Effective sample size

Convert a planned sample size into the simple-random-sample size that would give the same precision, n * resp_rate / deff. This is the mirror of design_effect() and takes the same arguments.

Usage

effective_n(x = NULL, ...)

# Default S3 method
effective_n(
  x = NULL,
  ...,
  n = NULL,
  deff = NULL,
  resp_rate = 1,
  icc = NULL,
  n_per_psu = NULL,
  n_per_ssu = NULL,
  var_ratio = 1,
  weights = NULL,
  strata = NULL
)

# S3 method for class 'svyplan_deff'
effective_n(x, ..., n = NULL, resp_rate = 1)

# S3 method for class 'svyplan_cluster'
effective_n(x, ..., n = NULL, resp_rate = NULL, weights = NULL, strata = NULL)

# S3 method for class 'svyplan_prec'
effective_n(x, ..., n = NULL, resp_rate = NULL, weights = NULL, strata = NULL)

# S3 method for class 'svyplan_varcomp'
effective_n(
  x,
  ...,
  n = NULL,
  resp_rate = 1,
  n_per_psu = NULL,
  n_per_ssu = NULL,
  weights = NULL,
  strata = NULL
)

# S3 method for class 'svyplan_n'
effective_n(x, ..., n = NULL, resp_rate = NULL, weights = NULL)

Arguments

x: A svyplan_deff from design_effect(), a n_cluster() or prec_cluster() allocation, a varcomp() estimate, an n_alloc() allocation, or NULL (default) to build the design effect from the component arguments. A n_prop() or n_mean() result is not one of these: its design effect is the deff you supplied rather than something to be derived, so pass the two directly as effective_n(n = x$n, deff = x$params$deff).
...: Additional arguments passed to methods. Unused arguments are rejected.
n: Gross planned sample size, counted as units issued. Required unless it can be derived from weights, strata$n, or x.
deff: Design effect to apply directly, instead of building one from components.
resp_rate: Expected response rate, in (0, 1]. Default 1. It nets n down to the units the design expects to analyze before the design effect is applied. When x is a plan, its own rate is used unless you override it here.
icc, n_per_psu, n_per_ssu, var_ratio, weights, strata: Design components, with the same meaning as in design_effect().

Value

A numeric scalar: the effective sample size, n * resp_rate / deff. It is not rounded, and it can exceed n when the design effect is below 1 (a stratification gain, for instance).

Details

The design effect is built exactly as in design_effect(), from whichever of the clustering, weighting, and stratification components you supply. n is the gross planned sample size; it is taken from the arguments when it can be (the length of weights, the total of strata$n, or the total of the plan you pass as x), and must be given explicitly otherwise.

Sizes are counted as units issued, so nonresponse has to be taken off before the design effect is applied: a design that issues n and analyzes n * resp_rate of them carries the information of n * resp_rate / deff simple random draws. This is the identity the allocation and precision functions plan on, and the one reported in the n_eff column of an n_alloc() table. Passing a plan as x picks up the response rate it was built with, so effective_n(plan) and that column agree; supply resp_rate yourself when you pass a bare n that has not already been netted down.

The design effect it divides by is a without-FPC planning quantity, so for an n_alloc() result the effective size inherits that scale: it answers how many simple random draws carry the same information under the planning model, not how many the finite-population variance from prec_alloc() would imply once sampling fractions are material. A generalized allocation has no single design effect and is refused here for the same reason it is in design_effect().

effective_n() is a planning tool. To compute the effective sample size realized by collected data, use survey::svymean(..., deff = TRUE) with the actual weights, strata, and clusters.

Methods (by class)

effective_n(default): Build the design effect from planning components.
effective_n(svyplan_deff): Apply a design effect already built by design_effect().
effective_n(svyplan_cluster): Use the total sample size and design features of a n_cluster() or prec_cluster() allocation.
effective_n(svyplan_prec): Use the total and design features of a prec_cluster() result. Other svyplan_prec types carry the deff you supplied rather than one to be derived, and are rejected.
effective_n(svyplan_varcomp): Use the design features of a varcomp() estimate. n and the stage takes are your design choice.
effective_n(svyplan_n): Use the total and design features of an n_alloc() allocation, dividing by the allocation's own variance ratio. The frame needs mean alongside N and sd, since without the stratum means the population variance that ratio divides by is not identified.

Examples