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Topic: Don't Let Math Pull the Wool Over Your Eyes
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Jerry P. Becker

Posts: 13,518
Registered: 12/3/04
Don't Let Math Pull the Wool Over Your Eyes
Posted: Jan 14, 2013 2:40 PM
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From the Wall Street Journal, Saturday, January
5, 2013. See
http://professional.wsj.com/article_email/SB20001424127887323374504578219873933502726-lMyQjAyMTAzMDAwNTEwNDUyWj.html?mod=wsj_valettop_email
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THE NUMBERS GUY

Don't Let Math Pull the Wool Over Your Eyes

By Carl Bialik

This column will make the case that many people,
including holders of graduate degrees,
professional researchers and even editors of
scientific journals, can be too easily impressed
by math. A mathematical model (Tpp = T0 - ŸT0d2f
- ŸTpdf) is developed to describe sequential
effects.

Did that second sentence make the first more
persuasive? It did for most participants in a
recent intriguing experiment whose result
suggests people often interact with math in a way
that isn't very logical. Other research has shown
that even those who should be especially
clear-sighted about numbers-scientific
researchers, for example, and those who review
their work for publication-are often
uncomfortable with, and credulous about,
mathematical material. As a result, some research
that finds its way into respected journals-and
ends up being reported in the popular press-is
flawed.

In the latest study, Kimmo Eriksson, a
mathematician and researcher of social psychology
at Sweden's Mälardalen University, chose two
abstracts from papers published in research
journals, one in evolutionary anthropology and
one in sociology. He gave them to 200 people to
rate for quality-with one twist. At random, one
of the two abstracts received an additional
sentence, the one above with the math equation,
which he pulled from an unrelated paper in
psychology. The study's 200 participants all had
master's or doctoral degrees. Those with degrees
in math, science or technology rated the abstract
with the tacked-on sentence as slightly
lower-quality than the other. But participants
with degrees in humanities, social science or
other fields preferred the one with the bogus
math, with some rating it much more highly on a
scale of 0 to 100.

"Math makes a research paper look solid, but the
real science lies not in math but in trying one's
utmost to understand the real workings of the
world," Prof. Eriksson said.

Several of the authors of the three papers whose
material Prof. Eriksson harvested said they
generally agreed with that conclusion.
"Disciplines with less math emphasis could
benefit from more exposure to mathematical logic
so that when it is used it is accepted for its
rigor rather than because it awes the reader,"
said Geoff Kushnick, co-author of the
evolutionary anthropology paper, published in
2002.

Prof. Eriksson's finding, published in November
in the journal Judgment and Decision Making under
the title "The Nonsense Math Effect," is
preliminary but unfortunately not surprising,
other researchers said. It documents a familiar
effect, said Daniel Kahneman, professor emeritus
of psychology and public affairs at Princeton
University. "People who know math understand what
other mortals understand, but other mortals do
not understand them. This asymmetry gives them a
presumption of superior ability."

Prof. Kahneman and other scholars have documented
how numbers can warp rather than enhance logical
thinking. For example, German researchers asked
52 lawyers to propose sentences for hypothetical
repeat shoplifters after having rolled dice to
determine the hypothetical sentencing demand by
prosecutors. Lawyers who rolled dice that showed
a higher requested sentence tended to hand out
longer sentences themselves, even with identical
facts in the case and the knowledge that the
demanded sentence was entirely random. Tying
decisions to a proposed number, even when it is
random or misguided, is known by psychologists as
anchoring and helps explain why a "50% off" sale
can seem so compelling even when the original
price was vastly inflated.

Prof. Eriksson's study shows how people can
stumble when exposed to math outside their field
of expertise. Articles in scientific journals,
however, typically are reviewed by experts who
read the whole paper, not just abstracts. Yet
even here, there is evidence that professional
researchers often botch statistics in their work,
but are allowed to publish problematic data.
Writing in Nature last month, cell biologist
David L. Vaux decried the continuing publication,
including in Nature, of papers with problems such
as miscalculated margins of error. "The fact that
these scientifically sloppy papers continue to be
published means that the authors, reviewers and
editors cannot comprehend the statistics, that
they have not read the paper carefully, or both,"
said Prof. Vaux, of the University of Melbourne
in Australia.

Martin T. Wells, a biostatistician at Cornell
University, has another explanation, chalking up
occasional sloppiness in statistics to the
pressure to publish early and often. "It's a bit
frustrating," he said. "As a biostatistician you
want to do things right, and some researchers
just want to get off on the cheap analyzing data."

Alan Sokal, the physicist who in 1996 hoaxed a
journal of cultural studies with an article he
wrote as a jest that the journal published,
called Prof. Eriksson's study "very interesting."
He would like it replicated with a more
credentialed group, such as university
professors, who are more likely to review
articles for publication.

Prof. Eriksson said he "would love to conduct a
follow-up study with other samples," adding his
paper didn't itself contain any deliberately
faulty statistics to test whether readers would
notice. "I wasn't clever enough to think of
putting in some nonsense math of my own," he said.
------------------------------------
A version of this article appeared Jan. 5, 2013,
on page A2 in some U.S. editions of The Wall
Street Journal, with the headline: Don't Let Math
Pull the Wool Over Your Eyes.
*******************************************
--
Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
625 Wham Drive
Mail Code 4610
Carbondale, IL 62901-4610
Phone: (618) 453-4241 [O]
(618) 457-8903 [H]
Fax: (618) 453-4244
E-mail: jbecker@siu.edu



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