Chance News 33

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4. Determine how much income is needed to be in "The richest 1 percent of American households."  Compare your answer to that of number 3.
 
4. Determine how much income is needed to be in "The richest 1 percent of American households."  Compare your answer to that of number 3.
 
Submitted by Paul Alper
 
 
==Quotation==
 
 
<blockquote>     
 
It is the mark of a truly intelligent person to be moved by statistics.
 
<br> <div align=right> George Bernard Shaw</div></blockquote>
 
 
==Forsooth==
 
 
The following Forsooths are from the January 2008 issue of RSS NEWS.
 
----
 
<blockquote>In terms of platform use trends among the respondents, 53% cited Windows as their primary technical computing platform, with Linux following closely at 51%.
 
 
<div align=right>NAGNews email (NAG User Survey 2006 on technical<br> computing trends)<br>
 
August 2006  </div></blockquote>
 
----
 
<blockquote>Clearly, any product with a large user base is going to throw up some problems.  Dell, for example, is shipping almost 40m PCs a year, so even if 95% of it users are happy, there could still be 6m or so with significant gripes.<div align=right>The Guardian <br>25 January 2007</div></blockquote>
 
 
==High altitude effects on athletic performance==
 
 
[http://www.bmj.com/cgi/content/full/335/7633/1278 Effect of altitude on physiological performance: a statistical analysis using results of international football games.] Patrick E McSharry. BMJ 2007; 335: 1278-1281 (22 December).
 
 
There is a strong belief that athletes who live and train at high altitudes have an unfair advantage over those athletes visiting from lower altitudes. In response,
 
 
<blockquote>football’s governing body, the Federation of International Football Associations (FIFA), banned international matches from being played at more than 2500 m above sea level.</blockquote>
 
 
There is a plausible mechanistic explanation for this concern.
 
 
<blockquote>At high altitude hypoxia, cold, and dehydration can lead to breathlessness, headaches, nausea, dizziness, and fatigue, and possibly altitude illness including syndromes such as acute mountain sickness, high altitude pulmonary oedema, and cerebral oedema. Activities such as football can exacerbate symptoms, preventing players from performing at full capacity.</blockquote>
 
 
What would the data say. An ideal database exists to explore whether high altitude has a detrimental effect on athletes visiting from lower altitudes. In South America, which has three large cities at high altitude (Bogota, Columbia, Quito, Ecuador, and La Paz, Bolivia), there are records of 1460 football matches played over a 100 year period at a wide range of altitudes. This data set included four variables:
 
 
<blockquote>(i) the probability of a win, (ii) the number of goals scored, (iii) the number of goals conceded, and (iv) the altitude difference between the home venue of a specific team and that of the opposition.</blockquote>
 
 
as well as indicators for individual countries. This study used a logistic regression model to predict the probability of a win by the home team, and two Poisson regression models: one to predict number of goals scored by the home team and a second to predict the number of goals conceded by the home team.
 
 
http://www.bmj.com/content/vol335/issue7633/images/medium/mcsp457549.f2.gif
 
 
The graph of the predicted equations appears above. These graphs show clearly that a thousand meter difference in altitude between the home team and the opposition produces a large change in the estimated probability of a win for the home team, the expected number of goals scored by the home team, and the expected number of goals allowed by the home team.
 
 
===Questions===
 
 
1. Although the graphs are non-linear, a linear approximation is quite reasonable for the predicted values. Estimate how much change in probability of home team winning, goals scored by the home team, and goals allowed by the home team changes for each 1,000 meter change in altitude.
 
 
2. There are many variables that were not considered in this analysis. List some of the more important variables that were not included. Consider whether these variables are easy to measure or hard to measure.
 
 
3. Is there an alternate explanation other than change in altitude that could account for the differential in home team win probability, goals scored by the home team, and goals allowed by the home team?
 
