How large a sample do you need?

Solves for n given the precision you want, rather than asking you to guess it. This is the step before draw(): you rarely know the sample size, you know the margin of error you can live with.

Usage

plan_size(
  margin,
  sd = NULL,
  p = 0.5,
  N = Inf,
  level = 0.95,
  deff = 1,
  response = 1,
  target = c("mean", "proportion", "total")
)

Arguments

margin: Half-width of the confidence interval you want.
sd: Standard deviation of the measure, for target = "mean" or "total".
p: Expected proportion, for target = "proportion".
N: Population size. Inf for an effectively unbounded frame.
level: Confidence level.
deff: Design effect to inflate by. 1 assumes simple random sampling.
response: Expected response rate, between 0 and 1.
target: "mean", "proportion" or "total". For "total" the margin is on the population total and N must be finite.

Value

A list with a print() method, holding:

n: Draw this many. Never more than N.
n_effective: What you expect to analyse once response has taken its share.
capped: TRUE when the frame is not large enough to reach the margin at all, however you sample it.
short: TRUE when the frame could reach the margin but not at this response rate, so n is the whole frame and the margin achieved will be wider than the one asked for.
margin, level, N, deff, response, target: The inputs, returned so the assumptions travel with the number.
n_needed: Rows that would reach the margin if everyone responded. Equal to n_effective unless short is TRUE.
spread: The standard deviation used — sd, or sqrt(p * (1 - p)) for a proportion.

What you need to supply

A margin of error, and some idea of how much the thing you are measuring varies:

For a mean or total, an sd — from a pilot, last year's data, or a range divided by four as a rough stand-in.
For a proportion, a p. Leave it at 0.5, the most pessimistic value, unless you have a better guess; that is the honest default because it maximises the required size.

The corrections

N applies a finite population correction: sampling 400 from 500 is very different from 400 from 500,000, and past a certain point a bigger frame stops mattering. deff inflates for the design — pass the deff() from a comparable past sample, since a clustered design of 400 may carry the information of 100. response inflates for non-response: at 0.6 you draw enough to end up with what you need.

Where the formula comes from

n0 = (z * spread / margin)^2 * deff, then Cochran's finite population correction n0 / (1 + (n0 - 1) / N), then division by response (Cochran 1977, section 4.4; Valliant, Dever and Kreuter 2018, chapter 3). z is the normal quantile. The interval ht_total() reports uses t on the design's degrees of freedom, which is slightly wider when those are few — with a handful of clusters, plan on more clusters rather than trusting the margin to the last digit.

References

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

Kish, L. (1965). Survey Sampling. Wiley.

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

Examples

# A proportion, no prior guess, 20,000 in the frame
plan_size(margin = 0.03, N = 20000, target = "proportion")
#> Sample size for a proportion
#>   draw           1,014
#>   margin         +/- 0.03 at 95% confidence
#>   assuming       sd 0.5, N 20,000

# A mean, when a pilot put the spread near 40
plan_size(margin = 5, sd = 40, N = 20000)
#> Sample size for a mean
#>   draw           243
#>   margin         +/- 5 at 95% confidence
#>   assuming       sd 40, N 20,000

# The same, in a clustered design with 70% response
plan_size(margin = 5, sd = 40, N = 20000, deff = 2.5, response = 0.7)
#> Sample size for a mean
#>   draw           853
#>   to analyse     597  (after 70% response)
#>   margin         +/- 5 at 95% confidence
#>   assuming       sd 40, deff 2.5, N 20,000

# A total, to within 100,000 across a 20,000-row frame
plan_size(margin = 1e5, sd = 40, N = 20000, target = "total")
#> Sample size for a total
#>   draw           243
#>   margin         +/- 1e+05 at 95% confidence
#>   assuming       sd 40, N 20,000