Sample from finite population with known number of true positives

Sample from finite population with known number of true positives

sample_finite_population(n, N, p = NULL, npositive = NULL,
  replicates = 1)

Arguments

n	sample size
N	Population size
p	positive probability (e.g. of being an LHN)
npositive	Number of true positives (e.g. actual number LHNs in a tract)
replicates	Number of samples to draw

Value

A vector of length replicates with counts of sample positives.

Details

Imagine we have integers 1:N (the population size). We say that the first npositive integers are the true positives in the population (npositive may be 0).

Now we draw a sample of size n from the integers 1:N. For this sample we say that the observed positives are those integers <=npositive.

NB this is the hypergeometric distribution.

See also

truepos_given_sample for estimating the true number of positives in a finite population given a sample.

Other population-sampling: prop.ci, required.sample.size, truepos_given_sample

Examples

# Draw a random sample of size 24 tracings for a population of 96 profiles in
# a tract known to have 36 LHNs
sample_finite_population(24, N=96, npositive=36)
#> [1] 9
# Draw 1000 random samples, plot the distribution of observed sample positives
rand.samples=sample_finite_population(24, N=96, npositive=36, replicates=1000)
mean(rand.samples)
#> [1] 8.994
quants=quantile(rand.samples, c(0.05,0.95))
library(ggplot2)
qplot(rand.samples, binwidth=1, xlab='Observed Sample Positives') +
  geom_vline(xintercept = quants, colour='red')

# Compare with binomial distribution
resdf=data.frame(x=popsample(10,50,p=.5, replicates = 100000), type='popsample')
#> Error in popsample(10, 50, p = 0.5, replicates = 1e+05): could not find function "popsample"
resdf=rbind(resdf, data.frame(x=rbinom(100000, size=10,p=.5), type='rbinom'))
#> Error in rbind(resdf, data.frame(x = rbinom(1e+05, size = 10, p = 0.5),     type = "rbinom")): object 'resdf' not found
library(ggplot2)
qplot(x, col=type, data=resdf, geom='density')
#> Error in ggplot(data, mapping, environment = caller_env): object 'resdf' not found