I am looking for at least five really good examples of statistically
valid but nonsensical correlations.  For example I believe I have
heard it said that if the American League wins the World Series, then
"X" is likely to happen whereas if the National League wins the World
Series then "Y" is likely to happen. Although historically the "X/Y"
phenomenon has been observed with a very high degree of accuracy
clearly neither "X" nor "Y" has anything to do with baseball. I
believe that there is another correlation that says if women's skirt
length in the new fall fashions is lower then "X" is likely to happen,
and if higher then "Y" is likely to happen. I am looking for examples
of correlations that actually exist and that can be documented with
hard numbers as existing, but where it is clear that the correlation,
though undeniable, is not the causation for the relationship that
statistically appears to exist. WAYNE C. CURTIS, STATISTICAL CONCEPTS
FOR ATTORNEYS 157 (Quorum Books 1983), states, "a high degree of
positive correlation . . . does not necessarily mean that there is a
cause-and-effect relationship between two variables. A high
correlation can occur by chance alone or because both variables are
related to some other variable which has not been considered in the
analysis.?   I would like to find at least 5 real life good examples
of the fact that a high degree of positive correlation does not equate
to cause and effect.  I am offering $200 for 5 documented examples of
nonsensical correlations (with specific numbers quantifying the degree
of correlation), but if you have fewer than 5, I would offer $40 per
example. It would be helpful if some of the examples were of the
variety caused by pure chance alone (such as the American
League/National  league example) and other examples were of the
variety caused by the fact that the two correlated events were
actually both caused or influenced by a third factor not considered in
the correlation. Thank you for your help.

Hi sl7-ga!

Your question, I must admit, was a rather fun one to investigate.

The fact that correlation never implies causation, which may be lost
on many people, is extremely important.  Causation is just one of
three possible relationships between two correlated variables:
a) Causation - a change in X causes a change in Y
b) Common Response - both X and Y change in common to some third, unseen variable
c) Confounding - the effect of X and Y is mixed up with the effects of
other explanatory variables on Y.  To establish causation, a carefully
controlled designed experiment must be run.

I have found many silly examples of correlation without causation. 
For example, ice cream sales and shark attack frequency are strongly
correlated.  This is not because sharks start attacking in response to
ice cream, but because the two variables exhibit a common response to
the warm season.  Another example is strong correlation exists between
the number of cavities in  elementary school children and their
vocabulary size.  No one advocates eating more candy to increase
knowledge though; these variables are both tied with age.

One class of relations you may be familiar with are economic
indicators.  Examples are skirt hemlines which rise with stock market
prices, or the 'Big Mac' index which uses the price of Big Macs around
the world to gauge the currency exchange market.  The following link
describes the Super Bowl index, which operates on the principle that
when a team from the National Football Conference or from the pre-1970
NFL wins the Super Bowl, stocks rise:
http://www.fool.com/Fribble/1996/Fribble960112.htm
This has held true for 26 of 29 Super Bowls!
Also, this link describes the correlation between the Napa Valley Wine
Auction and the Dow Jones:
://www.google.ca/search?q=cache:ngKUTO0F194J:biz.tizwine.com/stories/storyReader%244298&hl=en&lr=&ie=UTF-8&c2coff=1&safe=off&strip=1
There is not a direct causal relationship between the two, but a
rather indirect, confounded one.

Your question requested correlations which were backed by numbers and
generally these are only available with scientific studies; either
medical or psychological.  I have provided five such examples which I
feel seem like nonsensical links at first glance.  If you are
dissatisfied with any aspect of these for any reason, you only need to
let me know and I will be glad to work with you until you are
completely satisfied.

Cheers,
tox-ga


-----------------------------------------------------------------------------



----- Shaving habits and risk of stroke -----

It would be silly to think one could change their chances of having a
stroke by shaving more.  Yet, a study by British researchers has found
a correlation between shaving habits and stroke risk.  Shaving less
than once a day means increasing your risk for a stroke by 70%!  In
fact, your risk of dying from _any_ cause rises 30%.

