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Confidence interval for an unknown population size

Source: R/statpsych3.R
ci.popsize.Rd

Computes a Wald confidence interval for an unknown population size using mark-recapture sampling. This method assumes independence of the two samples. This function requires the frequency counts from an incomplete 2 x 2 contingency table for the two samples (f11 is the unknown number of people who were not observed in either sample). This method sets the estimated odds ratio (with .5 added to each cell) to 1 and solves for unobserved cell frequency. An approximate standard error is recovered from the confidence interval.

For more details, see Section 3.7 of Bonett (2021, Volume 3)

Usage

ci.popsize(alpha, f00, f01, f10)

Arguments

alpha

alpha level for 1-alpha confidence

f00

number of people observed in both samples

f01

number of people observed in first sample but not second sample

f10

number of people observed in second sample but not first sample

Value

Returns a 1-row matrix. The columns are:

  • Estimate - estimate of the unknown population size

  • SE - recovered standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.popsize(.05, 85, 196, 184)
#>  Estimate    SE  LL   UL
#>       889 67.35 777 1041

# Should return:
# Estimate    SE  LL   UL
#      889 67.35 777 1041