# Re: st: variance when using svy: mean

 From "David Merriman" <[email protected]> To [email protected] Subject Re: st: variance when using svy: mean Date Mon, 3 Dec 2007 12:26:02 -0600

```Thanks, I am understanding better.
Within each area I took a random (iid) sample from an infinite
population.  The sample sizes varied for reasons that are contextual
and difficult to explain without telling you all the details of the
project. (Can you help me with the computer code here?  How do I tell
stata that I took a random sample within psus?)

So, if I understand you correctly the variance of my estimate of the
population mean is roughly independent of how many observations I
have.  In other words, if I had gone to 100 different areas and
collected a single sample I would estimate the population mean with
about the same precision as if I had collected 10 samples within each
area?  I still have trouble getting my mind around that but your
example with a Census of the two areas does help.  Thanks again.

On Dec 3, 2007 12:08 PM, Steven Joel Hirsch Samuels
<[email protected]> wrote:
> Thanks, David that is clearer.
>
> Was there a sampling procedure within areas? If not, you can still
> apply the -svy- commands, but without a sampling procedure of some
> kind, the observations within a single area may not 'represent' that
> area in any statistical sense.
>
> In any case,  the major portion of the variance of sample estimates
> will still arise from PSU-to-PSU variation. The effective sample size
> is 100, the number of PSU's.  Thought experiment:  you take a sample
> of n= 2 areas and collect information about everybody (a census).
> Even if the number of observations is 200,000, your effective sample
> size is still n=2 for making inferences about the original
> population. As long as the two area means are different, the standard
> error will be nonzero.
>
> Your simulations are therefore correct in producing the same standard
> error for the two PSU's.  If you had simulated sampling within the
> PSU's, then the you would the SE's to change, as the sample
> proportions would vary from simulation to simulation.
>
> -Steven
>
>
> 4. The sampling weight for a PSU
>
> On Dec 3, 2007, at 12:21 PM, David Merriman wrote:
>
> > Thanks.  I do have a lot of trouble with the terminology.
> > I selected a weighted random sample of 100 geographic areas from 930
> > such areas.  The weights were designed so that my weighted random
> > sample would be representative of the population (e.g. I oversampled
> > areas with a high number of people).  I do not think I have any strata
> > (I did NOT for example oversample high poverty areas).  My psus are
> > the 100 geographic areas.
> >
> > I am afraid I still do not know what to do next.  It sounds like you
> > are saying that the variance should not differ between my two cases
> > but this does not make intuitive sense to me.  Any help you can
> > provide would be appreciated.
> >
> > On Dec 3, 2007 11:11 AM, Steven Joel Hirsch Samuels
> > <[email protected]> wrote:
> >> David, it doesn't sound like your study is a probability sample; if
> >> not, you  don't need -svy- commands.  Instead, use non-survey
> >> commands and assign an -iweight-  or other weight variable to
> >> properly represent your population.
> >>
> >> If your data do arise from a probability sample, your 'areas' appear
> >> to be strata, not primary sampling units (psu's). Strata are units
> >> which partition a population. A psu is the highest stage unit
> >> selected by random numbers within a stratum.  Standard errors for
> >> survey data depend mainly on the number of psu's, not on the number
> >> of observations within them.
> >>
> >> -Steven
> >>
> >> On Dec 3, 2007, at 11:19 AM, David Merriman wrote:
> >>
> >>> Dear Statalisters:
> >>> I am a long time Statauser but new to svy: commands and am quite
> >>> confused.
> >>> I apologize if this is long-winded I am trying to say it as
> >>> concisely
> >>> as possible.
> >>>
> >>> I have collected primary data in several geographic areas.  Each of
> >>> the geographic areas has a different weight so that my entire sample
> >>> should be representative of the population.  In each geographic
> >>> area I
> >>> have collected a number of observations but the number of
> >>> observations
> >>> in the area tells me nothing about the density of the activit
> >>
> >>> area.  I want to estimate the population mean (for all geographic
> >>> areas) and the variance of that estimate.  The problem is that
> >>> while I
> >>> get sensible means the variances do not seem to be a function of the
> >>> number of observations I have.  Intuitively I think that the
> >>> variance
> >>> ought to change (fall) as the number of observations increases.
> >>>
> >>> I tried using
> >>> svyset psuedo_psu [pweight=obs_weight]
> >>> svy:  mean psuedo_chicago_tax_paid
> >>>
> >>> where psuedo_psu is the variable indicating the primary sampling
> >>> unit,
> >>> obs_weight is the psu_weight divided by the number of
> >>> observations in
> >>> that psu and psuedo_chicago_tax_paid is the (zero-one) variable for
> >>> which I want to estimate the mean and variance.
> >>>
> >>> I created a simulated data set (the real one is more complex) with 2
> >>> psus.  In the first trial, each psu had 50 observations.  psu 1
> >>> weight of 1 and a 50 percent chance of a 1.  psu 2 had a weight of 5
> >>> and a 20 percent chance of a 1.  I get a sensible mean of .25 and a
> >>> standard error of .0833333.
> >>>
> >>> In the second trial, I also had two psu.  Psu 1 has 900 observations
> >>> and psu 2 has 100 observations.  psu 1 had a weight of 1 and a 50
> >>> percent chance of a 1.  psu 2 had a weight of 5 and a 20 percent
> >>> chance of a 1.  I get a sensible mean of .25 but the same standard
> >>> error of .0833333 as in case 1.   This does not make sense to me.  I
> >>> have more observations in case 2 so I think I should get a smaller
> >>> variance.
