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Date:         Thu, 10 Oct 2002 01:13:06 -0700
Reply-To:     John Hendrickx <john_hendrickx@yahoo.com>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         John Hendrickx <john_hendrickx@yahoo.com>
Subject:      Re: Sample vs Population
Comments: cc: SRMSNET@LISTSERV.UMD.EDU
In-Reply-To:  <3DA4B732.9070800@citrus.ucr.edu>
Content-Type: text/plain; charset=us-ascii

Software for complex survey designs can deal with samples from a "finite population", i.e. a relatively small population whose size is known. Wesvar and SUDAAN are stand-alone programs, Stata and SAS are packages with these facilities.

Of course you'd be making the very dubious assumption that the non-responses are missing at random and that your sample therefore constitutes a random sample of the population. When dealing with a large non-random sample of a population, sampling fluctuations aren't an issue. The problems you're dealing with now (in my opinion) are:

1. Is selective non-response leading to bias in my results? 2. How are confidence intervals affected by model misspecification (omitted variables, omitted interaction effects).

I don't suppose there's much you could say about (1). You could run a few simulations assuming a certain amount of bias in your sample to get an idea of the accuracy of your results in a "worst case" scenario. Maybe there are better methods available?

With regard to (2), you might get an answer using the software for comples surveys mentioned above. These can calculate "robust standard errors" that take model misspecification into account. For example, in a regression model the standard errors are weighted by the residuals of the model. This takes heteroscedasticity due to unequal sampling probabilities (weighted dataset) or omitted variables into account. But I'm not sure whether these standard errors would be meaningful if you're dealing with a non-random sample.

I've crossposted this to the survey research methods list, perhaps the folks there can shed some more light on this issue. The easiest advice of course is to forget statistical inference and to treat your results as the population parameters. But I wonder if perhaps more can be said when dealing with population data.

--- Jelani Mandara <jelani@citrus.ucr.edu> wrote: > Alison Neustrom wrote: > > >What would you say if you had 80% of a non-random sample of a > population (I > >sent them to everyone but only got back 80%)? Would you consider > that a > >sample or a population? > > > > > > > > Inferential stats rely on the size of the sample more than the % of > the > population sampled. This is a weakness, but since we rarely know > the > actual size of the population, it's understandable. > > So, I would argue that it depends on the size of the > sample/population. > If you have 80% of 100, then you may wish to increase alpha, since > you > risk the chance of Type II errors (i.e., incorrectly concluding a > null > result). I think increasing alpha will be more reliable than just > using > descriptives to test nulls in small samples when you have 80% of > the > population. In large samples (say, N > 1000) I doubt it matters. > Some > of the statisticians on the list may know for sure. > > >-----Original Message----- > >From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU]On > Behalf Of > >Jelani Mandara > >Sent: Wednesday, October 09, 2002 11:50 AM > >To: SPSSX-L@LISTSERV.UGA.EDU > >Subject: Re: Sample vs Population > > > > > >Fink, Steven wrote: > > > > > > > >>Recently, I've been asked by several analysts about analyzing > populations, > >> > >> > >that is, data not from a sample. > > > > > >>The purpose of a statistical test is to make estimates about the > >> > >> > >population. If my data set IS the population, are significant > tests > >appropriate? > > > > > >> > >> > >> > >No. Descriptives and Effect Sizes are still relevant, but not > >inferential stats. > > > > > > > >>What about if my response rate (survey/unit) is low, say 20%. > For example, > >> > >> > >I sent surveys to everyone in the population, but only received > 20% of > >responses. Does this change your answer to the first question? > > > > > >> > >> > >> > >> > > > >Then you only have a (probably nonrandom) sample of the > population. The > >logic of inferential stats applies. > > > > > > > >>Thanks > >> > >> > >> > >>Steve > >> > >> > >> > >> > >> > > > >-- > >Jelani Mandara > >Assistant Professor > >Human Development and Social Policy > >Northwestern University > >2120 Campus Drive > >Evanston, Il 60208 > > > >Office Phone: (847)491-3122 > >Web Page: > http://www.sesp.northwestern.edu/people/sp/j_mandara.html > > > > > > > > -- > Jelani Mandara > Assistant Professor > Human Development and Social Policy > Northwestern University > 2120 Campus Drive > Evanston, Il 60208 > > Office Phone: (847)491-3122 > Web Page: http://www.sesp.northwestern.edu/people/sp/j_mandara.html

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