Statistical power and sample size
Sample size is usually treated as a logistical afterthought — collect what you can, hope it’s enough. But how many participants you need is a question with a real answer, and getting it wrong quietly undermines everything that follows.
What statistical power really is
Statistical power is the probability that your study will detect a real effect — if one genuinely exists. A study with 80% power (the common standard) has an 80% chance of finding an effect that’s truly there, and a 20% chance of missing it. Power is the flip side of the false negative: low power means real effects slip through your fingers.
The four levers
Power, sample size, effect size, and significance level are locked together — fix any three and the fourth is determined:
- Effect size: bigger effects are easier to detect, so they need fewer participants.
- Sample size: more data means more power — this is the lever you usually control.
- Significance level (α): a stricter threshold (0.01 vs 0.05) reduces false positives but costs power.
- Power: the chance of detecting the effect, which the other three determine.
This is why you can’t sensibly ask “how many participants do I need?” without also saying how big an effect you care about and how sure you want to be.
An underpowered study is the worst of both worlds: it misses real effects, and the “significant” results it does find are more likely to be flukes.
Why underpowered studies are dangerous
It’s intuitive that a small study might miss a real effect. Less intuitive — and more damaging — is that when an underpowered study does hit significance, that result is disproportionately likely to be a false positive, and to overstate the effect’s size. Small studies don’t just find less; they find wrong, more confidently.
Plan the sample before you collect
The time to think about power is before you gather a single data point. A power analysis turns “I hope this is enough” into a defensible number you can put in a proposal or pre-registration. Our free sample-size calculator does exactly this: pick your design and the effect size you expect, and it solves for the participants you need — no sign-up, no data required.
And after you run
Power matters at the end, too. A non-significant result is only informative if the study had enough power to detect an effect worth caring about — otherwise it says nothing. That’s why a non-significant p-value is not proof of “no effect.” When you run an analysis on thericerca, it reports the achieved power and effect size alongside every result, so a null finding is honestly labelled as either “no effect” or “not enough data to tell.”
The takeaway. Decide the effect size you’d hate to miss, aim for at least 80% power, and size your sample accordingly — before you start. It’s the cheapest insurance in all of research design.