Math basics › Probability and statistics
Hypothesis tests and p-values
Two hypotheses
The null H₀ says nothing is going on. The alternative H₁ is what you suspect. The test assumes H₀ and looks for evidence against it.
The p-value
The chance of a result at least this extreme if H₀ were true. Below your significance level α (often 0.05) means reject H₀.
What it does not say
A p-value is not the chance that H₀ is true. And failing to reject H₀ does not prove it.
Confidence intervals
Estimate ± margin of error. A 95% interval comes from a method that catches the true value 95% of the time.