# Re: st: Equality of two multinomial distributions under complex survey designs

 From "Austin Nichols" To statalist@hsphsun2.harvard.edu Subject Re: st: Equality of two multinomial distributions under complex survey designs Date Mon, 28 Apr 2008 12:32:18 -0400

```Maury--
Suppose you make an indicator for which survey data is drawn from,
then use it to construct superstratum identifiers that are unique
across the two surveys and redefine weights so they each sum to the
same population size, then tab industry versus the indicator, like so:

webuse nhanes2f, clear
svyset
tempfile file1
save `file1'
webuse nhanes2, clear
svyset
g supstr=200+strat
g svy=2
append using `file1'
replace svy=1 if mi(svy)
replace supstr=100+stratid if mi(supstr)
egen pop=sum(finalw), by(svy)
g wt=finalw/pop
g suppsu=svy*100+psu
replace suppsu=svy*100+psuid if mi(suppsu)
svyset suppsu [pw=wt], strat(supstr)
svy: tab region svy

and interpret the F test as a test of equality of distribution across
svy.  This may or may not be defensible on theoretical grounds--with
any luck, others will comment.

On Fri, Apr 25, 2008 at 11:24 AM, Gittleman, Maury - BLS
<Gittleman.Maury@bls.gov> wrote:
> Hello,
>
> I'm wondering if someone out there can point me in the right direction
> with respect to the following problem:
>
> I am working with two independent surveys, both of which have complex
> survey designs.  Both are designed to measure what's going on in US
> labor markets.  In the first survey, establishments are selected in the
> 1st stage of sampling and then certain individuals within these
> establishments are randomly selected to participate in the survey.  In
> the second survey, households are first selected at random, and then
> individuals who are working are then surveyed.  From both surveys, it is
> possible to obtain industry of employment, and then one can calculate
> the (multinomial) distribution of employment across industries.  I want
> to test the hypothesis that the two distributions so derived are equal.
> Without the complex survey designs, I think it would be straightforward
> to do a chi-squared test, but I'm wondering what to do to take into
> account the design effects.
>
> Thanks in advance for any suggestions.
>
> Maury Gittleman
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