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Homework Help: Social Studies: Psychology: Is It Just a Coincidence?
by David A. Gershaw, Ph.D.
We are often surprised by events that seem very unlikely to occur by
chance. We may dream about a person the same night that the person dies.
Is this proof of a psychic link with the dead person? With identical twins
separated at birth, it may be found that they "both married women
named Jennifer, both drive Chevrolets, and both dislike mustard."
Is this proof of genetic dominance in determining behavior? Or are
both just coincidences?
Two statisticians, Perci Diaconis and Fred Mosteller (1989) defined
coincidence as, "a surprising occurrence of events, perceived as
meaningfully related, with no apparent causal connection." Coincidences
occur all around us all the time. However, we only notice them when the
coincidence is meaningful to us. A problem occurs when we try to use the
coincidence to "prove a point."
This is what happens with numerology, which attempts to find meanings
in numbers. One example is used by numerology to claim that William Shakespeare
translated the King James Bible. Their "proof" is that,
in Psalm 46 of the King James Bible, the 46th word is "shake"
and the 46th word from the end is "spear". Why is
the number 46 so significant? According to numerologists, it is because
Shakespeare was 46 years old when that version of the bible was published.
However, numerologists never specify in advance exactly where or what the
coincidence will be.
Another example is using any combination of the number "666"
to indicate that someone is the Beast of Revelation. Some said that
our ex-president, Ronald Wilson Reagan, was the Beast. Why? Each of his
names has six letters, therefore "666". However, if you
look long enough, you can probably find some arrangement of 666 with almost
anyone.
It seems that we humans try to find meaning in the things that occur
around us. With the Arizona lottery, out of 45 different numbers, the chance
of picking all six numbers is about one in 8 million. In other words, no
matter what these numbers are, the chance of any particular combination
of six numbers occurring in the next drawing is about one 8 million. Of
course, if you don't win any money, you don't consider that specific combination
of numbers as significant. If you only buy one ticket, only one combination
of numbers will any meaning for you. Each of the millions of other combinations
is just as unlikely as the one you picked. However, they are all lumped
together with one meaning - "I didn't win."
The method used by numerologists can be applied to psychological data.
Their method is called data dredging or data snooping. If you look at any
set of data in enough different ways, you can always come up with something
interesting. Suppose you have a large amount of random data - data that
occurs solely by chance. In this random data, if psychologists find something
that would occur just by chance less than 5% of the time, that information
is considered significant. However, this also means that - even if the
data is completely random - 5% of the time significance may be assumed
when none is there.
If more independent tests of significance are done on the same random
data, the probability goes up that you will find something that seems significant.
If you do 14 such tests, you will have better than even odds of finding
something "significant". If you do 20 such tests, the probability
is almost two out of three times.
Data dredging is like
"shooting the arrow first
and drawing the bull's eye later."
Both psychologists and numerologists can use data dredging. However,
this is like shooting an arrow first and drawing the bull's eye after it
lands. This is why it is necessary to distinguish between exploratory and
confirmatory data analysis. Exploratory analysis is done without predicting
exactly what is expected. You are looking through information to see if
you can find something interesting. However, if psychologists find something
interesting with exploratory analysis, they typically follow it up with
confirmatory analysis - they specify in advance exactly what they are
seeking. Most psychologists only consider the exploratory results truly
significant, if the same results show up in repeated independent analyses
as predicted.
In contrast, many people just accept the relationship as "proof"
of something they want to believe. They assume a "cause-and-effect"
relationship. Thus dreaming of a person when they die is accepted as
proof of a psychic link. Similarities among identical twins are taken as
evidence of the dominance of genetics. However, such similarities have
also been found between unrelated people.
So if you find some spectacular meaning in the relationship of two or
more factors, we are not asking you to reject it. However, you should be
critical. Can it be confirmed by other information, or is it just a coincidence?
* Adapted from Donald H. McBurney's How to Think Like a Psychologist:
Critical Thinking in Psychology, Prentice Hall Publishers, 1996, pages
73-78.
Homework Help: Social Studies: Psychology
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