At 02:04 PM 4/9/01 -0700, James Ankeny wrote:
> Hello,
> I have a question regarding the so-called normal approx. to the binomial
>distribution. According to most textbooks I have looked at (these are
>undergraduate stats books), there is some talk of how a binomial random
>variable is approximately normal for large n, and may be approximated by the
>normal distribution. My question is, are they saying that the sampling
>distribution of a binomial rv is approximately normal for large n?
well, yes, i think that is exactly the implication ...
with small n ... say n = 6 ... the only possible score values would be 0 up
to 6 ... so,
:
: : :
: : :
. : : : .
. : : : : : .
+---------+---------+---------+---------+---------+-------C1
0.0 1.2 2.4 3.6 4.8 6.0
note how large the GAPS are ... the gaps stand out ... if you wanted to
find the percentile rank for a score of 2.4 ... this is in an area where NO
scores are ... so, to think that z = (2.4 - mean) / sd ... is a little
stretch if you look up the area up to that point in a normal curve table
MTB > rand 1000 c2;
SUBC> bino 30 .5.
MTB > dotp c2
Dotplot: C2
Each dot represents up to 16 points
: : :
. : : : :
. : : : : : .
. . : : : : : : : .
. : : : : : : : : : : : : . . . .
-----+---------+---------+---------+---------+---------+-C2
9.0 12.0 15.0 18.0 21.0 24.0
MTB >
still are gaps ... have to be in binomial BUT, relatively speaking ... gaps
become less obvious ...
>Typically, a binomial rv is not thought of as a statistic, at least in these
>books, but this is the only way that the approximation makes sense to me.
>Perhaps, the sampling distribution of a binomial rv may be normal, kind of
>like the sampling distribution of x-bar may be normal? This way, one could
>calculate a statistic from a sample, like the number of successes, and form
>a confidence interval. Please tell me if this is way off, but when they say
>that a binomial rv may be normal for large n, it seems like this would only
>be true if they were talking about a sampling distribution where repeated
>samples are selected and the number of successes calculated.
>
>
>
>
>
>
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_________________________________________________________
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
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