Two German psychologists have found a better way to teach basic statistical concepts, based on the way people naturally weigh the odds. This approach can help patients, and the doctors who advise them, more accurately assess the meaning of test results. (Journal of Experimental Psychology: General, Sep-2001)
http://www.newswise.com/articles/2001/9/STATS.PSY.html
American Psychological Association
(APA)
STATISTICS TRAINING THAT WORKS WITH
OUR INNATE ABILITY TO ASSESS THE LIKELIHOOD OF EVENTS CAN HELP DOCTORS
AND PATIENTS FIGURE THE ODDS OF ILLNESS BETTER
'Natural-frequency' approach may
be superior for training people to interpret health tests, judge courtroom
evidence and more
WASHINGTON -- Does a positive mammogram
mean a woman has breast cancer? Does a positive HIV test mean someone is
infected with the virus? As ordinary people confront the laws of probability,
the odds of misinterpretation and false alarms rise. Two German psychologists
have found a better way to teach basic statistical concepts, based on the
way people naturally weigh the odds. This approach can help patients, and
the doctors who advise them, more accurately assess the meaning of test
results.
Peter Sedlmeier, Ph.D., of the Chemnitz
University of Technology and Gerd Gigerenzer, Ph.D., of the Max Planck
Institute for Human Development in Berlin, tested their approach using
computer-based tutorials that cover basic binary statistical literacy (the
outcome is either this or that), that took students up to two hours to
complete. The psychologists' findings appear in the September issue of
the Journal of Experimental Psychology: General, published by the American
Psychological Association (APA).
In their article, Sedlmeier and Gigerenzer
contrast two approaches to statistical training. Percentage-based rules
would state, for example (using hypothetical numbers), "If a woman undergoing
mammography has breast cancer, the probability that she will test positive
is 80%." Natural-frequency rules would state, using the same example, "Eight
of every 10 women with breast cancer who undergo mammography will test
positive." Whereas Percentages view probabilities in light of a fixed number,
100, natural frequencies don't share a common norm. Still, the authors
predicted that the latter approach would be easier for people to learn
because it taps a natural ability to count the observable, without having
to use symbolic abstraction. Previous research has shown that people calculate
the odds of any given event more easily and accurately using natural frequencies,
which the authors say represents information in a way that is attuned to
our "cognitive algorithms" for reasoning with certain kinds of data.
This may be one reason why typical
percentage-based statistical training has been ineffective, say the authors,
causing problems when health-care providers counsel patients -- often inconsistently
and/or inaccurately -- about the chances of disease associated with (for
example) positive HIV blood tests and positive mammograms. In these cases,
doctors and patients have to layer new information, such as an individual's
positive mammogram, onto more general information, such as how many people
in a given group have breast cancer and how many of those with positive
mammograms have breast cancer, to arrive at the odds that the individual
in question may actually have the disease.
Sedlmeier and Gigerenzer conducted
a series of studies with students at the University of Chicago, the Free
University of Berlin and the University of Munich; there was almost no
difference in the groups' results. Up to four dozen students took part
in each study. The authors created several different computer-based tutorials
that used percentage-based rules or natural-frequency rules, and predicted
that the latter would work better. The results were consistent: Students
who took the percentage-based rule tutorial showed a substantial short-term
increase in performance with excellent transfer, but it decayed over several
weeks. People who took the natural-frequency tutorial had a noticeably
higher training effect (i.e. they got more cases "right"), equally good
transfer to other problems, and, most significantly, no loss of performance
after 15 weeks.
Sedlmeier summarizes the results:
"Both groups learned, but the natural-frequency group learned better and
it lasted longer, with no decay." In their article, the authors propose
further research into multi-variable (not just binary) statistical training,
training for "shortcuts" in making probability estimates, and the uses
of such brief tutorial programs for mathematical and statistical literacy.
For example, they speculate about convenient, cost-effective computer-based
tutorials that could teach high-school students how best to evaluate the
results of pregnancy, HIV or drug tests. "The teaching of statistical literacy,"
the authors conclude, "can take advantage of human psychology."
Finally, they point out that statistical
smarts increasingly matter outside the doctor's office. For example, jurors
must evaluate a greater number of statistical averages and frequencies
presented as evidence, and citizens in a growing number of democracies
must intelligently evaluate the kinds of information that their governments
make public.
Article: "Teaching Bayesian Reasoning
in Less Than Two Hours," Peter Sedlmeier, Chemnitz University of Technology,
and Gerd Gigerenzer, Max Planck Institute for Human Development, Berlin;
Journal of Experimental Psychology -- General, Vol. 130., No. 3.
Peter Sedlmeier can be reached by
email at peter.sedlmeier@phil.tu-chemnitz
(Full text of the article is available
from the APA Public Affairs Office and at http://www.apa.org/journals/xge/press_releases/september_2001/xge1303380.html
)
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