{smcl}
{* 26 May 2008}{...}
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help for {hi:samplepps}{right: Stephen P. Jenkins (June 2005, help revised May 2008))}
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{title:Draw random sample, proportional to size, of n cases}

{p 4 12}{cmd:samplepps} {it:newvar} [{cmd:if} {it:exp}] [{cmd:in} {it:range}] 
	, {cmdab:n:cases(}{it:integer}{cmd:)} {cmdab:s:ize(}{it:sizevar}{cmd:)} 
	  [{cmdab:with:repl} ]

{title:Description}

{p 4 4}{cmd:samplepps} draws a random sample with {it:ncases} observations from
the current data set, with probabilities proportional to size (`pps'). The default
is to select cases without replacement; optionally cases may be selected with 
replacement. 

{p 4 4}If sampling is without replacement, the variable {it:newvar} is 
equal to 1 for selected cases, and 0 for non-selected cases. The program returns
an error if either the number of cases to be selected is greater than the 
number of valid observations, or if any observation has {it:newvar}/(SUM_i {it:newvar}) 
>= 1/{it:ncases}.

{p 4 4}If sampling is with replacement, the variable {it:newvar} is equal to a 
positive integer for selected cases (the integer is the number of times the case has 
been selected), and 0 for non-selected cases. For both types of sampling, 
{it:newvar} is missing if {it:sizevar} is missing.

{p 4 4}If you are serious about drawing random samples, you must first set the 
random number seed; see {help generate}.

{p 4 4}Methods for sampling with probabilities proportional to size are discussed by 
Lohr (1999). See also Levy and Lemeshow (1991, chapter 11) and Som (1973, chapter 5), 
who focus on the with-replacement case. The algorithm used by {cmd:samplepps} 
for the with-replacement case is the standard `cumulative method'.
For the without-replacement case, I used an algorithm described by Jean-Yves Pip 
Courbois (formerly at the University of Washington), orginally due to Madow (1949).
For more details, see Brewer and Hanif (1983) and Cochran (1997, p. 265) who cites 
Hartley and Rao (1962) and Madow (1949).

{title:Options}

{p 4 4}{cmd:ncases(}{it:integer}{cmd:)} specifies the number of observations to be selected.

{p 4 4}{cmd:size(}{it:sizevar}{cmd:)} specifies the name of the existing variable summarizing
`size'.

{p 4 4}{cmd:withrepl} specifies selection with replacement. (If the option
is specified, a given obs may be selected more than once.)

{title:Saved results}

{p 4 4}{cmd:r(ncases)} is the integer {it:ncases}.

{p 4 4}{cmd:r(nobs)} is the number of valid observations at risk of being sampled.

{p 4 4}{cmd:r(sizevar)} contains the name {it:sizevar}.

{p 4 4}{cmd:r(withrepl)} = 1 if the with-replacement option was specified.

{p 4 4}{cmd:r(sample)} contains the name {it:newvar}.

{title:Examples}

{p 8 12}{inp:. set seed 123517}

{p 8 12}{inp:. samplepps pick1, size(n_pupils) n(100) }

{p 8 12}{inp:. samplepps pick2, size(n_pupils) n(50) withrepl }

{title:Acknowledgements}

{p 4 4}Program written with support of ESRC grant number RES-000-22-0995 
("Social segregation in UK schools: benchmarking with international comparisons").
For helpful discussions, I thank project colleagues John Micklewright and 
Sylke Schnepf, and also Philippe Van Kerm. Steven Samuels due my attention to the
references by Cochran, Hartley and Rao, and Madow. Ben Jann drew my attention to the
Brewer and Hanif reference.

{title:Author}

{p 4 4}Stephen P. Jenkins, ISER, University of Essex, U.K.{break}
<stephenj@essex.ac.uk>


{title:References}


{p 4 8} Brewer, K. R. W. and Muhammad Hanif. 1983. Sampling with Unequal Probabilities. New York: Springer.

{p 4 8}Cochran, William G. 1977. {it:Sampling Techniques, 3rd Edition}. New York: Wiley.

{p 4 8}Madow, William G. 1949. On the theory of systematic sampling. II. {it:Annals of Mathematics and Statistics}, 19: 535{c -}545.

{p 4 8}Hartley, H.O. and J.N.K. Rao. 1962. Sampling with unequal probabilities and without replacement. 
{it:Annals of Mathematics and Statistics}, 33: 350{c -}374.

{p 4 8} Levy, Paul S. and Stanley Lemeshow. 1991. {it:Sampling of Populations: Methods and Applications, 2nd edition}.
New York: John Wiley and Sons.

{p 4 8} Lohr, Sharon L. 1999. {it:Sampling: Design and Analysis}. Pacific Grove CA: Duxbury Press.

{p 4 8} Som, Ranjan K. 1973. {it:Practical Sampling Techniques, second edition, revised and expanded}.
New York: Marcel Dekker.


{title:Also see}

{p 1 14}Manual:  {hi:[S-Z] sample}

{p 0 19}On-line:  help for {help sample}, and {help gsample} if installed. {p_end}