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An Election: Heads vs. Tails

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Yesterday during a tangent in my Algebra 2 class I realized how little understanding my students had about the voting process as well as how predictions are made and how, when, and why networks announce winners without all of the votes counted.

Today, I ran an activity that pitted Heads vs. Tails. Each student received a penny and flipped the coin to determine their vote: Heads or Tails.  The class consisted of 19 students.

In our first election, we strictly counted votes- a popular election.  Tails beat heads 10-9.

In our second election (everyone re-flipped their coin), the girls announced first: tails 6 and heads 5.  I asked our students, what do we EXPECT to happen with the remaining 8 votes?  Assuming fair coins, we expect 4 for heads and 4 for tails.  So if we had to bet, would we bet that heads would win or tails? Since tails already had a 1 vote lead, tails was most likely to win.  In fact, the scenario most likely to result in a win for heads was 5 heads and 3 tails.  This was not a probability class, but with some basic concepts we could have given percentages to each outcome.

Back to this specific election:  With only the girls reporting, the vote was 6 for tails and 5 for heads.  I asked one boy to announce his result.  He flipped tails, so the vote count was 7 for tails and 5 for heads.  I declared, “I am ready to call the election for tails!”  The students protested; there were 7 students still left to vote.  Could heads have come back and won?  Yes, but this was unlikely since 5 of the 7 remaining flips would need to be heads.  We counted the votes and tails won 10-9 (4 of the 7 remaining flips went to heads).  I did not have a specific percentage in mind when I “called” the election (the real chance when I declared tails victorious was around 75%, but I wanted to make a point).  We discussed how, when, why (and the implications) newspapers and television stations “call elections.”

In our third election, I told the class that the front row (5 students) always voted heads and were going to vote for heads again.  With 14 students left to flip, I said that I had enough information to call the election and was sure heads would win.  Again, with the likelihood around 75% that heads would win, there was a decent chance tails could come back, but again, I was making a point.  We then discussed how this activity mirrored the Electoral College with states like California consistently voting democrat.

Finally (and I did not have time to do this election), I was going to weight each row differently.  The first row would vote and their winner would receive 4 votes, the winner of the second row would receive 3 votes, the 3rd row two votes and the back row one vote.  I was going to have each row announce in order 1-4, then redo this system with the back row announcing first.

Please leave a comment if you have any ideas on improving this exercise or need any help implementing it in your class.

The Role of Gender and Tracking in Student Achievement at the Extremes

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The following is the abstract of a recent paper I wrote analyzing student performance data. Here is a link to the entire paper.

http://dl.dropbox.com/u/33186846/Student%20Achievement%20at%20Extremes.pdf

Measurement of student achievement is at the heart of educational policy and standardized testing has been both supported and contested as a genuine representation of student achievement. This study shows that the interpretations of standardized testing may have starkly contrasting meanings for different cohorts of students. By using quantile regression to account for conditional PSAT scores, educational factors such as gender and tracking are shown to effect students in varying ways. For the students in this study, gender was a significant indicator of performance on the PSAT test, with being male accounting for more than a five point “bump.” The conclusion from the quantile regressions is that students with extreme PSAT scores are outliers based on ability or inability, not because of their gender. Meanwhile, students that participated in the “honors” tracking system had more of an increase in their predicted score the higher their conditional PSAT score.

Education: Skills or Signals?

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It’s that time of year when almost 100 million Americans go back to school.  Yes, approximately 25% of the US population is enrolled at least part-time as a student at some level of kindergarten through graduate programs.  My question is whether these students are learning skills applicable outside of the classroom or are they just earning credentials for their resume?

The easy answer is both, but I would argue that after initial universal skills are learned, education acts as a signal of ability to comprehend and analyze. It is important to distinguish between learning a skill, such as the ability to problem solve, versus signaling that you have the ability to problem solve. Before going too deep, an example should clarify the difference.

Consider high school math, in Algebra or Geometry a student may learn the skill of deductive reasoning and problem solving. Then a few years later in Calculus, the students signal that they have the requisite skills needed to comprehend Calculus concepts. Note that this signal (the ability to understand Calculus) may not be an applicable “life skill,” but if you ask a college admissions officer they would tell you it is quite valuable to signal to colleges that you are able to complete a Calculus course.

What skills will be acquired in schools this fall that will be applicable? Obviously basic reading, writing, and arithmetic are necessary skills learned in the lower grade levels. Once these skills are mastered, the second level of thinking comes into play. That is, using factual knowledge to solve problems.  Finally third level thinking, including synthesizing (or combining) knowledge from various sources to derive original thoughts and conclusions. The last two “levels of thinking” are not necessarily taught on their own, yet students acquire these skills through high school and these attributes are the base argument for a “liberal arts education” promoted by colleges.

