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A Type I error is rejecting \(H_0\) when \(H_0\) is actually true (a false positive). The probability of a Type I error is \(\alpha\) (alpha), the significance level.
A Type II error is failing to reject \(H_0\) when \(H_0\) is actually false (a false negative). The probability of a Type II error is \(\beta\) (beta).
Power is the probability of correctly rejecting \(H_0\) when \(H_0\) is false. \(\mathrm{Power} = 1 - \beta\). Higher power means a better chance to detect a real effect.
The p-value is the probability, assuming \(H_0\) is true, of observing a test statistic as extreme or more extreme than the one observed. Smaller p-values indicate stronger evidence against H0.
\(\alpha\) (alpha) is the pre-chosen threshold for rejecting \(H_0\) (e.g., 0.05). It represents the maximum tolerated probability of a Type I error under the test procedure.
\(\beta\) (beta) is the probability of a Type II error. Lower \(\beta\) implies higher power (since \(\mathrm{Power} = 1 - \beta\)). \(\beta\) depends on effect size, variance/noise, sample size, and the chosen \(\alpha\).
Parametric tests assume a specific distributional form for the data/model (often normality of errors), plus conditions like independence and correct model specification; some also assume equal variances depending on the test.
When testing many hypotheses, the chance of at least one false positive increases. Without adjustment, the overall/experiment-wise Type I error can be much larger than \(\alpha\).