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Hypothesis Testing

Hypothesis testing formalises one question: could this result plausibly have arisen by chance alone?

The procedure

  1. State H0H_0 and H1H_1. The null is the boring default, usually "no effect": the strategy has zero edge, the coin is fair. The alternative is what you would need evidence for.
  2. Choose α\alpha, the tolerance for false alarms, conventionally 0.050.05.
  3. Compute a test statistic, which expresses the result in units of noise. For a mean:
The t statistic
t=xˉ−μ0s/nt = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}

How many standard errors the estimate sits from the null, which is the only question the test asks.

  1. Compare against the critical value, or equivalently compute a p-value and compare with α\alpha.

The test statistic is the whole idea in one expression: the gap between what you saw and what the null predicts, divided by how much such a gap would vary by chance.

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