Roger's original question was about elementary statistical inference, which
requires the use of simple random samples (SRSs). For Roger's assistance I
would like to repeat David S. Moore's definition of an SRS. The quotes are
from
Moore's The Basic Practice of Statistics, Chapter 7 Producing Data: Sampling.
"A simple random sample (SRS) of size n consists of n individuals from the
population chosen in such a way that every set of n individuals has an equal
chance to be chosen."
Moore comments, "An SRS not only gives each individual an equal chance to be
chosen (thus avoiding bias in the choice) but also gives every possible sample
an equal chance to be chosen."
Here is the Dictionary's example of a dyadic use of 6!:2
a=:?50 50$100
6!:2 '%.a'
0.091
10 (6!:2) '%.a' NB. Mean time of 10 executions
0.0771
It is a matter of judgment whether those ten executions would qualify as a
simple random sample. At first glance they appear to be a special kind of
sample in which the ten executions are very close together in time. (I am
ducking the question of what population the sample is chosen from.)
Thus the mean and standard deviation of the times of those ten executions can
serve to describe the sample (descriptive statistics), but for this sample it
may be unwise to draw conclusions from a confidence interval or hypothesis test
(inferential statistics).
Correct sampling is essential for statistical inference.
On 10/21/2011 7:40 AM, Brian Schott wrote:
> This thread makes me think that the dyadic form of 6!:2 would be
> better if it produced the individual times and not the average of the
> times because then the mean and the standard deviation or some other
> measure of dispersion could be extracted directly from the results.
>
> Also, perhaps a similar dyadic form could be added to 7!:2, but this
> is not as important for most operations.
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