st: sampling query

[Richard Goldstein <richgold@ix.netcom.com>]

all,

I have received a report in which the report writer was stuck with the
following design (already implemented before his involvement): a number
of "cohorts" were set up (22 of them in fact) and the definitions of
these cohorts were not mutually exclusive (i.e., there was some overlap
in membership so that a given observation could appear in more than 1
cohort); to calculate the probability weights, the report writer first
calculated the probability of inclusion for each cohort (simply as n/N
where n is sample size from cohort and N is population size of cohort).

For observations in more than one cohort, who were actually selected, he
then multiplied the inclusion probabilities of each cohort that
observations was in. Since each inclusion probability is less than 1,
the combined inclusion probability is smaller than the individual
inclusion probabilities for the individual cohort. And then, of course,
the weights are greater for these people (since the weight is just the
inverse of the inclusion probability).

However, since these observations are in more than one cohort, shouldn't
the combined probability be greater for them (rather than smaller)?

How should the combined inclusion probability be calculated?

Or am I just wrong and the writer of the report is correct?

Any references on dealing with overlapping "cohorts" would also be
greatly appreciated.

Rich

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