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

 From Yuval Arbel To statalist 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
> 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.
>>
>>
>> --
>> Dr. Yuval Arbel
>> 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