Chance News 53: Difference between revisions
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"In my opinion, it sounds more like an investment banker," he said of the detailed billing. "It doesn't sound like someone in medicine." | "In my opinion, it sounds more like an investment banker," he said of the detailed billing. "It doesn't sound like someone in medicine." | ||
Submitted by Paul Alper | Submitted by Paul Alper<br> | ||
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[http://online.wsj.com/article/SB124940692698405243.html “When Precision Is Only 92.11567% Accurate”]<br> | |||
by Charles Forelle, <i>The Wall Street Journal</i>, August 5, 2009<br> | |||
Temporarily substituting for Carl Bialik (The Numbers Guy), Forelle reports about the government’s cash-for-clunkers program and critiques the EPA’s recently revised definition of a clunker. | |||
The EPA stated that “more precise” data calculated “to four decimal places” led it to revise its miles-per-gallon cutoff figures. | |||
"It is ludicrous to suggest that you can get fuel-consumption accuracy anywhere past the first decimal place, let alone the second," says … an independent U.K. auto tester. | |||
Forelle discusses the “faux precision” of estimates that are often based on sampling, but reported as final counts or measurements without their sometimes large margins of error, as in the case of population or unemployment-rate estimates. | |||
He cites another issue involved in misleadingly precise estimates, that is, lack of adherence to conventional rules relating to the issue of significant figures in arithmetic. | |||
The principle is simple: When combining measured numbers, the final answer is only as precise the least-precise piece of data that went into it; you can't just add a tail of decimal places, even if they show up on the calculator. So a room that's 2.5 meters (two significant digits) by 3.87 meters (three) has an area of 9.7 square meters, though the two numbers multiply to 9.675. | |||
Fuel mileage is apparently based upon tailpipe emissions, where released carbon dioxide from burning fuel provides a more accurate measure of gas consumption than direct measurement of consumed fuel. Not only does the EPA believe that the results of two lab tests on each car must be recorded to four decimal places by law, but it also added tests that were not done on older cars, and “created a formula that estimated from the old data what would happen had the new tests been run,” this despite the different precision levels of numbers that went into the formulas. An EPA spokesman said, "Repeatability and accuracy is something we spend a lot of time on." | |||
Discussion<br> | |||
1. What’s the difference between accuracy and precision?<br> | |||
2. How do you count significant digits in arithmetic?<br> | |||
3. A blogger commented [http://online.wsj.com/article/SB124940692698405243.html#articleTabs%3Dcomments], “Regards your room area example, if both length and width are measured by a person who makes the same direction of error on each measurement -- so that both are either too high or too low -- then the area will not only have almost twice the percentage error of either measurement, it will, on average be too high.” Do you agree with this statement?<br> | |||
4. The author described a 1991 court case in which an Alaskan man failed a bar exam and “missed by 0.5 point the threshold needed for a re-evaluation of his test.” The man claimed that, since the essays were graded with integers, his score should have been rounded up to the next integer. Although the man lost the case, the Alaska Supreme Court found his argument “convincing from a purely mathematical standpoint.” A blogger argued [http://online.wsj.com/article/SB124940692698405243.html#articleTabs%3Dcomments] that there are an infinite number of significant digits in counting things (<i>e.g.</i>, 1.000…), because “the error in the value of these numbers is ZERO,” and so arithmetic results “can be rounded to as many sig figures as you want to.” Do you agree with the Alaskan man or with the blogger?<br> | |||
Revision as of 13:56, 7 August 2009
Quotations
If they would only do as he did and publish posthumously
we should all be saved a lot of trouble
in reference to followers of Rev. T. Bayes
If your experiment needs Bayesian statistics,
you ought to have done a better experiment
N. Gilbert (Biometrical Interpretation, 1973)
These quotations occur in
Bayesian statistics for experimental scientists written by Hal Stern, Department of Statistics, University of California, Irvine.
