Compute an upper bound the sample size based on two pilot samples.

Based on the procedure described by Chakraborti, Hong, & van de Wiel (2006)

n_locshift_bound(
  s1,
  s2,
  delta,
  alpha = 0.05,
  power = 0.9,
  quantile = 0.9,
  n_resamples = 500,
  q = 0.5
)

Arguments

s1, s2: Pilot samples
delta: numeric value, location shift parameter \(\delta\)
alpha: Type I error probability
power: 1 - Type II error probability, the desired statistical power
quantile: Quantile to use as the upper bound.
n_resamples: number of resamples to use in bootstrapping
q: size of group0 relative to total sample size.

Value

Returns an object of class "sample_size". It contains the following components:

n: the total sample size
n0: sample size in Group 0 (control group)
n1: sample size in Group 1 (treatment group)
two_sided: logical, TRUE, if the estimated sample size refers to a two-sided test
alpha: type I error rate used in sample size estimation
power: target power used in sample size estimation
effect: effect size used in sample size estimation
effect_type: short description of the type of effect size
comment: additional comment, if there is any
call: the matched call.

Details

WARNING: Note that the underlying estimation has high variability due to its dependence on pilot samples. The smaller the pilot sample, the more uncertain is the estimation of the required sample size. In a simulation study, we found that the underlying method may also be inaccurate on average, depending on the investigated data.

References

Chakraborti, S., Hong, B., & van de Wiel, M. A. (2006). A note on sample size determination for a nonparametric test of location. Technometrics, 48(1), 88–94. https://doi.org/10.1198/004017005000000193

Examples

if (FALSE) {
n_locshift_bound(s1 = rexp(10), s2 = rexp(10),
           delta = 0.35, alpha = 0.05, power = 0.9, n_resamples = 5)}