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Statistical power is the probability of detecting a true effect. It increases with sample size, effect size magnitude, and alpha level. Effect size quantifies the magnitude of an effect independent of sample size. A-priori power analysis plans sample size to achieve adequate power (typically 0.80). Underpowered studies risk Type II error (missing true effects); overpowered studies waste resources.
Use power analysis software (G*Power) to compute required sample sizes for typical effect sizes and power levels. Review published papers reporting effect sizes and power. Discuss why small-sample studies are common in psychology and their implications.
You've already encountered the concept that statistical significance depends on both the size of an effect and the precision of your estimate. Statistical power and effect size formalize this relationship and turn it into a design tool. Power is the probability that your study will detect a true effect when one exists — in other words, the probability of *not* making a Type II error (false negative). Power depends on three things under your control as a researcher: the effect size you're trying to detect, the sample size you collect, and the significance threshold you set.
Effect size is the metric that links statistical results to scientific meaning. It quantifies the magnitude of a difference or relationship in a scale-free way. Common effect size metrics include Cohen's d (for mean differences — a d of 0.5 means the group means are half a standard deviation apart), r (the correlation coefficient, which is its own effect size measure), and η² (proportion of variance explained in ANOVA). Cohen's benchmark guidelines — small (.2), medium (.5), large (.8) for d — are rough calibrations, not laws. What counts as a meaningful effect depends entirely on the domain: a d of 0.2 might be clinically important for a serious disease intervention but trivial for an attitude measure. Effect size connects your result to the world outside the p-value, which is why reporting it is now required by most journals.
A-priori power analysis is the practice of calculating required sample size *before* collecting data, given your target power (typically .80), your chosen alpha (.05), and your expected effect size. The mechanics work like this: power increases as sample size increases, because larger samples reduce sampling error, making it easier to distinguish real effects from noise. If you expect a small effect (d = 0.2), you need a much larger sample to reliably detect it than if you expect a large effect (d = 0.8). Underpowered studies — those with power below .80 — not only fail to detect true effects; they also produce unstable effect size estimates, because small samples vary widely. A study with 30% power that happens to find p < .05 likely observed an inflated effect by chance, which then fails to replicate.
The replication crisis in psychology was partly caused by widespread use of underpowered studies with flexible stopping rules — collecting data until p < .05 emerged. Understanding power helps you see exactly why this is problematic: if you stop when you first cross the significance threshold, you've created an implicit multiple-comparison problem (the more you look, the higher the false positive rate) and you've exploited sampling variability rather than estimated a true effect. The remedy is to commit to a sample size before you start, justify it with a power analysis, and pre-register your hypotheses. Power analysis is not a bureaucratic requirement — it is the tool that connects the precision of your measurement to the scientific claims you're entitled to make.