Sampling Precision for a Proportion

Compute the sampling error (SE, margin of error, CV) for estimating a population proportion given a sample size. This is the inverse of n_prop().

Usage

prec_prop(p, ...)

# Default S3 method
prec_prop(
  p,
  n,
  alpha = 0.05,
  N = Inf,
  deff = 1,
  resp_rate = 1,
  method = "wald",
  ...
)

# S3 method for class 'svyplan_n'
prec_prop(p, ...)

Arguments

p

For the default method: expected proportion, in (0, 1). For svyplan_n objects: a sample size result from n_prop().

...

Additional arguments passed to methods.

n

Sample size.

alpha

Significance level, default 0.05.

N

Population size. Inf (default) means no finite population correction.

deff

Design effect multiplier (> 0). Values < 1 are valid for efficient designs (e.g., stratified sampling with Neyman allocation).

resp_rate

Expected response rate, in (0, 1]. Default 1 (no adjustment). The effective sample size is deflated by resp_rate.

method

One of "wald" (default), "wilson", or "logodds".

Value

A svyplan_prec object with components $se, $moe, and $cv.

Details

Computes the standard error for the given sample size and design parameters, then derives the margin of error and coefficient of variation. The effective sample size is n * resp_rate / deff, with optional finite population correction.

The Wald FPC uses the Cochran (1977, Ch. 3) form: the finite-population correction for a Bernoulli proportion is (N - n_eff) / (N - 1), not the simpler 1 - n_eff / N used for means.

See also

n_prop() for the inverse (compute n from a precision target), prec_mean() for continuous variables.

Examples

# Precision with n = 400
prec_prop(p = 0.3, n = 400)
#> Sampling precision for proportion (wald)
#> n = 400
#> se = 0.0229, moe = 0.0449, cv = 0.0764

# With design effect and response rate
prec_prop(p = 0.3, n = 400, deff = 1.5, resp_rate = 0.8)
#> Sampling precision for proportion (wald)
#> n = 400 (net: 320)
#> se = 0.0314, moe = 0.0615, cv = 0.1046