The lead researcher feels that the cause behind this correlation has
to do with hormones.  Testostorone has already been used to link
baldness to higher risk for heart disease.

Source:  Shaving habits linked to stroke risk
         http://news.bbc.co.uk/1/hi/health/2729457.stm



----- Developing breast cancer and working the nightshift -----

Of course having breast cancer does not cause one to take a job with a
nightshift; neither could working at night cause breast cancer.  Yet,
there appears to be a statistical connection.  In fact, women who, for
at least six months, worked predominantly at night are 50% more likely
to develop breast cancer.  This is the result of a Danish study of
7000 women, which were adjusted to consider other possible factors,
including alcohol consumption and age at birth of first and last kids.
 This is not the first study to link the two, but it is the most
statistically sound.

It is not known how the two are linked.  One theory is that the
exposure to light during nighttime hours triggers hormonal changes
which lead to breast cancer.

Source:  Nightshift link to breast cancer
         http://news.bbc.co.uk/1/hi/health/1108590.stm



----- Prayer and successful impregnation -----

Can you increase your chances of conceiving a child through prayer? 
If correlation implied causation, then this study would suggest that
is true.  A team of scientists from Columbia University found that a
group of women undergoing in-vetro fertilization had double the chance
of concieving when they were being prayed for.  The scientists were
confident that their study was methodically sound because the women
did not know they were being prayed for.  In fact, they were so
confident, they published their findings in the Journal of
Reproductive Medicine.

I have no idea why this worked and neither do the scientists.  I
believe this may fall under the category of correlations caused by
chance alone.


Source:  Study finds prayer 'double chance of IVF success'        
         http://www.ananova.com/news/story/sm_414237.html?menu=news.latestheadlines.wor



----- Breast implants and suicide rates -----

It does not make any sense to think that anything about breast
implants--simple bags of silicone--could impact mental health,
especially to the point of causing suicide.  Neither is there any
reason to believe that being suicidal leads a woman to get breast
impants.  Nevertheless, a Swedish study involving over 7000 women
found triple the suicide rate among those with breast implants as
compared to an otherwise similar group of women.

The likely explanation for this strange correlation is that a desire
for breasts strong enough to get surgery could be, in some women, a
symptom of insecurity and self esteem issues.  In a few cases, these
greater issues could lead to a suicide attempt.

Source:  Breast implant suicide link
         http://news.bbc.co.uk/1/hi/health/2826933.stm



----- Tooth loss and heart disease -----

It is intuitively nonsense that losing teeth can lead to heart
disease, or that heart disease causes tooth loss.  However, a strong
correlation was found between the two by American researchers. 
Studying their subjects, they found that "in those who had lost up to
nine teeth, 45% had carotid artery plaque. Just under two-thirds of
those with 10 or more teeth missing had plaque build-up in the
vessels."

The source of the relationship is not entirely clear.  Some studies
have linked gum disease to heart disease, while others link infectious
diseases to increasing the risk of blocked arteries.  Some doctors
simply see tooth loss as an indicator of lifestyle.

Source:  Tooth loss link to heart disease
         http://news.bbc.co.uk/1/hi/health/3114013.stm

Thank you for a really terrific and prompt response to my question.
You were 100% on point with reference citations to back up your
examples.  I'm impressed.

Thank you very much for your generous rating, feedback, and tip!  It
is certainly appreciated.  I'm very glad that you were satisfied.  I
look forward to having an opportunity to work with you in the future.

Cheers,
tox-ga

Great work, Tox! Your answer was both educational and entertaining. 

~Pink

One example of this that I remember from college is that people who
own washing machines are more likely to die in a car accident.  I
don't know what the actual numbers were. No, clean clothes don't make
you a bad driver, people who own washing machines are more likely to
own a car and therefore more likely to be driving.

This might be a little out of the scope, but a friend of mine
determined that (x) the shorter her skirt and/or the lower her top
was, (y) the more free drinks she received.