It is the ability of the test to find an effect if indeed there is one.
It is the sensitivity of the test to detect a difference in the parameters if one actually exists.
Depends on n, α, σ, and δ.
| 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. Test is positive. | FP
🗙Reject true H0. 🗙"Accept" false HA. Type 1 error. Probability=α | TP
✔Reject false H0. ✔"Accept" true HA. Power=1-β |
| Fail to reject H0
("reject" HA) Test is not significant. Test is negative. | TN
✔"Accept" true H0 ✔"Reject" false HA. | FN
🗙"Accept" false H0. 🗙"Reject" true HA. Type 2 error. Probability=β |
"Positive" test (or statistical test rejects H0).
"Negative" test (fail to reject H0).
Power is the ability of the test to correctly reject a false H0, i.e. TP.
It is the ability of the test to find an effect if indeed there is one.
It is the sensitivity of the test to detect a difference in the parameters if one
actually exists.
Depends on n, α, σ, and δ.
s↑ → power↓ (curves widen, so overlap more, β↑)
n↑ → power↑ (SEM ↓ so curves narrow, so overlap less, β↓)
α↑ → power↑ (e.g. from α=0.01 to α=0.05, β↓)
δ↑ → power↑ (curves' separation increases, β↓)