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Topic: Awfully small sample (9 msgs / 245 lines)
1) From: Paul Helbert
http://www.sciencedaily.com/releases/2008/08/080826135937.htm"...adding that though the sample was small, the results were statistically
and clinically significant. "Oh? Why, because it is his study? Seriously
question the professor's assertion that anything much can be projected from
one ten by ten sample.
Maybe so, maybe not.
-- 
Paul Helbert
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2) From: Jim Gundlach
Sample size is built into the calculation of all significance tests.   
In fact, it takes a strong relationship to show significance with  
small samples.  One way to think about the probability value  
calculated in significance tests is that it shows the probability you  
are wrong when you say the relationship found in your sample exists in  
the population your sample is randomly drawn from.  Here is how I used  
to introduce the concept to my stat classes:
      I tell them we are going to pretend to gamble using a coin  
toss.  I will toss this coin and every time it comes up heads you all  
owe me a dollar and every time it comes up tails I owe each of you a  
dollar.
      I then toss the coin and without showing any of them the coin I  
call "Heads".  I then say that if they are halfway rational they will  
have a hypothesis in their mind that we can begin to test.  That is,  
Dr. Gundlach is cheating.  They don't have to be willing to assert  
that it is true at this point, but that it is just a possibility.   
What we can do is calculate the probability that they are wrong when  
they say I cheated.  Given that the coin has two side, there is a  
fifty-fifty chance that it came up heads as I called it so the  
probability they are wrong when they say I am cheating at this point  
is .5.   I then introduce the notion of the traditional level of  
certainty of .05 and that if the probability of being wrong is more  
than .05 they don't have a statistical leg to stand on when they  
assert that I am cheating.  I then toss the coin again and we  
calculate the probability of being wrong again which is .5 * .5 or . 
25, still more than .05.  I toss and call heads a third time and we  
calculate a probability of .125 so it is still not significant.  A  
fourth time yields a p of .0625, which is close but this is not horse  
shoes or hand grenades and they need that .05 or less before they will  
tell the world that their statistics professor is cheating them.  A  
fifth toss with a call of heads yields a p=.03125 which is less than . 
05 so they can now go tell my department head, the dean, and even the  
president that I am cheating and that they have statistically  
significant evidence to back it up.
    But to bring this back to the issue of significance with small  
samples, here with a n of 5, there are significant results.  So if  
studies are done with small samples and show significant results, you  
should not automatically doubt the results because of the sample  
size.  And, the reality is that in using this teaching tool for over  
thirty years, at about one and a half times per year on average, I won  
without actually cheating once, which was about 2.2% of the time.  So  
among the approximately 45 classes that concluded that I was indeed  
cheating, only one was factually wrong.
       pecan jim
On Aug 27, 2008, at 8:04 AM, Paul Helbert wrote:
<Snip>
"...adding that though the sample was small, the results were  
statistically
and clinically significant. "Oh? Why, because it is his study? Seriously
question the professor's assertion that anything much can be projected  
from
one ten by ten sample.
Maybe so, maybe not.
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3) From: Paul Helbert
Thanks, Jim. I enjoyed that.
Possible outcomes for a coin toss = 2. Possible factors influencing human
hypertension = ? Surely much greater than two. So, yes, I follow and agree
with you that one should not dismiss a study out of hand because of small
sample; but unless we can hold all the other (known and unknown)  variables
constant, we might best enlarge the sample. It took the Harvard Physician's
Health Study I http://phs.bwh.harvard.edu/phs1.htm)over twenty years using
more than twenty thousand individuals to conclude that aspirin really
provided some protection from myocardial infarction. Wonder they didn't just
flip a coin ;>)
On Wed, Aug 27, 2008 at 10:47 AM, Jim Gundlach wrote:
<Snip>
-- 
Paul Helbert
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4) From: Mike Koenig
I didn't go and read the original paper, but this seems to be proving
the obvious.
Maybe I can get some grant money to prove that water is wet.
--mike
On 8/27/08, Paul Helbert  wrote:
<Snip>
-- 
Sent from my mobile device
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5) From: raymanowen
"...grant money to prove that water is wet."
<Snip>
On Wed, Aug 27, 2008 at 10:55 AM, Mike Koenig  wrote:
<Snip>
-- 
"When the theme hits the bass, I dance the Jig!" - -Virgil Fox at the Mighty
Wichita (ex- NYC Paramount) WurliTzer- 1976
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6) From: Morris Nelson
Who knows, maybe ask the guy that discovered that circulation of atmosphere
affected Mediterranean climate 20,000 years ago.

7) From: raymanowen
Actually reminds me of Day 1 in Physics 101 class at Bradley U with Dr.
Ernst Ising. "You have just one thing to learn all year, F" he said.
The Ising Effect came later, but it took the whole first year to plumb the
elementary possibilities of F for us Freshmen would-be EE's.
25 years later, Dad and I met Dr. Ising at a Victor Borge concert, and he
still remembered my innovative (erroneous) solution to a problem involving
the centripetal force on a line as it unwound a ball from a pole + angular
speed, angle of the line as a function of time.
Now I can build a Heck of a Door Bell! Never had statics (math) by itself,
only with dynamics- more physics...
Cheers, Mabuhay -RayO, aka Opa!
Got Grinder?
On Wed, Aug 27, 2008 at 8:47 AM, Jim Gundlach wrote:
<Snip>
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8) From: Seth Grandeau
Ray, your story reminds me of a guy I met the other day with a shirt that
read
2 + 2 = 5
for very large values of 2
It made me smile. :)
On 8/28/08, raymanowen  wrote:
<Snip>
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9) From: silascoelho
another way to see it:
2+2=5, when 2 'tends' to infinite
:-)


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