cong2_estima_razao_media: Estimate the population mean via ratio estimator (two-stage...

In sampleone: Survey Sampling Methods for Teaching and Practice

Estimate the population mean via ratio estimator (two-stage cluster sampling, M unknown)

Description

Analogous to cong2_estima_media() but for the case where the total population size M is unknown, using the ratio estimator of Eqs. (6.19)-(6.23) of the course notes, with m_barra (the sample average cluster size) substituted for M_barra = M/Nc.

Usage

cong2_estima_razao_media(
  dados = NULL,
  Mi = NULL,
  mi = NULL,
  yi_bar = NULL,
  si2 = NULL,
  Nc,
  M = NULL,
  conf = 0.95,
  ...
)

Arguments

dados	A data.frame (or list of data frames / a list with one element per cluster) with, for every sampled element, at least the columns conglomerado (cluster id), Mi (cluster population size), and y (the measured value for that element). Alternatively, supply Mi, mi, yi_bar, and si2 directly (pre-summarised per cluster) – see Details.
Mi	Optional numeric vector with the population size of each sampled cluster (used instead of dados when the data are already summarised per cluster).
mi	Optional numeric vector with the number of sampled elements in each cluster.
yi_bar	Optional numeric vector with the sample mean of each cluster.
si2	Optional numeric vector with the sample variance within each cluster (Eq. 6.15).
Nc	Total number of clusters in the population.
M	Ignored for this estimator (kept for signature symmetry with cong2_estima_media() so extra arguments from a broader problem can be passed without error); m_barra is estimated from Mi instead.
conf	Confidence level, default 0.95.
...	Ignored (see package overview on tolerated extra arguments).

Value

A sampling_result object with the ratio-estimated mean, its variance, and confidence interval.

Examples

Mi <- c(50, 65, 45, 48, 52, 58, 42, 66, 40, 56)
mi <- c(10, 13, 9, 10, 10, 12, 8, 13, 8, 11)
yi_bar <- c(5.4, 4.0, 5.6667, 4.8, 4.3, 3.8333, 5.0, 3.8462, 4.875, 5.0)
si2 <- c(11.3778, 10.6667, 16.75, 13.2889, 11.1222, 14.8788, 5.1429,
         4.3077, 6.125, 11.8)
cong2_estima_razao_media(Mi = Mi, mi = mi, yi_bar = yi_bar, si2 = si2, Nc = 90)

sampleone documentation built on Oct. 13, 2026, 5:07 p.m.