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Power Analysis for Means

Source: R/power_mean.R
power_mean.Rd

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 = NULL,
  var,
  n = NULL,
  power = 0.8,
  alpha = 0.05,
  N = Inf,
  deff = 1,
  resp_rate = 1,
  sides = 2,
  overlap = 0,
  rho = 0
)

Arguments

effect

Absolute difference in means (effect-size magnitude, positive). Leave NULL to solve for MDE.

var

Within-group variance (required).

n

Per-group sample size. 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

Per-group population size. Inf (default) means no finite population correction.

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.

sides

1 for one-sided or 2 (default) for two-sided test.

overlap

Panel overlap fraction in [0, 1], for repeated surveys.

rho

Correlation between occasions in [0, 1].

Value

A svyplan_power object with components:

n

Per-group sample size.

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

The effective variance for the difference in means is:

$$V = 2 \cdot \text{var} \cdot (1 - \text{overlap} \cdot \rho)$$

The factor of 2 accounts for the two independent groups, reduced by the panel overlap term (Kish, 1965, Ch. 11).

  • Solve n: \(n_0 = (z_{\alpha/s} + z_\beta)^2 \cdot V \cdot \text{deff} / \delta^2\), then finite population correction.

  • Solve power: Compute SE, then \(\text{power} = \Phi(\delta / \text{SE} - z_{\alpha/s})\).

  • Solve MDE: Analytical formula, \(\delta = (z_{\alpha/s} + z_\beta) \sqrt{V \cdot \text{deff} \cdot (1-f) / n}\).

References

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

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

See also

power_prop() for proportions, n_mean() for estimation precision.

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)