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Simulation 3 · Statistical power

Power Explorer

Power is the chance your study detects an effect that really exists. Two overlapping worlds: the null (no effect) and the truth (effect = d). Your critical value draws a line between them — power is how much of the true world lands past that line.

Effect size d 0.5
n per group 30
α
Tails
Null world (d = 0) True world (d as set) α — false-alarm zone Power — correct detections
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Power
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β (miss rate)
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Critical z
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n/group for 80% power

Normal approximation of the two-sample test (the picture and the logic are what matter; exact t-based numbers differ slightly at small n).

Try this:
  1. Set d = 0.5 (a typical social-psych effect) and n = 20 per group. Power is around a coin flip — half of all real effects would be missed. Find the n that gets you to 80%.
  2. Drop α from .05 to .001 and watch power fall. Stricter false-alarm control costs detection — there's no free lunch, only trade-offs.
  3. Set d = 0.2 (a small effect). Look at the n needed for 80% power. Now you know why big claims from n = 15 studies deserve suspicion.
Sigma says: Underpowered studies don't just miss effects — when they DO hit significance, the estimated effect is often inflated. Plan the n before you collect. Your future self (and your prereg) will thank you.