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Re: st: How do I demonstrate that a sample is randomly drawn from a population?

From   David Hoaglin <>
Subject   Re: st: How do I demonstrate that a sample is randomly drawn from a population?
Date   Sun, 14 Apr 2013 19:56:20 -0400

Dear Yuval,

The only conclusive way of showing that a sample is a random sample
from a given population is to demonstrate that the method of selection
produces random samples.

The students who filled in a questionnaire via the net selected
themselves into the sample, so the details of the mechanism are
unknown.  Thus, those students are not a random sample.

They might be an adequate approximation to a random sample.  A common
approach in such situations is to examine all the relevant
characteristics in the population and determine how closely the joint
distribution of those characteristics in the sample resembles the
joint distribution in the population.  That will require a much
greater effort than comparing the mean of the sample and the mean of
the population. You can start with the distribution of each
characteristic and move on to each pair of characteristics and then
each combination of three characteristics, and so on.

If some characteristics of the sample differ from those of the
population, it may be acceptable to reweight the sample, so that the
weighted distributions match those of the population.  This process is
used in surveys, where it is known as poststratification (though
usually the sampling mechanism is of better quality).

David Hoaglin

On Sun, Apr 14, 2013 at 3:00 PM, Yuval Arbel <> wrote:
> Dear statalisters,
> I have two files:
> 1) The first file contains the grades of all population of Open
> University students.
> 2) The second file contains the grades of Open University students,
> who filled a questionnaire via the net.
> I would like to show that the second file is a random sample drawn
> from the first file.
> The question is can I provide a statistical evidence that the sample
> is indeed random? what are the appropriate commands in stata?
> P.S. I thought to run the test of difference of means between two
> populations. Having reconsidered, however, I'm not talking here about
> two populations, but rather a sample,which is drawn from a given
> population.
> As always, your answers will be very much appreciated
> --
> Dr. Yuval Arbel
> School of Business
> Carmel Academic Center
> 4 Shaar Palmer Street,
> Haifa 33031, Israel
> e-mail1:
> e-mail2:
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