. This course sharpens your understanding of these and scores of other statistical concepts and shows how, properly used, they can extract meaning from data.

Become Statistically Savvy

These challenging yet accessible lectures assume no background in mathematics beyond basic algebra. While most introductory college statistics courses stress technical problem solving and plugging data into formulae, this course focuses on the logical foundations and underlying strategies of statistical reasoning, illustrated with plenty of examples. Professor Michael Starbird walks you through the most important equations, but his emphasis is on the role of statistics in daily life, giving you a broad overview of how statistical tools are employed in risk assessment, college admissions, drug testing, fraud investigation, and a host of other applications.

Statistical Adventures

Professor Starbird is a master at conveying concepts through examples. Some of these include:

  • When is a Lottery not a Lottery? When it is not truly random. The 1969 Vietnam War draft lottery assigned young draft-age men a ranking for induction based on their birthdays, which were placed in capsules and drawn from a container, supposedly at random. But by computing the statistical correlation for the order-of-draw, it's clear that a nonrandom variable was at play. The most likely explanation is that the capsules with the dates were not thoroughly mixed.
  • The Birthday Challenge: What is the probability that out of 50 random people, two of them share the same birthday? The chances are much higher than most people think.
  • The Chicken Soup Method: How can 1,000 randomly chosen people serve as a predictor for the behavior of hundreds of millions of voters? This is the essence of a political poll, and its effectiveness should be no more surprising than the fact that that a single taste of chicken soup is enough to predict the overall saltiness of the batch, whether the batch is in a cup or a giant vat.
  • Beware of Fallacious Reasoning: At the O. J. Simpson murder trial, Simpson's lawyer Johnnie Cochran countered evidence that Simpson had beat his wife with a statistic that only 1 in 1,000 wife beaters go on to kill their wives. Therefore, Cochran argued, there was only a 1 in 1,000 chance that Simpson went on to commit the murder. Professor Starbird discusses the fallacies in this argument, including the fact that a wife was actually murdered in this case, so the relevant question should be: What is the probability that she had previously been beaten?
  • Who Really Won the 1860 Presidential Election? Establishing the will of the people in an election can be tricky, especially when three or more candidates are involved. Professor Starbird shows how the results of the four-way presidential race of 1860 can be interpreted as giving victory to each of three candidates, depending on the voting scheme employed. Abraham Lincoln won according to the rules in place, but given other equally valid rules, the victor—and history—would have been very different.

Statistics Is Everywhere

Statistical information is truly everywhere. You can't look at a newspaper without seeing statistics on virtually every page. You can't talk about the weather forecast without invoking statistics. Statistics obviously arises in business and social science but even enters the arts in analyzing manuscripts. And you'd better not go to a casino without understanding statistics. "It's really harder to find somewhere where statistics isn't important than to find the places where it is," says Professor Starbird.

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24 Lectures
  • 1
    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? x
  • 2
    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. x
  • 3
    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. x
  • 4
    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. x
  • 5
    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. x
  • 6
    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. x
  • 7
    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. x
  • 8
    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. x
  • 9
    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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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?" x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x
  • 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. x

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Michael Starbird
Ph.D. Michael Starbird
The University of Texas at Austin

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.

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Reviews

Rated 4 out of 5 by 48 reviewers.
Rated 5 out of 5 by Ideal Introductory Course This is an excellent basic introduction to statistics. In-depth and relevant examples are presented by Dr. Starbird, who is clearly enthusiastic and knowledgeable about his subject. The course is light on math, which makes it a good overview prior to more intensive study. The focus is on fundamental concepts, strategies, and basic understanding, as well as potential shortcomings, of statistical approaches. Highly recommended. December 9, 2014
Rated 3 out of 5 by Sloppy presentation, cannot recommend Personable professor with friendly folksy style. A useful course if you want to learn about statistics, what they mean and how they're used: it is an illustrated introduction to the subject and its applications, suitable for high school as well as mature students. The first 12 lectures explain the concept and structure of statistics & data compilation, but I found the lecture on standard deviation very clumsy in presentation... this professor at times is hesitant and frequently stumbles over his words. The final 12 lectures present scenarios applying statistics, including a difficult-to-follow talk on distorting, misleading and lying statistics! The one remarkable aspect of this lecture series to me is how statistics can be used and interpreted, to produce many very different results from the same data. This is shown to be particularly the case with voting and elections, fascinating and somewhat alarming! Overall, I cannot recommend this course; I feel strongly that it could -- and assuredly should -- have been a lot better, in terms of presentation and clarity. It appears that all lectures were solo-takes whereas several ought to have been re-recorded because of the hesitancy and stumbling. I think a well-illustrated short book might be a finer investment. December 31, 2013
Rated 4 out of 5 by Great content but not deep enough This was a wonderful introduction to statistics. The professor has a great style of presentation and a wonderful sense of humor. He explains concepts well, especially the limitations of statistics. The strengths of the course were the clear explanations of the basics and how they apply to fields such as sports, voting, and the justice system. There is also a brilliant lecture on the misuse of statistics. My main concern was that some concepts should have been presented in greater detail (ANOVA, t-test, Fisher exact test, etc). Also the limitations of the normal distribution curve were not covered in sufficient detail. If your goal is a simple overview of statistics, then this course is very enjoyable and presents material that everyone should know. If, however, you need to use statistics at work or study, then you certainly need more detail than the course provides. I personally found this detail in the book 'Statistics in Plain English' by T Urdan which I also highly recommend. Overall, a very enjoyable course. November 27, 2013
Rated 5 out of 5 by Significant Insight, not a how-to If you want insight into how to extract meaning from statistical summaries then this course is for you. I wish everyone graduating from high school was required to take a course like this one. Few topics are as dry as statistics but Dr. Starbird makes it interesting and relevant. His delivery is very good, his sense of humor pleasing without being silly or annoying. The material is well chosen from real life examples of how to use and how to detect misuse of statistics. If some reviewers think that Dr. Starbird is boring or unprepared for teaching this course then they have probably never had a typical college class in statistics. My professors were mind-numbingly boring and never presented the concepts clearly, however well they did the math. I am surprised that some people bought this course expecting a tutorial how-to approach. Until the new calculus series came out none of the non-highschool courses are how-to's and the title is "Meaning from Data" not "How to Calculate Batting Averages". If that's what you want, buy this course and any of the many mathematical how-to texts out there. You will then have both a deep understanding and the ability to use statistics yourself. I have used statistics professionally and academically for decades and still this course gave me new insights into the use and abuse of statistics. Many concepts that were vague from academic studying and took years of experience to clarify are clearly revealed in this wonderful short course. By the way, it has an excellent companion in the probability course. The two subjects are so intertwined they really belong together but Dr. Starbird has done a good job of making two separate courses that complement without too much overlap. That takes deep knowledge of both subjects and good organization and planning. June 15, 2013
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