 
4. Should international football matches be allowed in high altitude locations?
 
 
Submitted by Steve Simon
 
 
==What happened to the margin of error in New Hampshire?==
 
 
We will not be able to answer this question until the Pollsters have time to analyze their data and perhaps not even then.
 
 
At the  [http://www.pollster.com/ Polster.com] website we find  [http://www.pollster.com/blogs/polling_errors_in_new_hampshire here] the following graphs  that show how far the polls were from the classical 5% margin of error. The origin is the percentages of the votes that Obama and Clinton obtained in the voting: 39.1% for Clinton and 36.4% for Obama. The dots indication the percentages predicted by the polls for  Obama and Clinton.  To have a margin of error 5% or less a poll's dot would have to fall in the first circle, a feat not accomplished by any of the polls.
 
 
<center>http://www.pollster.com/blogs/1NHPollErrorDem19.png</center>
 
 
And here  is the corresponding graphic for the republican candidates with the highest percentage of votes: McCain 37% and Romney 31.5%:
 
 
<center>http://www.pollster.com/blogs/2NHPollErrorRep19.png </center>
 
 
From this you see that the  pollsters did a pretty good job.
 
 
===Discussion===
 
 
Andrew Kohut wrote  an [http://www.nytimes.com/2008/01/10/opinion/10kohut.html op-ed] "Getting it Wrong" for the ''New York Times'', October 10, 2008.
 
Kohut is a well known Independent pollster and President of the Pew Research Center.  In this op-ed he considers possible explanations and concludes that the the most likely cause was race.  He writes:
 
<blockquote>Poorer, less well-educated white people refuse surveys more often than affluent, better-educated whites. Polls generally adjust their samples for this tendency. But here’s the problem: these whites who do not respond to surveys tend to have more unfavorable views of blacks than respondents who do the interviews.<br><br>
 
 
I’ve experienced this myself. In 1989, as a Gallup pollster, I overestimated the support for David Dinkins in his first race for New York City mayor against Rudolph Giuliani; Mr. Dinkins was elected, but with a two percentage point margin of victory, not the 15 I had predicted. </blockquote>
 
(1) What do you think of this explanation?
 
 
(2) How did later polls do in predicting the Obama, Clinton votes? See  [http://www.pollster.com/blogs/where_was_the_error_bigger_nh.php Where was the error greater: NH or SC] by Mark Blumenthal.
 
 
(3) What other explanation might explain the pollsters getting it wrong?
 
 
Submitted by Laurie Snell
 
 
==Cholesterol Significance==
 
 
The distinction between “statistical significance” and “practical significance” seems to evade the lay public despite valiant efforts on the part of instructors and textbook writers.  Alex Berenson, writing in the New York Times on January 15, 2008, provides an excellent example for distinguishing the two forms of significance.  The article also reveals the tenuous connection between a cholesterol count and heart attacks.  And the strong connection between pharmaceutical companies and a profit motive.
 
 
The clinical trial known as Enhance “covered 720 patients and lasted two years.”  Those in the control arm “received either Zocor—an older cholesterol drug” and those in the treatment arm received “a combination of Zocar and Zetia, in the pill form known as Vytorin.”  During the course of “the two years of the trial, patients who took Zocor alone reduced their LDL [the bad cholesterol] by 41% on average, while patients who took Vytorin reduced their [LDL] cholesterol by 58%.”  Assuming that 360 patients were in each arm, Minitab shows that the results are clearly statistically significant:
 
 
Test and CI for Two Proportions<br>
 
 
<table width="50%" border="1">
 
  <tr>
 
    <td width="26%" height="31">
 
      <div align="center">Sample</div></td>
 
    <td width="20%"><div align="center">X</div></td>
 
    <td width="32%"><div align="center">N Sample</div></td>
 
    <td width="22%"><div align="center">p</div></td>
 
  </tr>
 
  <tr>
 
    <td><div align="center">1</div></td>
 
    <td><div align="center">148</div></td>
 
    <td><div align="center">360</div></td>
 
    <td>0.411111</td>
 
  </tr>
 
  <tr>
 
    <td><div align="center">2</div></td>
 
    <td><div align="center">209</div></td>
 
    <td><div align="center">360</div></td>
 
    <td>0.580556</td>
 
  </tr>
 
</table>
 
 
 
