| H0 is true
(HA is false, there is no effect) | H0 is false
(HA is true, there is an effect) | |
|---|---|---|
| Reject H0
("accept" HA) Test is significant. | 🗙Reject true H0.
🗙"Accept" false HA: FP. Type 1 error. Probability=α | ✔Reject false H0.
✔"Accept" true HA: TP. Power=1-β |
| Fail to reject H0
("reject" HA) Test is not significant. | ✔"Accept" true H0
✔"Reject" false HA: TN. | 🗙"Accept" false H0.
🗙"Reject" true HA: FN. Type 2 error. Probability=β |
Power is the ability of the test to correctly reject a false H0.
It is the ability of the test to find an effect if indeed there is one.
s↑ → power↓ (curves widen, so overlap more, β↑)
n↑ → power↑ (curves narrow, so overlap less, β↓)
δ↑ → power↑ (curves' separation increases, β↓)