So, when does education stop being skill based and start becoming a signaling device? My conclusion is that this balance transfer occurs in the midst of the traditional high school years. The American high school curriculum (including calendar and schedule), include many requirements that act as hurdles. Also, many advanced graduate programs fail to provide students with necessary skills. These degrees simply act as acknowledgement that a student has read the core literature of a field and does not enable students to go out into the world ready to produce original ideas.

Below are two graphs that I believe represent traditional educational paths for American students and the subsequent returns of skill development from that education. The first graph represents a student whose returns to schooling are negative, that is each year fewer skills are acquired.  Unfortunately, I believe this is the path of the majority of American students.  The second graph represents a student that take a career orientated path and ends their education in a trade school or college or graduate program that gives the student real skills to be applied outside of the classroom.

If we want education to have meaning for our students, we should gear curriculum to achieve the second path shown above.  Ideally, we could create a skill development graph that is a horizontal line where students are constantly acquiring applicable skills. This may seem far off, but if we want our future citizens to be equipped to face the challenges of an ever-changing economy and job market, we need to be sure that they are prepared with applicable skills, not a diploma that recognizes that they jumped through the appropriate hoops.

The Facebook Bubble

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An economic bubble can be defined as an overvaluation of a product or asset.  In the case of Facebook and its looming IPO (initial public offering) this week, I want to describe three potential bubbles relating to facebook.

First is in the literal sense.  By most estimations, Facebook will have the largest IPO in history: $100 Billion.  Simply, Facebook stock may simply be overvalued.  With an inflated price, a classic bubble burst may be on Facebook’s horizon.  The rationale for the inflated value may be because of two social networking bubbles.

Facebook uses each user’s personal information to sell ads.  That’s how Facebook makes its money.  Their ads are targeted based on users’ likes and clicks; they can sell their ads for a higher price because of the targeted audience.  The bubble occurs as more people become fed up by the exploitation of their personal information.  Once this practice becomes more common knowledge, I believe there will be an exodus from social networking sites that are simply shills for data gathering.

The third potential Facebook bubble is a mass departure by the people who were Facebook’s initial constituents.  Now approaching their thirty-somethings, the college students that Facebook originally targeted may be bored by a decade of the social networking site.  Many adults (mainly forty-plus) are only on Facebook because of their children.  Maybe the hype will catch up with users who are departing their roaring twenties where sharing everything was a way to connect.  Those users are now entering into their adult lives and may no longer feel the need to constantly share or to delve into their friends’ every matter.

Whether Facebook repels users by sharing their information or users finally lose interest in social networking, the company faces many unknowns while it emerges as a public company.  While twenty years from now Facebook may be the largest company in the world, if I had to put money on it, I would bet that we all look back and see Facebook as an another instance of a dot-com bubble.

An Explanation of Conditional Expectations… Part Two

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In my first (found here) of a three part series on statistical analysis, I discussed how data can inform decisions within countless industries.  My research in human capital, and specifically education, provides for various usages of data in decision making.  Specifically, available data can be used for predictions of when, where, and which students may have trouble, determinants of parental satisfaction, admission decisions (at both secondary and collegiate levels), and student achievement both academically, on standardized tests, and in future wages.

This post is intended to shed light on the science of data analysis, specifically conditional expectations.  The mathematical approach to conditional expectation is based on heavy statistical concepts, some of which are not appropriate for this venue.  That being said, my intention is to provide an accessible explanation of the techniques used in statistical analysis.  For a mathematical approach, I recommend the seminal text Econometric Analysis, by William Greene, 2002; or Econometric Analysis of Cross Section and Panel Data, by Jeffrey Wooldridge.

Econometrics, and essentially any data analysis, is based on determining a prediction.  In statistical terms, this is called an expectation.  A conditional expectation is a prediction based on available information.

For instance, consider guessing the height of a random human being.  The average human height is 5 foot 6 inches, so, this would be a logical starting point for our prediction.  But if we know more information about this random person, we can improve our expectation.  Specifically, if we knew the person was male, we would want to change our expectation conditional on that fact.  The average height of an adult man is 5 foot 9.5 inches, so that would be our new prediction given some information.

If we also knew that the person weighed 240 pounds, we may want to increase our expected height.  Note here that there is no causal assumption, just a change in our expectation, given some piece of information.  This is correlation: the taller a person is the more, on average, we expect that person to weigh.  We may predict 6 foot 1 inch for our random male weighing 240 pounds.  Data analysis can help us with our predictions, given some imperfect information.