Difference = p (1) - p (2)<br>
 
Estimate for difference:  -0.169444<br>
 
95% CI for difference:  (-0.241429, -0.0974597)<br>
 
Test for difference = 0 (vs not = 0):  Z = -4.61  P-Value = 0.000<br>
 
 
Fisher's exact test: P-Value = 0.000
 
 
 
Nevertheless, in spite of “the larger cholesterol reduction, patients taking Vytorin actually had more growth of fatty plaque in their carotid arteries than those patients on Zocor”  alone and thus more likely to experience heart attacks.  More strongly, a leading cardiologist warns that “Millions of patients may be taking a drug that does not benefit them, raising their risk of heart attacks and exposing them to potential side effects.”  Clearly this is a situation in which the practical (i.e., clinical) significance is suspect.
 
 
Discussion
 
 
1. “Sales of the two drugs were $5 billion in 2007.” In addition, “Worldwide, about one million prescriptions are written for Zetia and Vytorin each week, and about five million people are now taking the drugs worldwide.”  The Enhance trial ended in April, 2006 but the announcement of the results was delayed until January, 2008.  “The drug companies blamed the complexity of the data for the delay.”  A spokesman for one of the drug companies “said the delay was unrelated to the negative findings and that the companies had not known the result until two weeks ago.”  Determine the cost of a one month supply of Zocor and Vytorin, respectively, to see how that helps in explaining the announcement delay.
 
 
2. Zocor is a statin drug and Zetia is drug with a different mechanism and thus, the notion that combining the two would have a serendipitous effect.  Do some research on prostate cancer, glaucoma or other afflictions to see if treatment combinations with different mechanisms are recommended and what side effects the patients are warned about due to the combination.
 
 
3. Merck and Schering-Plough submitted a large two-page advertisement in many newspapers on January 22, 2008 stating, "you may be worried about recent news stories questioning the benefit of these medicines...on the basis of a single study that has generated a lot of confusion."  Find the advertisement and determine whether Zocor is ever mentioned.  If not, why not?  If so, how?  Ask your local newspaper what the cost of such an advertisement is.
 
 
Submitted by Paul Alper
 
 
==What the boss looks like determines how he performs==
 
 
[http://www.economist.com/displaystory.cfm?story_id=10559771 Face value,] The Economist, Jan 24th 2008.<br>
 
 
What does it take to run a company successfully?
 
More than a pretty face, according to a recent Tufts University study, by psychologists Nicholas Rule and Nalini Ambady, who attempt to relate the performance levels of America’s top companies to the first impressions made by their chief executive officers (CEOs).
 
 
The data consist of photographs of the faces of the chief executives of the top and bottom 25 companies in the Fortune 1,000 list, along with their rankings to determine which of these faces were characteristic of a leader, according to 100 undergraduate college students.
 
 
The objective is to distinguish between the successful and the not-so-successful CEOs
 
based on rating the faces on five criteria:
 
competence, dominance, likeability, facial maturity and trustworthiness.
 
Success is based on the CEO's company's profits.
 
 
The students were not told the job titles of the faces,
 
who happened to be all white, male,
 
cropped to the face, put into grayscale and standardized in size.
 
They were also of a similar age, the authors' claim.
 
The study even controlled for age, the emotional expression in the photos and the physical attractiveness of the individuals by obtaining separate ratings of these from other students and using statistical techniques to remove their effects.
 
 
The authors claim
 
<blockquote>
 
These findings suggest that naive judgments may provide more accurate assessments of individuals than well-informed judgments can.
 
Our results are particularly striking given the uniformity of the CEOs’ appearances.
 
