Power of a two-sided test under a complex survey design

A clustered design does not reduce the sample size, it reduces the information: the effective sample size is n / DEFF. Both tails are kept, so a zero effect returns alpha exactly rather than alpha/2.

Usage

Powsrv(effect_size, alpha = 0.05, DEFF = 1, n = 100)

Arguments

effect_size: Standardised effect size (Cohen's d).
alpha: Two-sided significance level in (0, 1).
DEFF: Design effect, positive.
n: Nominal sample size, at least 1.

Value

List with estimate, power, n_eff, ncp, z_crit, DEFF, n.

Details

Formula: n_eff = n / DEFF; power = Phi(d sqrt(n_eff) - z) + Phi(-d sqrt(n_eff) - z) with z = Phi^-1(1 - alpha/2).

References

Lumley, T. (2010). Complex Surveys: A Guide to Analysis Using R, Wiley. doi:10.1002/9780470580066 . Standard form.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Powsrv(V)
#> $estimate
#> [1] 1 1 1 1 1 1 1 1
#> 
#> $power
#> [1] 1 1 1 1 1 1 1 1
#> 
#> $n_eff
#> [1] 100
#> 
#> $ncp
#> [1] 10 20 30 40 50 60 70 80
#> 
#> $z_crit
#> [1] 1.959964
#> 
#> $DEFF
#> [1] 1
#> 
#> $n
#> [1] 100
#> 
#> $method
#> [1] "Two-sided z power with the design effect discount"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"