Submitted by Paul Alper
Forsooths
Kuklo's Fellow Infuse Worker
From The Pioneer Press we learn that there is more to the Kuklo story. "Dr. David Polly, the University of Minnesota spine surgeon ... received nearly $1.2 million in consulting fees from medical device giant Medtronic over a five-year period." The details "of Polly's billing records were released this week by Sen. Charles Grassley, R-Iowa, as an attachment to a letter to University of Minnesota President Robert Bruininks. The letter raised questions about how the U polices conflicts of interest among doctors."
Polly's recordkeeping was indeed detailed:
Download CDs from meeting, 15 minutes, $125
Dinner meeting, 240 minutes, $2,000
E-mail Medtronic employee, five minutes, $49.48
Conference call, 90 minutes, $890.63
Teach at scoliosis meeting, 330 minutes, $2,750
According to the newspaper, Dr. Charles Rosen, a spine surgeon in California who leads a medical ethics group, said he was among those surprised by the details.
"I've not seen anybody bill the way he did," said Rosen, of the University of California-Irvine, who acknowledged that he doesn't do paid consulting work with the device industry.
"In my opinion, it sounds more like an investment banker," he said of the detailed billing. "It doesn't sound like someone in medicine."
Submitted by Paul Alper
==
“When Precision Is Only 92.11567% Accurate”
by Charles Forelle, The Wall Street Journal, August 5, 2009
Temporarily substituting for Carl Bialik (The Numbers Guy), Forelle reports about the government’s cash-for-clunkers program and critiques the EPA’s recently revised definition of a clunker.
The EPA stated that “more precise” data calculated “to four decimal places” led it to revise its miles-per-gallon cutoff figures. "It is ludicrous to suggest that you can get fuel-consumption accuracy anywhere past the first decimal place, let alone the second," says … an independent U.K. auto tester.
Forelle discusses the “faux precision” of estimates that are often based on sampling, but reported as final counts or measurements without their sometimes large margins of error, as in the case of population or unemployment-rate estimates.
He cites another issue involved in misleadingly precise estimates, that is, lack of adherence to conventional rules relating to the issue of significant figures in arithmetic.
The principle is simple: When combining measured numbers, the final answer is only as precise the least-precise piece of data that went into it; you can't just add a tail of decimal places, even if they show up on the calculator. So a room that's 2.5 meters (two significant digits) by 3.87 meters (three) has an area of 9.7 square meters, though the two numbers multiply to 9.675.
Fuel mileage is apparently based upon tailpipe emissions, where released carbon dioxide from burning fuel provides a more accurate measure of gas consumption than direct measurement of consumed fuel. Not only does the EPA believe that the results of two lab tests on each car must be recorded to four decimal places by law, but it also added tests that were not done on older cars, and “created a formula that estimated from the old data what would happen had the new tests been run,” this despite the different precision levels of numbers that went into the formulas. An EPA spokesman said, "Repeatability and accuracy is something we spend a lot of time on."
Discussion
1. What’s the difference between accuracy and precision?
2. How do you count significant digits in arithmetic?
3. A blogger commented [1], “Regards your room area example, if both length and width are measured by a person who makes the same direction of error on each measurement -- so that both are either too high or too low -- then the area will not only have almost twice the percentage error of either measurement, it will, on average be too high.” Do you agree with this statement?
4. The author described a 1991 court case in which an Alaskan man failed a bar exam and “missed by 0.5 point the threshold needed for a re-evaluation of his test.” The man claimed that, since the essays were graded with integers, his score should have been rounded up to the next integer. Although the man lost the case, the Alaska Supreme Court found his argument “convincing from a purely mathematical standpoint.” A blogger argued [2] that there are an infinite number of significant digits in counting things (e.g., 1.000…), because “the error in the value of these numbers is ZERO,” and so arithmetic results “can be rounded to as many sig figures as you want to.” Do you agree with the Alaskan man or with the blogger?