</blockquote>
 
 
The Economist refers to two related articles:
 
* Reserachers from Yale and the University of Pittsburgh failed to discover a link between a company's success and the personality of its boss, based on asking senior managers to score their bosses for traits like <em>an ability to communicate an exciting vision of the future</em> or <em>to stand as a good model for others to follow</em>.
 
* However, a few years before this, a team led by Nalini Ambady (the author of the study in this Economist article) discovered that perceptions generated from two-second-long film-clips of professors lecturing were found to match those of students taught by those professors for a full semester.
 
 
===Questions===
 
* A priori, would you prefer to about know a manager's personality or what he/she looks like?
 
** Does it matter when each CEO's photo was taken? What if the CEO was having 'a bad hair day' when the photo was taken, could that influence the outcome? If you were the CEO of a Fortune company that was in the bottom 1/4 of 1% (bottom 25 out of 1,000), how secure would you feel in your job and would you expect any insecurity to be reflected in your appearance?
 
** Previous studies that looked at managers' personalities failed to detect a meaningful relationship. Does this influence the outcome you might expect from focusing on a manager's looks?
 
 
* Which of the two sets of variables (managers' looks versus companies rankings) would you expect is easier to assess?
 
** How meaningful are company rankings relative to others?
 
** What is the minimum period over which the company's performance might be measured before a CEO's contribution can be detected?
 
 
* What 'statistical techniques' might have been used by the authors to control for the effects of emotional expression in the photos and the physical attractiveness of the individual CEOs?
 
 
* Assuming a strong connection between appearances and success, how might you measure which came first, the powerful-looking CEO or their successful career?
 
 
===Further reading===
 
* The study, <em>The Face of Success: Inferences From Chief Executive Officers' Appearance Predict Company Profits,</em> appears in the February 2008 issue of [http://www.blackwellpublishing.com/journal.asp?ref=0956-7976 Psychological Science,] a journal of the [http://psychologicalscience.org/media/releases/2008/rule.cfm Association for Psychological Science.]
 
 
Submitted by John Gavin.
 
 
==State of the Union==     
 
 
Whether or not you were pleased with the January 28, 2008 State of the Union address by President Bush, you should be depressed that hardly anyone noted his statistical gaff when he urged to make his tax cuts permanent.  He either does not know the difference between the mean and the median or he is knowingly prevaricating.  To make matters worse, he used the same logic early in his administration to convince Congress and the American public to institute the tax cuts in the first place.
 
 
President Bush said:
 
<blockquote> Some in Washington argue that letting tax relief expire is not a tax increase,..Try explaining that to 116 million American taxpayers who would see their taxes rise by an average of $1,800. . . . This budget will keep America on track for a surplus in 2012.</blockquote>
 
 
In an article, [http://www.washingtonpost.com/wp-dyn/content/article/2008/01/28/AR2008012803080.html FOR THE RECORD: ECONOMY], January 29, 2009,  Washington Post's Steve Mufson and Jonathan Weisman  write:
 
 
<blockquote>Here's another way of looking at it: the median American household will pay roughly $828 more in taxes in 2011 if the Bush tax cuts expire, according to the Tax Policy Center, a non-ideological think tank venture. The richest 1 percent of American households, in contrast, would have to pay an extra $64,154 a year when the tax cuts expire.</blockquote>
 
 
===Discussion===
 
 
1. When Bill Gates walks into a crowded room the average income goes up.  What happens to the median and what happens to the mean?
 
 
2. If incomes were distributed symmetrically, why would it make no difference whether one was referring to the mean or to the median?
 
 
3. Determine the median American household income.
 
 
4. Determine how much income is needed to be in "The richest 1 percent of American households."  Compare your answer to that of number 3.
 
 
 
  
 
Submitted by Paul Alper
 
Submitted by Paul Alper

Revision as of 15:33, 2 February 2008

Contents

Quotation

It is the mark of a truly intelligent person to be moved by statistics.
George Bernard Shaw

Forsooth

The following Forsooths are from the January 2008 issue of RSS NEWS.


