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


From   Yuval Arbel <yuval.arbel@gmail.com>
To   statalist <statalist@hsphsun2.harvard.edu>
Subject   Re: st: How do I demonstrate that a sample is randomly drawn from a population?
Date   Sun, 14 Apr 2013 21:40:53 -0700

Nick and David, thank you very much for your very good advises. The
idea to weight the sample based on the population sounds great!!!

On Sun, Apr 14, 2013 at 4:56 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
> 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 <yuval.arbel@gmail.com> 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: yuval.arbel@carmel.ac.il
>> e-mail2: yuval.arbel@gmail.com
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-- 
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
e-mail1: yuval.arbel@carmel.ac.il
e-mail2: yuval.arbel@gmail.com
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/


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