sampling question

[Sebastián Daza]

list,
somebody knows how to carry out a sampling pps without replacement. the module complex samples has the option but always appears me the error: The maximum Measure of Size (MOS) valued across population units cannot be greater than total the MOS in the population divided by the sample size.

some recommendation? thank you for the help. greetings.

[Jeff-125]

At 10:42 AM 4/12/2007, you wrote:
>somebody knows how to carry out a sampling pps without replacement.
>the module complex samples has the option but always appears me the
>error: The maximum Measure of Size (MOS) valued across population
>units cannot be greater than total the MOS in the population divided
>by the sample size.
>
>some recommendation? thank you for the help. greetings.


It's not an error. I fought with this recently myself and finally got
it. Let me see if I can explain with an extreme example. You have 100
organizations in a population. The 20 largest contain 5 times more
employees than do the 80 smallest. So each of the top 20 should be 5
times more likely to be selected than any of the bottom 80.

You decide to sample 50 organizations with probability proportionate
to size. Forgetting for a minute about the 20 largest, 50/100 is .5.
So the minimum probability of selection is .5. You can't get
lower.  ...but you want the largest 20 to be 5 times more likely than
the smallest 80. So therefore, each of the top 20 must be chosen with
a probability of 5 x .5 = 2.5 (or 250% chance of being
chosen).  Clearly, you must use pps with replacement to achieve this
(can't do it with pps w/o and thus the nature of your error).

The solution to my recent problem was to use techniques that
generally are considered the use of "self-representing" units where
the largest are chosen with a probability of 1 and after a certain
point, the smaller units are chosen with pps w/out replacement. You
then have to use a slightly more complex weighting scheme. See the
Kish text below for the classic discussion on this, as well as Lohr
text that is updated, but still refers the reader to Kish for the basics.

You might also search the SAS list archives, which have mentioned the
problem for years, as Proc surveyselect has been around longer than
the SPSS version.

Kish, L. (1965). Survey Sampling. New York, John Wiley and Sons.

Lohr, S. L. (1999). Sampling: Design and Analysis. Pacific Grove, CA,
Brooks/Cole.


Jeff

[Sebastián Daza]

thank you jeff for your complete answer. my design included self-representing units, and your recommendation works perfect.

I will study the topic of the weight.
greetings and thank you.