Re: Test for randomness?

Stugrad98@xxxxxxx wrote:
Hi,

Let's say I have 4,000,000 SAT scores... assume a reasonable
expectation, as with most tests, that the population follows a
normal
distribution (bell curve).

Now let's say someone gave you only 14 of those scores. You were
unsure of whether or not you had a random sampling of the scores.
However, you plot the scores on a normal probability plot and find
that most of the data points fit the line. Would you be safe in
assuming that you have a random sample?

No. One way in which the points supplied might be selected and still
show the above feature would be to order the 4 million scores and
extract 14 sample quantiles defined in an obvious way to give equal
coverage over 0 to 100%. Of course, you could test for this by seeing
if your line had too good a fit.

Should you feel comfortable
using those 14 scores to draw statistical inferences about the
entire
population of SAT scores?

Possibly, depending on what you did with them.

David Jones


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