Statistical power is the probability of detecting an effect that is genuinely there. A study with 20% power will miss a real effect four times in five — and, less intuitively, the significant results it does produce will be badly inflated. This is the part that surprises people: underpowered studies do not merely fail to find things, they systematically overestimate whatever they find, because only the largest noise-inflated estimates clear the significance threshold.
That mechanism explains a good deal of the replication difficulty in brain-behaviour research. Effect sizes for individual-difference associations in neuroimaging are typically small, samples have historically been in the dozens, and the published estimates were correspondingly optimistic. It is also why the large consortium cohorts documented in this book — UK Biobank, ABCD, ADNI — exist in the form they do.
Power analysis is most useful before data collection, but scholars here are usually working with a fixed existing cohort. In that situation the honest version of the question is inverted: given this sample, what is the smallest effect I could reliably detect, and is that plausibly the size of the effect I am looking for?
Related¶
Multiple comparisons — corrections cost power
Mixed models — repeated measures change the calculation
Working with imbalanced data — effective n is smaller than it looks