Statistics for Researchers › Module 5: Power and sample size
Why small studies mislead
Lesson 1 of 3 · 2 min
Statistical power is the chance that a study will detect an effect if it is really there. A common target is 80%.
Low power is common
In 2013, Button and colleagues estimated that the median power of studies in neuroscience was about 21%. Most studies had less than a one-in-four chance of detecting the effects they were looking for.
Low power does more than miss effects
You might think a weak study just finds nothing. Worse things happen:
- Inflated effects. With a small sample, only results that happen to be unusually large cross the significance line. So the effects that get published are exaggerated. This is sometimes called the winner's curse.
- More false positives among the "hits". When power is low, a larger share of significant results are flukes.
- Failure to replicate. A bigger follow-up study finds a much smaller effect, or none.
ExampleA small study of 15 students finds a new study method raises scores by 20 points, p = 0.04. A follow-up with 500 students finds 3 points. The first study wasn't necessarily dishonest; small studies that "win" tend to overestimate.
What to do
- Be sceptical of surprisingly large effects from small samples.
- Look for replications and larger studies.
- In your own work, plan the sample size before collecting data.
RememberSmall studies don't just miss effects; when they find one, it's often exaggerated. Big claims need big samples.