Power Analysis for Difference-in-Differences Designs

Compute sample size, power, or minimum detectable effect (MDE) for a two-group, two-period difference-in-differences (DiD) contrast. Leave exactly one of n, power, or effect as NULL.

Usage

power_did(treat, ...)

# Default S3 method
power_did(
  treat,
  control,
  outcome = c("mean", "prop"),
  var = NULL,
  effect = NULL,
  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

treat: Numeric length-2 vector for treated group outcomes: c(baseline, endline).
...: Additional arguments passed to methods.
control: Numeric length-2 vector for control group outcomes: c(baseline, endline).
outcome: Outcome scale: "mean" (default) or "prop".
var: Outcome variance for outcome = "mean". Length 1: common variance for all four cells. Length 2: group-specific variances c(var_treat, var_control), assumed equal across waves. Length 4: cell-specific variances in order c(var_treat_baseline, var_treat_endline, var_control_baseline, var_control_endline).
effect: Absolute DiD effect size to detect (> 0). Leave NULL to solve for MDE.
n: Per-arm sample size per wave. Scalar (equal treated/control) or length-2 vector c(n_treat, n_control). Leave NULL to solve for n.
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. Scalar applies to both arms; length-2 vector c(N_treat, N_control). Inf (default) disables FPC.
deff: Design effect multiplier (> 0).
resp_rate: Expected response rate, in (0, 1]. Default 1.
alternative: Character: "two.sided" (default) or "one.sided".
ratio: Allocation ratio n_treat / n_control (default 1). Used only when solving for n (n = NULL).
overlap: Panel overlap fraction in [0, 1] within each arm across baseline and endline.
rho: Correlation between baseline and endline outcomes within overlapping units, in [0, 1].
plan: Optional svyplan() object providing design defaults.

Value

A svyplan_power object with components:

n: Per-arm sample size (scalar or length-2).
power: Achieved power.
effect: DiD effect size.
type: "did_prop" or "did_mean".
solved: Which quantity was solved for ("n", "power", or "mde").
params: List of input parameters.

Details

The DiD estimand is (treat_endline - treat_baseline) - (control_endline - control_baseline).

Per-arm variance of the before-after change accounts for panel overlap:

$$V_{\text{arm}} = V_{\text{pre}} + V_{\text{post}} - 2 \cdot \text{overlap} \cdot \rho \cdot \sqrt{V_{\text{pre}} \cdot V_{\text{post}}}$$

The DiD test statistic variance is then:

$$V_d = \text{deff} \left( \frac{V_{\text{trt}} \cdot \text{fpc}_t}{n_t} + \frac{V_{\text{ctrl}} \cdot \text{fpc}_c}{n_c} \right)$$

When overlap = 0, this reduces to the classical flat-variance formula.

References

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

Examples

# DiD sample size for means
power_did(
  treat = c(50, 55), control = c(50, 52),
  outcome = "mean", var = 100, effect = 3
)
#> Power analysis for DiD means (solved for sample size)
#> n = 349 (per group), power = 0.800, effect = 3.0000
#> (treat = (50.000, 55.000), control = (50.000, 52.000), alpha = 0.05, var = (100.00, 100.00, 100.00, 100.00))

# DiD power for proportions
power_did(
  treat = c(0.30, 0.36), control = c(0.30, 0.33),
  outcome = "prop", effect = 0.03, n = 800, power = NULL
)
#> Power analysis for DiD proportions (solved for power)
#> n = 800 (per group), power = 0.149, effect = 0.0300
#> (treat = (0.300, 0.360), control = (0.300, 0.330), alpha = 0.05)

# MDE for means with n = 500
power_did(
  treat = c(50, 55), control = c(50, 52),
  outcome = "mean", var = 100, effect = NULL, n = 500
)
#> Power analysis for DiD means (solved for minimum detectable effect)
#> n = 500 (per group), power = 0.800, effect = 2.5058
#> (treat = (50.000, 55.000), control = (50.000, 52.000), alpha = 0.05, var = (100.00, 100.00, 100.00, 100.00))

# Panel overlap reduces required n
power_did(
  treat = c(0.50, 0.55), control = c(0.50, 0.48),
  outcome = "prop", effect = 0.07, overlap = 0.5, rho = 0.6
)
#> Power analysis for DiD proportions (solved for sample size)
#> n = 1119 (per group), power = 0.800, effect = 0.0700
#> (treat = (0.500, 0.550), control = (0.500, 0.480), alpha = 0.05, overlap = 0.50, rho = 0.60)