In terms of platform use trends among the respondents, 53% cited Windows as their primary technical computing platform, with Linux following closely at 51%.
NAGNews email (NAG User Survey 2006 on technical
computing trends)
August 2006

Clearly, any product with a large user base is going to throw up some problems. Dell, for example, is shipping almost 40m PCs a year, so even if 95% of it users are happy, there could still be 6m or so with significant gripes.
The Guardian
25 January 2007

High altitude effects on athletic performance

Effect of altitude on physiological performance: a statistical analysis using results of international football games. Patrick E McSharry. BMJ 2007; 335: 1278-1281 (22 December).

There is a strong belief that athletes who live and train at high altitudes have an unfair advantage over those athletes visiting from lower altitudes. In response,

football’s governing body, the Federation of International Football Associations (FIFA), banned international matches from being played at more than 2500 m above sea level.

There is a plausible mechanistic explanation for this concern.

At high altitude hypoxia, cold, and dehydration can lead to breathlessness, headaches, nausea, dizziness, and fatigue, and possibly altitude illness including syndromes such as acute mountain sickness, high altitude pulmonary oedema, and cerebral oedema. Activities such as football can exacerbate symptoms, preventing players from performing at full capacity.

What would the data say. An ideal database exists to explore whether high altitude has a detrimental effect on athletes visiting from lower altitudes. In South America, which has three large cities at high altitude (Bogota, Columbia, Quito, Ecuador, and La Paz, Bolivia), there are records of 1460 football matches played over a 100 year period at a wide range of altitudes. This data set included four variables:

(i) the probability of a win, (ii) the number of goals scored, (iii) the number of goals conceded, and (iv) the altitude difference between the home venue of a specific team and that of the opposition.

as well as indicators for individual countries. This study used a logistic regression model to predict the probability of a win by the home team, and two Poisson regression models: one to predict number of goals scored by the home team and a second to predict the number of goals conceded by the home team.

http://www.bmj.com/content/vol335/issue7633/images/medium/mcsp457549.f2.gif

The graph of the predicted equations appears above. These graphs show clearly that a thousand meter difference in altitude between the home team and the opposition produces a large change in the estimated probability of a win for the home team, the expected number of goals scored by the home team, and the expected number of goals allowed by the home team.

Questions

1. Although the graphs are non-linear, a linear approximation is quite reasonable for the predicted values. Estimate how much change in probability of home team winning, goals scored by the home team, and goals allowed by the home team changes for each 1,000 meter change in altitude.

2. There are many variables that were not considered in this analysis. List some of the more important variables that were not included. Consider whether these variables are easy to measure or hard to measure.

3. Is there an alternate explanation other than change in altitude that could account for the differential in home team win probability, goals scored by the home team, and goals allowed by the home team?

4. Should international football matches be allowed in high altitude locations?

Submitted by Steve Simon

What happened to the margin of error in New Hampshire?

We will not be able to answer this question until the Pollsters have time to analyze their data and perhaps not even then.

At the Polster.com website we find here the following graphs that show how far the polls were from the classical 5% margin of error. The origin is the percentages of the votes that Obama and Clinton obtained in the voting: 39.1% for Clinton and 36.4% for Obama. The dots indication the percentages predicted by the polls for Obama and Clinton. To have a margin of error 5% or less a poll's dot would have to fall in the first circle, a feat not accomplished by any of the polls.

http://www.pollster.com/blogs/1NHPollErrorDem19.png

And here is the corresponding graphic for the republican candidates with the highest percentage of votes: McCain 37% and Romney 31.5%:

http://www.pollster.com/blogs/2NHPollErrorRep19.png

From this you see that the pollsters did a pretty good job for predicting the outcome for the Republican candidates.


Discussion

Andrew Kohut wrote an op-ed "Getting it Wrong" for the New York Times, October 10, 2008. Kohut is a well known Independent pollster and President of the Pew Research Center. In this op-ed he considers possible explanations and concludes that the most likely cause was race. He writes:

Poorer, less well-educated white people refuse surveys more often than affluent, better-educated whites. Polls generally adjust their samples for this tendency. But here’s the problem: these whites who do not respond to surveys tend to have more unfavorable views of blacks than respondents who do the interviews.

