Sampling Precision for a Mean

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

Usage

prec_mean(var, ...)

# Default S3 method
prec_mean(
  var,
  n,
  mu = NULL,
  alpha = 0.05,
  N = Inf,
  deff = 1,
  resp_rate = 1,
  plan = NULL,
  ...
)

# S3 method for class 'svyplan_n'
prec_mean(var, ...)

Arguments

var: For the default method: population variance $S^2$. For svyplan_n objects: a sample size result from n_mean().
...: Additional arguments passed to methods.
n: Sample size.
mu: Population mean magnitude (positive). Required for the CV component.
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 n * resp_rate.
plan: Optional svyplan() object providing design defaults.

Value

A svyplan_prec object with components $se, $moe, and $cv. $cv is NA when mu is not provided.

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.

Round-trip with n_mean

prec_mean() is the inverse of n_mean(): if you compute res <- n_mean(var = 100, moe = 2) and then call prec_mean(res), you will recover moe = 2. You can also pass an svyplan_n object directly: prec_mean(res).

Precision of a total

A separate prec_total() is not needed. The precision of the estimated total $\hat{Y} = N \bar{y}$ is a rescaling of the mean precision:

$SE(\hat{Y}) = N \times SE(\bar{y})$
$MOE(\hat{Y}) = N \times MOE(\bar{y})$
$CV(\hat{Y}) = CV(\bar{y})$

Call prec_mean() and multiply $se and $moe by $N$ for the total. The $cv component is identical. See Examples below.

Examples

# Precision with n = 400
prec_mean(var = 100, n = 400, mu = 50)
#> Sampling precision for mean
#> n = 400
#> se = 0.5000, moe = 0.9800, cv = 0.0100

# Without mu (CV will be NA)
prec_mean(var = 100, n = 400)
#> Sampling precision for mean
#> n = 400
#> se = 0.5000, moe = 0.9800

# Round-trip from n_mean
res <- n_mean(var = 100, moe = 2)
prec_mean(res)
#> Sampling precision for mean
#> n = 97
#> se = 1.0204, moe = 2.0000

# --- Precision of a total ---
# Precision of a mean, then scale to total
N <- 10000
p <- prec_mean(var = 2500, n = 400, mu = 300, N = N)
p$moe * N   # MOE for the estimated total
#> [1] 48009.12
p$se * N    # SE for the estimated total
#> [1] 24494.9
p$cv        # CV is the same for mean and total
#> [1] 0.008164966