Power Analysis for Interactions in R

An interaction lets one predictor's effect depend on the level of another. This rung builds on the satisfaction model from rung 01 by asking a sharper question: does the treatment effect vary with age?

The model

The formula satisfaction ~ treatment * age uses the * shorthand, which the engine expands to treatment + age + treatment:age — both main effects plus their product term. If you want the product alone, use : directly; see formula syntax for details.

Three calls are all it takes:

• set_variable_type marks treatment as binary, same as before;
• set_effects now includes a third entry, treatment:age=0.35, the standardised interaction effect to detect;
• target_test = "treatment:age" restricts the power report to the term we care about — the main effects are modelled but not the focus of the budget calculation.

library(mcpower)

# `*` expands to treatment + age + treatment:age
model <- MCPower$new("satisfaction ~ treatment * age")
model$set_variable_type("treatment=binary")
model$set_effects("treatment=0.5, age=0.3, treatment:age=0.35")

result <- model$find_power(sample_size = 200, target_test = "treatment:age", verbose = FALSE)
print(summary(result))

==================================================
  MCPower · Power Analysis
==================================================
formula: satisfaction ~ treatment * age
estimator: OLS  N=200  sims=1600  α=0.05  target=80%
effects: treatment=0.50, age=0.30, treatment:age=0.35

Per-test power
───────────────────────────────────
Test                 Power   Target
───────────────────────────────────
treatment:age        68.7%      80%
───────────────────────────────────

Power & 95% CI
───────────────────────────────────────────
Test                 Power           CI 95%
───────────────────────────────────────────
treatment:age        68.7%   [66.4%, 70.9%]
───────────────────────────────────────────
95% CIs are Monte-Carlo (Wilson), n_sims=1600.

Joint significance distribution
────────────────────────
k     Exactly   At least
────────────────────────
0       31.3%       100%
1       68.7%      68.7%
────────────────────────

Plots: plot(result) to view, plot(result, 'chart.png') to save.

Read the numbers

treatment:age lands at 68.7% at N = 200 — well short of the 80% target, even though the individual main effects would be comfortably powered at that size. This is the central lesson of interactions: the product term absorbs variance from both predictors, which means the effective signal-to-noise ratio is lower. Detecting it reliably typically demands a noticeably larger sample than detecting either constituent main effect alone.

If 80% is the floor for your study, plug the interaction label into find_sample_size with the same grid approach from rung 01 to find where the curve crosses the threshold.

next → Correlations