Minimum Detectable Effect (MDE) Calculator — mde

Computes the Minimum Detectable Effect (MDE) for a range of experimental designs including simple two-sample t-tests, DiD, RD, and clustered randomized trials. Also produces power curves for visualization.

Usage

mde_calc(
  n,
  per_arm = FALSE,
  design = c("ttest", "did", "rd", "cluster"),
  sd = 1,
  alpha = 0.05,
  power = 0.8,
  two_sided = TRUE,
  icc = 0,
  cluster_size = 1,
  r2 = 0,
  kappa = 1,
  plot = TRUE
)

Arguments

n: Numeric. Total sample size (or sample per arm if per_arm = TRUE).
per_arm: Logical. If TRUE, n is interpreted as sample per arm. Default FALSE.
design: Character. Experimental design: "ttest" (default), "did", "rd", "cluster".
sd: Numeric. Standard deviation of the outcome. Default 1.
alpha: Numeric. Type I error rate. Default 0.05.
power: Numeric. Desired power. Default 0.80.
two_sided: Logical. Whether the test is two-sided. Default TRUE.
icc: Numeric. Intraclass correlation for cluster designs. Default 0.
cluster_size: Integer. Average cluster size. Default 1.
r2: Numeric. R-squared of covariates (variance reduction from regression adjustment). Default 0 (no adjustment).
kappa: Numeric. Ratio of control to treated observations (1 = equal sizes, 2 = twice as many controls). Default 1.
plot: Logical. Whether to produce a power curve. Default TRUE.

Value

A list with:

mde: Numeric. Minimum detectable effect (in outcome units).
mde_std: Numeric. Standardized MDE (Cohen's d).
design_effect: Numeric. Design effect from clustering.
effective_n: Numeric. Effective sample size after design effect.
plot: ggplot2 power curve, or NULL if plot = FALSE.

Details

The MDE is the smallest true effect that would be detected with probability power at significance level alpha: $$MDE = (t_{1-\alpha/2} + t_{1-\beta}) \cdot SE(\hat{\tau})$$

For clustered designs, the design effect is: $$DEFF = 1 + (\bar{m} - 1)\rho$$ where $\bar{m}$ is the average cluster size and $\rho$ is the ICC.

Examples

# Simple t-test
mde_calc(n = 200)

# DiD with clustering
mde_calc(n = 500, design = "did", icc = 0.05, cluster_size = 25)

# With covariate adjustment (reduces variance)
mde_calc(n = 200, r2 = 0.3)