Power Analysis for Means

Compute sample size, power, or minimum detectable effect (MDE) for a two-sample test of means. Leave exactly one of n, power, or effect as NULL to solve for that quantity.

Usage

power_mean(effect, ...)

# Default S3 method
power_mean(
  effect = NULL,
  var,
  n = NULL,
  power = 0.8,
  alpha = 0.05,
  N = Inf,
  deff = 1,
  resp_rate = 1,
  alternative = c("two.sided", "one.sided"),
  ratio = 1,
  overlap = 0,
  rho = 0,
  plan = NULL,
  ...
)

Arguments

effect: Absolute difference in means (effect-size magnitude, positive). Leave NULL to solve for MDE.
...: Additional arguments passed to methods.
var: Within-group variance. Scalar (equal variances in both groups) or length-2 vector c(var1, var2) for unequal group variances.
n: Per-group sample size. Scalar (equal groups) or length-2 vector c(n1, n2) for unequal groups. Leave NULL to solve for sample size.
power: Target power, in (0, 1). Leave NULL to solve for power.
alpha: Significance level, default 0.05.
N: Population size for finite-population correction. A scalar applies to both groups; a length-2 vector c(N1, N2) sets group-specific population sizes. Inf disables FPC for the corresponding group.
deff: Design effect multiplier (> 0). Values < 1 are valid for efficient designs (e.g., stratified sampling with Neyman allocation).
resp_rate: Expected response rate, in (0, 1]. Default 1 (no adjustment). The sample size is inflated by 1 / resp_rate.
alternative: Character: "two.sided" (default) or "one.sided".
ratio: Allocation ratio n1/n2 (default 1). Only used when solving for n (n = NULL). For example, ratio = 2 means group 1 gets twice the sample of group 2.
overlap: Panel overlap fraction in [0, 1], for repeated surveys. Defined as the fraction of group 1 that also appears in group 2 (overlap = n12 / n1).
rho: Correlation between occasions in [0, 1].
plan: Optional svyplan() object providing design defaults.

Value

A svyplan_power object with components:

n: Per-group sample size (scalar or length-2 for unequal groups).
power: Achieved power.
effect: Effect size (difference in means).
solved: Which quantity was solved for ("n", "power", or "mde").
params: List of input parameters.

Details

To specify the effect in terms of Cohen's d (standardized effect size), convert via effect = d * sqrt(mean(var)), where d follows Cohen's conventions: 0.2 (small), 0.5 (medium), 0.8 (large).

When var is a length-2 vector, the variance of the difference is:

$$V = \sigma^2_1 / r + \sigma^2_2 - 2 \cdot \text{overlap} \cdot \rho \cdot \sigma_1 \sigma_2$$

where r is the allocation ratio n1/n2 (default 1). When var is scalar and ratio = 1, this simplifies to the familiar V = 2 * var * (1 - overlap * rho).

References

Valliant, R., Dever, J. A., & Kreuter, F. (2018). Practical Tools for Designing and Weighting Survey Samples (2nd ed.). Springer. Chapter 4.

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

Examples

# Sample size to detect a difference of 5 with variance 100
power_mean(effect = 5, var = 100)
#> Power analysis for means (solved for sample size)
#> n = 63 (per group), power = 0.800, effect = 5.0000
#> (alpha = 0.05)

# Power given n = 200
power_mean(effect = 5, var = 100, n = 200, power = NULL)
#> Power analysis for means (solved for power)
#> n = 200 (per group), power = 0.999, effect = 5.0000
#> (alpha = 0.05)

# MDE with n = 500
power_mean(var = 100, n = 500)
#> Power analysis for means (solved for minimum detectable effect)
#> n = 500 (per group), power = 0.800, effect = 1.7719
#> (alpha = 0.05)

# With design effect
power_mean(effect = 5, var = 100, deff = 1.5)
#> Power analysis for means (solved for sample size)
#> n = 95 (per group), power = 0.800, effect = 5.0000
#> (alpha = 0.05, deff = 1.50)

# Unequal group variances
power_mean(effect = 5, var = c(80, 120))
#> Power analysis for means (solved for sample size)
#> n = 63 (per group), power = 0.800, effect = 5.0000
#> (alpha = 0.05)

# Allocation ratio 2:1
power_mean(effect = 5, var = 100, ratio = 2)
#> Power analysis for means (solved for sample size)
#> n_treat = 95, n_control = 48 (total = 143), power = 0.800, effect = 5.0000
#> (alpha = 0.05, ratio = 2)