Re: A test for randomness?

Stugrad98@xxxxxxx wrote:
Here might be a way of simplying this question.

Given the same parameters: 4,000,000 SAT scores with a expected
normal distribution; you do not know the mean and standard deviation
however. You have a sample of 14 test scores and you do not know if
your sample is a random, representative sample. However, you do know
that you plot these 14 scores on a normal probability plot.

Person A argues that however large his sampling error may be, he is
still safe in assuming he has a random sample because, in a broad way,
the 14 sized sample fits the expected (normal) distribution.

Person B argues that this is a non-sequitir... you cannot make *ANY*
infererence to population based on these 14 data points simply because
they fit an expected distribution type. This is not a reliable test
to see if you have a random sample; it may simply be that, given the
small sample size, you got lucky in fitting most of the data to a
normal probability graph. You cannot infer a mean and standard
deviation for the overall population from these 14 data points.

Who is right: Person A or Person B?

Thanks
-Stu

Thanks for your replies clarifying your question. Anon
and m00es gave good replies. Here's mine, FWIW.

Who's right, A or B? Both, or neither. If you force
me to make a choice between A or B being right, I'll
say B, but sometimes one has to take A's approach.
Again IMO it depends on the use to which the data
will be put. If a decision *must* be made, then the
best estimates from the data at hand should be used,
with the clear and strong caveat that such a small
sample may not be representative (even though it
appears to be consistent with your model as far as
can be determined). If the decision is not robust to
this fact or the use to which the data is being put
(such as determining the tails of the distribution) is
highly dubious given the sample size, then either
demand more data or refuse to be held responsible
for the consequences if things turn out poorly. If the
consequences for being wrong are minor, don't worry.
If the consequnces are severe, worry, or demand
more data.

Cheers,
Russell

.

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