Fwd: st: Illustrate SRS in a graph

[Richard Ohrvall <richard.ohrvall@gmail.com>]

Just an additional small question, is there some way that I can
extract all the proportions and their lower and upper bonds from the
simulation by using some sort of loop? I have made it by repeating the
code for each group, i.e. [x:1], [x:2] and so on. But to make the code
a bit leaner when I have many groups I assume there is some way to
loop this, but my tries with -foreach var- did not work well. Any
suggestions?

Richard

2010/9/17 Richard Moverare <richard.moverare@gmail.com>
>
> Thank you Maarten, this really helped me.
>
> All the best,
> Richard
>
> 2010/9/17 Maarten buis <maartenbuis@yahoo.co.uk>
>>
>> --- 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).
>>
>> For such an excercise I would use the -simulate- command,
>> like in the example below. I recovered the confidence
>> intervals as discussed in (Buis 2007).
>>
>> *------------------- begin example --------------------
>> program drop _all
>> program define sim, rclass
>>
>>    // create population
>>    drop _all
>>    set obs 10000
>>    gen x = cond(_n <=  500, 1, ///
>>            cond(_n <= 5000, 2, 3))
>>
>>    // draw a 1% sample without replacement
>>    sample 1
>>
>>    // estimate the proportions and return the results
>>    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
>>
>> // repeat this 20 times and store the results in a dataset
>> simulate p=r(p) lb=r(lb) ub=r(ub), reps(20) : sim
>>
>> //graph the results
>> gen sample = _n
>> twoway scatter sample p || ///
>>       rcap lb ub sample, horizontal xline(.05)
>> *-------------------- end example --------------------------------
>> (For more on examples I sent to the Statalist see:
>> http://www.maartenbuis.nl/example_faq )
>>
>> Hope this helps,
>> Maarten
>>
>> M.L. Buis (2007), "Stata tip 54: Where did my p-values go?",
>> The Stata Journal, 7(4), pp.584-586.
>>
>>
>> --------------------------
>> Maarten L. Buis
>> Institut fuer Soziologie
>> Universitaet Tuebingen
>> Wilhelmstrasse 36
>> 72074 Tuebingen
>> Germany
>>
>> http://www.maartenbuis.nl
>> --------------------------
>>
>>
>>
>>
>> *
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>

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