Statistical significance, p, z, t, alpha, ...

p-value

The p-value is a probability that measures the strength of evidence against the null hypothesis (H_0​). It helps determine whether the observed data is consistent with the assumption that H₀ is true.

• A small p-value (close to 0) suggests that the observed results are unlikely under H0​, providing evidence to reject H0.

• A large p-value suggests that the observed results are consistent with H0, meaning there is no strong evidence against it.

Interpreting p-value with a Significance Level (α)

• The significance level (α,alpha) is a threshold (commonly 0.05 or 0.01) set before the test.

• The decision rule:

  • If p-value ≤ α, reject H0 (there is significant evidence against H0​).

  • If p-value > α, fail to reject H0 (not enough evidence against H0).

Interpreting p-value Without a Significance Level

• p < 0.01: strong evidence against H0 (highly significant result)

• 0.01 ≤ p < 0.05: moderate evidence against H0 (statistically significant)

• 0.01 ≤ p < 0.1: week evidence against H0 (marginal significance)

• p ≥ 0.1: no significant evidance against H0 (likely due to chance)

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