Statistical power is the probability that your study detects an effect that is really there. You pick a target — conventionally 80%, the MCPower default — and MCPower finds the sample size that reaches it, or the power a given sample size buys. At 80% power a real effect is found four times in five; the missing fifth is the false-negative risk.

Formally, power is the chance of rejecting the null hypothesis when it is genuinely false, so the missing 20% at 80% power is the false-negative risk you accept in exchange for a manageable sample. 80% is convention, not law — chasing 90% or 95% shrinks that risk but demands a larger N, while a lower target accepts more missed effects for a smaller study. Set the target to whatever your field expects and your resources allow.

What power depends on

Power is never a single number — it is the product of every modeling choice you make. Each driver below has its own page; together they trace the path from a research idea to a defensible sample size.

  • Effect size — how large the effect you expect is; the single most important input. See effect sizes.
  • Sample size (N) — more observations mean more power; this is the lever a power analysis usually solves for.
  • Significance level (α) — the false-positive rate you allow, 0.05 by default; a stricter α lowers power. See simulation settings.
  • Correlations — how predictors move together, which can raise or lower power. See correlations.
  • Variable types — whether each predictor is continuous, binary, or a factor. See variable types.
  • Multiple testing — how many coefficients you test, and how you correct for it. See multiple testing.
  • Clustering — grouped or repeated-measures data and its intraclass correlation. See mixed-effects models.
  • Robustness — how sensitive your power is to all of the above. See scenario analysis.
  • Model specification — the model you test, not just the data you generate, decides what you can detect. See model misspecification.
  • Required N — how the sample-size answer itself is estimated, and what the curve and CI mean. See how required N is estimated.