I’ve experienced this myself. In 1989, as a Gallup pollster, I overestimated the support for David Dinkins in his first race for New York City mayor against Rudolph Giuliani; Mr. Dinkins was elected, but with a two percentage point margin of victory, not the 15 I had predicted.

(1) What do you think of this explanation?

(2) How did later polls do in predicting the Obama, Clinton votes? See Where was the error greater: NH or SC by Mark Blumenthal.

(3) What other explanation might explain the pollsters getting it wrong?

Submitted by Laurie Snell

Cholesterol Significance

The distinction between “statistical significance” and “practical significance” seems to evade the lay public despite valiant efforts on the part of instructors and textbook writers. Alex Berenson, writing in the New York Times on January 15, 2008, provides an excellent example for distinguishing the two forms of significance. The article also reveals the tenuous connection between a cholesterol count and heart attacks. And the strong connection between pharmaceutical companies and a profit motive.

The clinical trial known as Enhance “covered 720 patients and lasted two years.” Those in the control arm “received either Zocor—an older cholesterol drug” and those in the treatment arm received “a combination of Zocar and Zetia, in the pill form known as Vytorin.” During the course of “the two years of the trial, patients who took Zocor alone reduced their LDL [the bad cholesterol] by 41% on average, while patients who took Vytorin reduced their [LDL] cholesterol by 58%.” Assuming that 360 patients were in each arm, Minitab shows that the results are clearly statistically significant:

Test and CI for Two Proportions

Sample
X
N Sample
p
1
148
360
0.411111
2
209
360
0.580556


Difference = p (1) - p (2)
Estimate for difference: -0.169444
95% CI for difference: (-0.241429, -0.0974597)
Test for difference = 0 (vs not = 0): Z = -4.61 P-Value = 0.000

Fisher's exact test: P-Value = 0.000

Nevertheless, in spite of “the larger cholesterol reduction, patients taking Vytorin actually had more growth of fatty plaque in their carotid arteries than those patients on Zocor” alone and thus more likely to experience heart attacks. More strongly, a leading cardiologist warns that “Millions of patients may be taking a drug that does not benefit them, raising their risk of heart attacks and exposing them to potential side effects.” Clearly this is a situation in which the practical (i.e., clinical) significance is suspect.

Discussion

1. “Sales of the two drugs were $5 billion in 2007.” In addition, “Worldwide, about one million prescriptions are written for Zetia and Vytorin each week, and about five million people are now taking the drugs worldwide.” The Enhance trial ended in April, 2006 but the announcement of the results was delayed until January, 2008. “The drug companies blamed the complexity of the data for the delay.” A spokesman for one of the drug companies “said the delay was unrelated to the negative findings and that the companies had not known the result until two weeks ago.” Determine the cost of a one month supply of Zocor and Vytorin, respectively, to see how that helps in explaining the announcement delay.

2. Zocor is a statin drug and Zetia is drug with a different mechanism and thus, the notion that combining the two would have a serendipitous effect. Do some research on prostate cancer, glaucoma or other afflictions to see if treatment combinations with different mechanisms are recommended and what side effects the patients are warned about due to the combination.

3. Merck and Schering-Plough submitted a large two-page advertisement in many newspapers on January 22, 2008 stating, "you may be worried about recent news stories questioning the benefit of these medicines...on the basis of a single study that has generated a lot of confusion." Find the advertisement and determine whether Zocor is ever mentioned. If not, why not? If so, how? Ask your local newspaper what the cost of such an advertisement is.

Submitted by Paul Alper

What the boss looks like determines how he performs

Face value, The Economist, Jan 24th 2008.

What does it take to run a company successfully? More than a pretty face, according to a recent Tufts University study, by psychologists Nicholas Rule and Nalini Ambady, who attempt to relate the performance levels of America’s top companies to the first impressions made by their chief executive officers (CEOs).

