Re: st: Illustrate SRS in a graph

[Maarten buis <maartenbuis@yahoo.co.uk>]

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------


--- On Thu, 16/9/10, Richard Moverare wrote:
> I would like to illustrate the uncertainty of a SRS
> (without replacement) by first creating a dataset with
> one variable that identifies a number of different
> groups in the population (N), e.g. 415 units in group A,
> 634 units in group B, on so forth. Then I would like to
> draw a number of samples from that population, e.g. 20
> different samples and get estimates for the proportion of
> the population belonging to group A, B, ..., and the
> confidence interval (95 percent) for those estimates. And
> finally I would like to, in a graph, illustrate the true
> population proportion and the 20 different samples with
> their confidence intervals. This in order to illustrate
> the uncertainty but also that the confidence interval
> sometimes do not include the true population value.

As I understand Simple Random Sampling, it would be sampling
with replacement (but if the population is large compared
to the sample that should not matter too much).

*------------------- begin example --------------------
program drop _all
program define sim, rclass

    drop _all
    set obs 10000
    gen x = cond(_n <=  500, 1, ///
            cond(_n <= 5000, 2, 3))
    sample 1
	proportion x
	return scalar p  = _b[x:1]
	return scalar lb = _b[x:1] - invttail(e(df_r),0.025)*_se[x:1]
	return scalar ub = _b[x:1] + invttail(e(df_r),0.025)*_se[x:1]
end
simulate p=r(p) lb=r(lb) ub=r(ub), reps(20) : sim
gen sample = _n
twoway scatter sample p || ///
       rcap lb ub sample, horizontal xline(.05)



      

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