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Hypothesis testing and p-value

A hypothesis test checks whether data is consistent with a null hypothesis $H_0$ . The p-value is the probability of a result at least as extreme as the one observed, given that $H_0$ is true. If the p-value is below the significance level $\alpha$ , $H_0$ is rejected.

p < \alpha \Rightarrow \text{reject } H_0

decision rule

Symbols

$\alpha$	significance level, often 0.05
$p$	p-value from the test

Example

With $\alpha = 0.05$ and $p = 0.02$ , $H_0$ is rejected: the data fits it poorly.

A low p-value means the data is unlikely under

H_0

— it does not mean

H_0

is certainly false.

Practise inference and risk for free →

← Mean, median and standard deviation · Confidence interval →

Part of Statistics and Risk Analysis: Inference and risk.