Next, consider that we also knew this random person’s SAT score was 1200.  We probably would not consider changing our expectation of height.  If we had data on a sample of people with the variables height, sex, weight, and SAT score, some variables may be good predictors of height and be statistically significant while others, SAT score in this example, would not be statistically significant and would not persuade us to change our expectation.

Multiple Regression Analysis essentially considers a sample of data and determines the predictive success of each variable.  Using the information from a statistical data program (even excel can do this reasonably well), we can arrive at a predictive equation for the most logical expectation conditional on the information we have at our disposal.

The data will find the coefficients- the “B’s”- and also determine the likelihood that each “B” is a significant predictor.  In this case, I suspect B3 would not be statistically significant.

In part three, I will discuss an example of student achievement data from a nation-wide sample and how conditional expectations can be used to inform decisions in many fields.

The Rise of Big Data… From Moneyball to the Classroom and Back Again

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This is the first of a three-part series of posts discussing the importance of data analysis and introducing readers to the importance and value in statistical and econometric analysis.

Last Sunday, Steve Lohr wrote a great piece in the New York Times explaining the importance of “big data” in today’s society.  He explained that increasingly “businesses make sense of an explosion of data-  Web traffic and social network comments, as well as software and sensors that monitor shipments, suppliers and customers- to guide decisions, trim costs and lift sales.”

The explosion of data Lohr is referring to is accessible to any field- not just a profit maximizing business- and when used properly, that data can be used to enhance and enrich any institution.  Clearly businesses utilize data to inform their decisions, but increasingly, political campaigns, public health officials and advertising agencies are innovating their traditional practices by developing methods and metrics based on data analysis.

The most glorified example is illustrated in the book and recent film “Moneyball,” written by Michael Lewis describing the revolution in baseball by Billy Beane and the Oakland Athletics.  The short story is that the team began to analyze players using complex statistical analyses instead of traditional benchmarks.  Billy Beane is not the only front office executive to develop and exploit new statistical methods; the general manager of the Houston Rockets, Daryl Morey wrote a piece for Grantland.com regarding the “stats movement in sports” and how the success of Moneyball has transcended sports and become impacted countless industries.

Morey briefly describes how statistical analyses have entered the realm of education: the Gates foundation is gathering data to evaluate teachers.  But Morey and the Gates foundation are only scratching the surface.  Education at all levels is ripe for a takeover of objective data analyses.  Statistics currently used within schools to evaluate programs or students rely on static data.  Static data consists of the most basic statistics we remember from high school: averages and percents.  New data- big data- is about how information, records, numbers move over time and how a fact or figure can be broken down to find relationships and meaning behind the numbers.

Consider a static piece of data such as: In a specific district, 28% of parents are unhappy about their child’s school.  This does not tell an administrator much- probably only something that she already knows.  But, a deeper look into the data could reveal important information such as “of the 28% of parents who are unhappy, 70% of their students play a varsity sport.”  This has more value; specifically, there is a trend among unhappy parents.

The next two posts will dig deeper into the “why” and “how” of how data can be used to improve decision making.  At the most basic level, data can help shape expectations, specifically conditional expectations given some sort of observed trend in the data.  I will explain the concept of conditional expectation in part two.

Favorite Articles of the Year

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Every year at this time, David Brooks of the New York Times Presents the “Sydney Awards” for the best magazine essays of the year. His first installment of this year’s awards can be found here.

In a similar fashion, throughout the year I have listed my favorite newspaper and magazine pieces in the section titled “The Article I’m Reading” in the right hand column of this page. Below is a collection of four of my favorite articles from this past year; they are all well worth a read.

The biggest news story of the year was the killing of Osama Bin Laden; Nicholas Schmidle wrote a great insider piece in the New Yorker about the raid. Getting Bin Laden – Nicholas Schmidle

 In the New York Times Magazine, John Tierney described scientific findings that our decision-making worsens as we make more and more decisions. Do You Suffer from Decision Fatigue? – John Tierney

I love sports, not just for the drama on the field, but for the reality television it creates off the field. Many events transcend sports and spill over into our everyday culture. The next two pieces are indicative of how sports is intertwined, whether we like it or not, into the fabric of our lives.

Jeffery Toobin’s New Yorker piece about the New York Mets owner Fred Wilpon and his dealings with Bernie Madoff is an eye-opening account that sheds light on the interactions that impacted the Mets franchise forever.  Madoff’s Curveball – Jeffery Toobin Warning: long

Wesley Morris wrote my favorite piece of the year. His Grantland.com piece The Rise of the NBA Nerd delves into numerous social and cultural issues surrounding the NBA and American Culture itself. This is a must read. 

Check back for the next “Article I’m Reading” and for next year’s collection of My Favorite Articles of the Year!