The data consist of photographs of the faces of the chief executives of the top and bottom 25 companies in the Fortune 1,000 list, along with their rankings to determine which of these faces were characteristic of a leader, according to 100 undergraduate college students.

The objective is to distinguish between the successful and the not-so-successful CEOs based on rating the faces on five criteria: competence, dominance, likeability, facial maturity and trustworthiness. Success is based on the CEO's company's profits.

The students were not told the job titles of the faces, who happened to be all white, male, cropped to the face, put into grayscale and standardized in size. They were also of a similar age, the authors' claim. The study even controlled for age, the emotional expression in the photos and the physical attractiveness of the individuals by obtaining separate ratings of these from other students and using statistical techniques to remove their effects.

The authors claim

These findings suggest that naive judgments may provide more accurate assessments of individuals than well-informed judgments can. Our results are particularly striking given the uniformity of the CEOs’ appearances.

The Economist refers to two related articles:

  • Researchers from Yale and the University of Pittsburgh failed to discover a link between a company's success and the personality of its boss, based on asking senior managers to score their bosses for traits like an ability to communicate an exciting vision of the future or to stand as a good model for others to follow.
  • However, a few years before this, a team led by Nalini Ambady (the author of the study in this Economist article) discovered that perceptions generated from two-second-long film-clips of professors lecturing were found to match those of students taught by those professors for a full semester.

Questions

  • A priori, would you prefer to about know a manager's personality or what he/she looks like?
    • Does it matter when each CEO's photo was taken? What if the CEO was having 'a bad hair day' when the photo was taken, could that influence the outcome? If you were the CEO of a Fortune company that was in the bottom 1/4 of 1% (bottom 25 out of 1,000), how secure would you feel in your job and would you expect any insecurity to be reflected in your appearance?
    • Previous studies that looked at managers' personalities failed to detect a meaningful relationship. Does this influence the outcome you might expect from focusing on a manager's looks?
  • Which of the two sets of variables (managers' looks versus companies rankings) would you expect is easier to assess?
    • How meaningful are company rankings relative to others?
    • What is the minimum period over which the company's performance might be measured before a CEO's contribution can be detected?
  • What 'statistical techniques' might have been used by the authors to control for the effects of emotional expression in the photos and the physical attractiveness of the individual CEOs?
  • Assuming a strong connection between appearances and success, how might you measure which came first, the powerful-looking CEO or their successful career?

Further reading

Submitted by John Gavin.

State of the Union

Whether or not you were pleased with the January 28, 2008 State of the Union address by President Bush, you should be depressed that hardly anyone noted his statistical gaff when he urged to make his tax cuts permanent. He either does not know the difference between the mean and the median or he is knowingly prevaricating. To make matters worse, he used the same logic early in his administration to convince Congress and the American public to institute the tax cuts in the first place.

President Bush said:

Some in Washington argue that letting tax relief expire is not a tax increase,..Try explaining that to 116 million American taxpayers who would see their taxes rise by an average of $1,800. . . . This budget will keep America on track for a surplus in 2012.

In an article, FOR THE RECORD: ECONOMY, January 29, 2009, Washington Post's Steve Mufson and Jonathan Weisman write:

Here's another way of looking at it: the median American household will pay roughly $828 more in taxes in 2011 if the Bush tax cuts expire, according to the Tax Policy Center, a non-ideological think tank venture. The richest 1 percent of American households, in contrast, would have to pay an extra $64,154 a year when the tax cuts expire.

Discussion

1. When Bill Gates walks into a crowded room the average income goes up. What happens to the median and what happens to the mean?

2. If incomes were distributed symmetrically, why would it make no difference whether one was referring to the mean or to the median?

3. Determine the median American household income.

4. Determine how much income is needed to be in "The richest 1 percent of American households." Compare your answer to that of number 3.

Submitted by Paul Alper

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