> >>>
> >>> I imagine I am not using the correct design.  Can anyone help?
> >>> Below,
> >>> I show the computer code for my simulation (fake data set) but you
> >>> don't need to read this if you understand the comments above.
> >>> Thanks
> >>> so much.
> >>>
> >>>
> >>> #delimit ;
> >>> ****************************************************************
> >>> * created the simulated data
> >>> ***********************************************************;
> >>> set obs 100;
> >>> ****************************************************************
> >>> * generate psu
> >>> ***********************************************************;
> >>> gen psuedo_psu=1 if _n<51;
> >>> replace psuedo_psu=2 if _n>=51;
> >>> ****************************************************************
> >>> * generate chicago_tax_paid
> >>> ***********************************************************;
> >>> gen psuedo_chicago_tax_paid=1 if _n<=25;
> >>> replace psuedo_chicago_tax_paid=0 if _n>25 & _n<=50;
> >>> replace psuedo_chicago_tax_paid=1 if _n>50 & _n<61;
> >>> replace psuedo_chicago_tax_paid=0 if _n>=61;
> >>> ****************************************************************
> >>> * generate psu weights
> >>> ***********************************************************;
> >>> gen sample_weight=1 if psuedo_psu==1;
> >>> replace sample_weight=5 if psuedo_psu==2;
> >>> summarize;
> >>> ****************************************************************
> >>> * generate OBSERVATION weights
> >>> ***********************************************************;
> >>> sort psuedo_psu;
> >>> by psuedo_psu: gen obs_weight= sample_weight/_N;
> >>> summarize;
> >>> svyset psuedo_psu [pweight=obs_weight];
> >>> **********************************************************
> >>> * psu1 has a mean of .5 and a weight of 1
> >>> * psu2 has a mean of .2 and a weight of 5
> >>> * (5*.2)+(1*.5)=1.5
> >>> * 1.5/6=.25
> >>> *
> >>> * so the mean estimate makes sense to me
> >>> *******************************************************;
> >>> svy : mean psuedo_chicago_tax_paid;
> >>> mean psuedo_chicago_tax_paid;
> >>> *********************************************************
> >>> * do a second round with unequal size groups
> >>> *****************************************************;
> >>> clear;
> >>> #delimit ;
> >>> ****************************************************************
> >>> * created the simulated data
> >>> ***********************************************************;
> >>> set obs 1000;
> >>> ****************************************************************
> >>> * generate psu
> >>> ***********************************************************;
> >>> gen psuedo_psu=1 if _n<901;
> >>> replace psuedo_psu=2 if _n>=901;
> >>> ****************************************************************
> >>> * generate chicago_tax_paid
> >>> ***********************************************************;
> >>> gen psuedo_chicago_tax_paid=1 if _n<=450;
> >>> replace psuedo_chicago_tax_paid=0 if _n>450 & _n<=900;
> >>> replace psuedo_chicago_tax_paid=1 if _n>900 & _n<921;
> >>> replace psuedo_chicago_tax_paid=0 if _n>=921;
> >>> ****************************************************************
> >>> * generate PSU weights
> >>> ***********************************************************;
> >>> gen sample_weight=1 if psuedo_psu==1;
> >>> replace sample_weight=5 if psuedo_psu==2;
> >>> ****************************************************************
> >>> * generate OBSERVATION weights
> >>> ***********************************************************;
> >>> sort psuedo_psu;
> >>> by psuedo_psu: gen obs_weight= sample_weight/_N;
> >>> summarize;
> >>> svyset psuedo_psu [pweight=obs_weight];
> >>> **********************************************************
> >>> * psu1 has a mean of .5 and a weight of 1
> >>> * psu2 has a mean of .2 and a weight of 5
> >>> *
> >>> * I get the same answer for the mean in case 1 and case 2
> >>> * which I think is correct but
> >>> * I also get the same answer for the variance which I think is not
> >>> correct
> >>> *
> >>> * I think I should have a lower variance in case 2
> >>> *******************************************************;
> >>> svy : mean psuedo_chicago_tax_paid;
> >>> mean psuedo_chicago_tax_paid;
> >>>
> >>>
> >>>  --
> >>> David Merriman
> >>> [email protected]
> >>> *
> >>> *   For searches and help try:
> >>> *   http://www.stata.com/support/faqs/res/findit.html
> >>> *   http://www.stata.com/support/statalist/faq
> >>> *   http://www.ats.ucla.edu/stat/stata/
> >>
> >> Steven  Samuels
> >>
> >> [email protected]
> >> 18 Cantine's Island
> >> Saugerties, NY 12477
> >> Phone: 845-246-0774
> >> EFax: 208-498-7441
> >>
> >>
> >>
> >>
> >>
> >> *
> >> *   For searches and help try:
> >> *   http://www.stata.com/support/faqs/res/findit.html
> >> *   http://www.stata.com/support/statalist/faq
> >> *   http://www.ats.ucla.edu/stat/stata/
> >>
> >
> >
> >
> > --
> > David Merriman
> > [email protected]
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/support/faqs/res/findit.html
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
>
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

--
David Merriman
[email protected]
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
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*   http://www.ats.ucla.edu/stat/stata/
```