Statistically Significant Math
I have spent the last 4 and a half hours searching the
internet for an artical
that uses the term "statistically significant." I need it for my science
class so I can write a paragraph
describing how the test was used.
Statistically significant really just means that the thing you are talking
about seems to be real.
You might be talking about kids who have sore throats. Somebody might claim
that if you eat a cold popsickle, that it will cure your sore throat. You
don't belive this, so you send out a survey, you ask alot of kids, some who
ate a popsickle, some that didn't. If you find that all the kids got better
in 3 days, regrardless of the popsickle, then you could say that the number of
kids who got better was not statiscally significant-- your "statistics" is
your survey, and "significant" means that you did (or here did not) see any
Another way the term is used is when people are trying to be very accurate.
Suppose somebody tells you that 54.34995345323 percent of the people in the US
can stand on one leg and pat their head at the same time. Well I would think
that maybe the "true" number is "about half" of the people in the US. But do
all those numbers, the .349953 etc. etc. really mean anything? How can the
speaker know this SO accurately??? They can't. These numbers are just
nonsense. Numbers are not statically significant if they extend the precision
of the measurement further than is really the case. You really don't know
THAT well, so don't give us all these extra numbers.
Dr. S. Ross
Great question. Here is an example which can clarify its meaning.
Assume you have come up with a new drug to treat cancer. After some
investigation in the lab, you are ready to try it on say, rats, and see if
it works for them.
Say, you find 100 sick rats and give them the medicine and 20 of them get
well. OK, the question is this: does this drug work? You'd say, sure it
does, it cured 20 rats.
Someone else will say: no, not necessarily because 20 out of 100 rats would
overcome their illness even if left alone.
You'd say, OK, lets try a new method. We take 200 randomly selected sick
rats. We divide them randomly into two groups of 100. We tread one of the
groups with real drug and the other half with a fake pills. The person
giving them the drug and taking care of them will not know which pills are
real and which fake.
At the end of the experiment, you count the number of rats surviving. If
you see that of the group getting the real drug 20 survived and of those
getting fake medicine 5 survived, then you'd say that a "statistically
significant" number of rats benefited from your drug. If, on the other
hand, 18 of those rats that received fake drug also survived, then you have
a problem: You do not really know for sure if your drug has had any effect,
because the difference between survival rates (20 vs. 18) is not
"statistically significant". It can be just normal variations of some sort.
As you can imagine, "statistically significant" is a very important concept
and is used anytime you like to know if "on average" something works or
does not work. It works if the results is statistically (that is, on
average, everything else considered) significant.
Dr. Ali Khounsary
Click here to return to the Mathematics Archives
Update: June 2012