Generalizing About a Small Population

[ar7347]

All,

I am citing a study conducted by someone else that surveyed the lead state official, for every state, on a certain issue.

Thus, the population size is 50. Twenty-five officials responded.

24 out of the 25 responders answered "they use a particular approach to address a certain issue" . I would like to use this survey to state (paraphrasing) that this is evidence that "this particular approach" is the most widely used across the U.S. and that "virtually every state uses this particular approach."

My concern is that this is a small sample (only 25 observations) from which to make a statement about an entire population. However, I reassure myself that the population is also small and, indeed, the sample is 50% of the population. Thus, I believe that this is a fair statement.

Am I on firm ground here? Is there specific technical language someone would recommend I use to make this point? I do not think that this rises to the level of reporting any further statistical information. A web search did not prove to very helpful and I cannot find a text that addresses the issue.

As an aside, if this is applicable and helpful, consider a  certain issue. I know that is conducing surveys I have seen it stated that one can stop collecting additional observations if one keeps on obtaining the same response to this issue. Thus, in this example, it seems to me like there is really little point in seeking answers from additional states.

Thanks much for any thoughts,

Rayman
Rayman Mohamed
Assistant Professor
Wayne State University
College of Liberal Arts and Sciences
Department of Geography and Urban Planning
656 West Kirby Street
3198 Faculty/Administration Building
Wayne State University
Detroit, Michigan  48202
Tel: [phone]
Fax: [phone]
http://www.clas.wayne.edu/GUP/

[Hector Maletta]

         Rayman,
         The problem is that your sample is not of 25 cases. Your sample
size is 50, i.e. all states were asked the question, but 25 chose not to
respond. Therefore, the 25 respondents are not a random sample of the 50
states, and therefore no inference can be drawn on the other 25, unless you
can show that not responding is something completely independent of the
approach used in the state.

         Hector

         -----Mensaje original-----
De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de
Rayman Mohamed
Enviado el: 26 May 2007 20:12
Para: [hidden email]
Asunto: Generalizing About a Small Population

         All,

         I am citing a study conducted by someone else that surveyed the
lead state official, for every state, on a certain issue.

         Thus, the population size is 50. Twenty-five officials responded.

         24 out of the 25 responders answered "they use a particular
approach to address a certain issue" . I would like to use this survey to
state (paraphrasing) that this is evidence that "this particular approach"
is the most widely used across the U.S. and that "virtually every state uses
this particular approach."

         My concern is that this is a small sample (only 25 observations)
from which to make a statement about an entire population. However, I
reassure myself that the population is also small and, indeed, the sample is
50% of the population. Thus, I believe that this is a fair statement.

         Am I on firm ground here? Is there specific technical language
someone would recommend I use to make this point? I do not think that this
rises to the level of reporting any further statistical information. A web
search did not prove to very helpful and I cannot find a text that addresses
the issue.

         As an aside, if this is applicable and helpful, consider a  certain
issue. I know that is conducing surveys I have seen it stated that one can
stop collecting additional observations if one keeps on obtaining the same
response to this issue. Thus, in this example, it seems to me like there is
really little point in seeking answers from additional states.

         Thanks much for any thoughts,

         Rayman
         Rayman Mohamed
         Assistant Professor
         Wayne State University
         College of Liberal Arts and Sciences
         Department of Geography and Urban Planning
         656 West Kirby Street
         3198 Faculty/Administration Building
         Wayne State University
         Detroit, Michigan  48202
         Tel: [phone]
         Fax: [phone]
         http://www.clas.wayne.edu/GUP/