Regression power analysis - MCPower app

Regression covers two outcome types in one panel — a continuous outcome (OLS) and a binary outcome (logistic regression). Pick the outcome with the toggle at the top; the controls below adapt. Top to bottom:

1. Formula

Enter the right-hand side of your model — e.g. y = x1 + x2 + x1:x2. Operators follow R: + adds a predictor, : is the interaction term on its own, and * expands to the main effects and their interaction (a * b = a + b + a:b, so don't also write a*b alongside a + b). See formula syntax.

2. Predictors

Each predictor is one card. Pick its type next to the name — continuous, binary, or factor (the type sets how it is simulated and how its effect size is read) — then set the standardised effect size to detect in the same card (larger effects need fewer observations). A factor with k levels expands into k − 1 indicator rows, one per non-reference level; each interaction term gets its own card. Benchmarks: continuous 0.10 / 0.25 / 0.40, binary or factor 0.20 / 0.50 / 0.80 (small / medium / large) — prefer a value justified by prior evidence. See variable types and effect sizes.

3. Robustness scenarios

The Robustness scenarios toggle in the status bar repeats every run under three perturbation sets — Optimistic (your exact settings, no perturbations), Realistic (moderate assumption violations: effects vary between studies, correlations fluctuate, distributions drift from normal), and Doomer (severe violations, a worst case) — so you get a range of power instead of one optimistic number. If even Doomer clears your target, the design is robust; if only Optimistic reaches it, increase the sample size. Each set's knobs are editable under Settings → Scenarios. See scenario analysis.

4. Optional settings

• Correlations — a collapsed, optional sub-section: set pairwise correlations if predictors are not independent; correlated predictors share information and usually lower power. Leave it collapsed (all zero) for independence. Only continuous predictors appear in the triangle — binary and factor predictors are excluded. predictor correlations
• Baseline probability (binary only) — the outcome probability when every predictor is at its reference level. It fixes the logistic intercept and strongly affects power (outcomes near 0 or 1 are harder). Hidden for continuous outcomes.
• Tests & corrections — test all coefficients, the first only, or a custom subset; correcting several (Bonferroni, Holm, Benjamini–Hochberg) controls the error rate at the cost of power. multiple testing
• Advanced — number of simulations (continuous defaults to 1,600), α (0.05), seed (2137), and the failed-simulation tolerance.

Find power at a sample size

The Find power card takes a fixed sample size and reports the power your design has at that n — type the planned number of observations into the single n field and run. It is the complement of Find sample size, which instead searches a range of n for the sample size that hits a target power; here n is the input and power is the result. Use it to check "how much power does the study I can afford actually have?"

Both modes share the same model, predictors, and effect sizes — only the run card differs. Find power answers one n with one power number per tested effect; Find sample size sweeps a from/to grid and reads the required n off the fitted power curve. See how required N is estimated.