Re: Statistics Question

"David in NYC" <sorry@xxxxxxxxxxxxxxx> queries:

OK, this is not specific to baseball, but I am trying to learn
statistics to better understand baseball, so maybe one of the
math wizards around here can help me out.

I have reading a basic statistics text, and have been working
out a few equations as a sanity check. In particular, I am trying
to see if a P value I get for a series of coin tosses jibes with the
probability I would get from a binomial distribution.

Lets say I flip a coin 40 times, and get 16 heads. If my null
hypothesis is that the coin is not biased towards tails, then
I would figure I would calculate the P value by:

Figuring out the standard error, which is the square root
of .5*(1-.5)/40, which equals 0.079056942

Converting the difference between my expected proportion
of heads (.5) and my observed proportion (.4) into a standard
score. This would be a difference of .1, so it would
be 1.264911064 standard errors.

In Excel, NORMSDIST(1.264911064) == 0.897048395.
Subtracting that from 1, I get a P-Value of .103. Alternatively,
using the TDIST function with 39 degrees of freedom gives
me a P-Value of .107

OK, so assuming I got the P value correct (which I am starting
to doubt), I would think that using the BINOMDIST function
would give me a similar result. But =BINOMDIST(16,40,0.5,TRUE),
which should tell me the probability of getting 16 or fewer heads,
is 0.134. Should this not equal my P-Value from above?
If so, what am I doing wrong?

You are trying to estimate the *discrete* binomial distribution
with the *continuous* normal distribution.

On a continuous distribution, 16 runs from 15.5 to 16.5,
so you want the probability of 16.5 or fewer heads.

z = (20 - 16.5) / SQRT (.5 * .5 * 40) = 1.107; p. = .134

or .5 - (16.5 / 40) / .079 = 1.107; p. = .134 QED

So using 16.5 as the upper limit of 16 on a continuous
distribution yields a much more accurate estimate of the
actual discrete binomial probability.

--
Don

Facts are stubborn things, but statistics are much more pliable.
~ Mark Twain


.

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