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Sample Size for a Mean

Source: R/n_mean.R
n_mean.Rd

Compute the required sample size for estimating a population mean with a specified margin of error or coefficient of variation.

Usage

n_mean(var, ...)

# Default S3 method
n_mean(
  var,
  mu = NULL,
  moe = NULL,
  cv = NULL,
  alpha = 0.05,
  N = Inf,
  deff = 1,
  resp_rate = 1,
  ...
)

# S3 method for class 'svyplan_prec'
n_mean(var, moe = NULL, cv = NULL, ...)

Arguments

var

For the default method: population variance \(S^2\). For svyplan_prec objects: a precision result from prec_mean().

...

Additional arguments passed to methods.

mu

Population mean magnitude (positive). Required when cv is specified.

moe

Desired margin of error. Specify exactly one of moe or cv.

cv

Target coefficient of variation. Specify exactly one of moe or cv.

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 sample size is inflated by 1 / resp_rate.

Value

A svyplan_n object.

Details

Two modes:

  • MOE mode: n = z^2 * var / (moe^2 + z^2 * var / N), then multiplied by deff.

  • CV mode: Computes CVpop = sqrt(var) / mu, then n = CVpop^2 / (cv^2 + CVpop^2 / N), multiplied by deff.

The FPC is the standard Cochran (1977) one-step form. Unlike n_prop(), no N/(N-1) adjustment is needed because var is already defined on N-1 degrees of freedom.

All methods use the normal (z) quantile. This is standard for survey sampling where the sample size is large enough for the CLT to apply.

References

Cochran, W. G. (1977). Sampling Techniques (3rd ed.). Wiley.

Valliant, R., Dever, J. A., and Kreuter, F. (2018). Practical Tools for Designing and Weighting Survey Samples (2nd ed.). Springer.

See also

n_prop() for proportions, n_cluster() for multistage designs, n_multi() for multiple indicators, prec_mean() for the inverse.

Examples

# MOE mode
n_mean(var = 100, moe = 2)
#> Sample size for mean
#> n = 97 (var = 100.00, moe = 2.000)

# CV mode
n_mean(var = 100, mu = 50, cv = 0.05)
#> Sample size for mean
#> n = 16 (var = 100.00, cv = 0.050)

# With FPC, design effect, and response rate
n_mean(var = 100, moe = 2, N = 5000, deff = 1.5, resp_rate = 0.8)
#> Sample size for mean
#> n = 177 (net: 142) (var = 100.00, moe = 2.000, deff = 1.50, resp_rate = 0.80)