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# Re: st: weight in a field survey

 From Steve Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: weight in a field survey Date Tue, 23 Mar 2010 11:14:10 -0400

```Estelle, I think that by "stratum weight", you mean the first-stage,
selection of villages within strata, and that by "cluster weight", you
mean the second-stage selection of households within village.  Please
use standard terminology to avoid confusion. The general rule for
constructing weights is as you say: multiply together the first and
second-stage probabilities, then invert. (Or invert and then
multiply).

The 5 HH per village design might not be PPS.  Suppose the measure of
size at the first stage is the estimated population size of each
village. Two villages in the same stratum, both with estimated
population N = 2000, would have the same first-stage probability of
selection. If there are 500 HH in the first village, 600 in the
second, and a simple random sample of HH is taken in each, the second
stage probabilities will differ.  See Kish, Survey Sampling, 1965,
Wiley, page 223.

Michael is not correct about having to add a weight for household size
to analyze individual data.  Each person in a selected household
shares the selection probability of the household and gets the same
sampling weight.

If there is external information about the stratum characteristics,
including the distribution of age, village sizes, gender, sizes of
households, for example, the sampling weights can be "raked" so that
totals of these characteristics estimated from the sample match the
known population totals. See Nick Winter's -survwgt- package,
available at SSC.

describe the algorithm that you used or intend to use.
Steve

On Mon, Mar 22, 2010 at 5:43 PM, Michael I. Lichter
<mlichter@buffalo.edu> wrote:
> Estelle,
>
> If this is a true PPS design, you shouldn't have to weight for anything
> except for unequal probabilities of selection across strata. (Unequal
> probabilities for village selection are balanced out by unequal
> probabilities for household selection.) That weight would be, as I think
> you're saying, weight for stratum i = 1/(proportion of total population in
> stratum i). Of course, you will also want to add a weight for household size
> when doing individual-level tabulations.
>
> Michael
>
> Estelle PASQUIER wrote:
>>
>> Dear statlist,
>>  We are conducting a field survey on
>> malaria. Our population is sampled by stratifying it in rural and urban
>> settings (first step) then selecting villages with a probability
>> proportional
>> to their population sizes. The last step consists in selecting randomly a
>> fixed
>> number of households in the village. I am a little bit concern with the
>> sample
>> weights I have to choose with svy: my suggestion would be to calculate the
>> stratum weight as the ratio of total population on population in each
>> stratum;
>> to calculate the cluster weight as the inverse of the sampling
>> probability, and
>> then to use the product of these two weights as final weight. Am I right?
>> My second concern is to know if I there is
>> anything to do for the last step of this sampling design? Thanks for any
>> help,
>>  Estelle
>>
>>
>>
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>
> --
> Michael I. Lichter, Ph.D. <mlichter@buffalo.edu>
> Research Assistant Professor & NRSA Fellow
> UB Department of Family Medicine / Primary Care Research Institute
> UB Clinical Center, 462 Grider Street, Buffalo, NY 14215
> Office: CC 126 / Phone: 716-898-4751 / FAX: 716-898-3536
>
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>

--
Steven Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
Voice: 845-246-0774
Fax:    206-202-4783

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```