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?

Just imagine if the person who gave you the data was evil and intent on confusing you. Could they give you data that would fool this test?

Bob

--
Bob O'Hara

Dept. of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland

Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: http://www.jnr-eeb.org

.

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