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Type I and Type II Errors

Every test can be wrong in two directions, and they are not symmetric in cost.

H0H_0 true H0H_0 false
Reject H0H_0 Type I error (α\alpha) Correct (1−β1-\beta)
Fail to reject Correct Type II error (β\beta)
The two errors
α=P(reject H0∣H0 true)β=P(fail to reject H0∣H0 false)\alpha = P(\text{reject } H_0 \mid H_0 \text{ true}) \qquad \beta = P(\text{fail to reject } H_0 \mid H_0 \text{ false})

Alpha convicts the innocent, beta acquits the guilty, and at fixed n lowering one raises the other.

A Type I error is a false positive: concluding an edge exists when it does not. A Type II error is a false negative: missing a real edge.

Power is 1−β1 - \beta, the probability of detecting an effect that is genuinely there.

The tradeoff

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