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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
Michael Starbird, Ph.D.
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 51 reviewers.
Rated 4 out of 5 by My review of "Meaning From Data: Statistics Made Clear" by Michael Starbird: Professor Starbird does a good job of not only covering the concepts of statistics, but also relating them to real-world applications, such as medicine, education, health, polls, and so on. When the viewers see how the field is used in other disciplines, it becomes more relatable and meaningful. May 23, 2015
Rated 5 out of 5 by Mathematics 0ver a 24 Hour Day Professor Starbird converts mathematics into a discipline that can be directly applied to our everyday lives. He uses statistics as one more dimension to our our external rational filters that increases our appreciation of world in which we live and how we might use statistics to increase our understanding of common events we previously did not question and usually took for granted. January 31, 2015
Rated 2 out of 5 by Statistics For this specific course the instructor should have been more specific about some essential key elements of this complicated field of statistics. He jumps from linear regression to Z values without explaining basic elements of what a bell shape is or why a sample is used to extrapolate data to make conclusions. No what i was expecting from this course. December 29, 2014
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
  • 2015-05-29T17:44:24.642-05:00
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