Definition
The null hypothesis, written H0, is the conservative default claim that a statistical test is set up to challenge. It typically asserts that there is no effect, no difference, or no association — that any pattern observed in the data is the kind of thing that could plausibly happen by chance alone. The competing claim, the alternative hypothesis H1, says the opposite: that a real effect or difference exists.
The asymmetry is intentional. Just as a courtroom presumes innocence until evidence pushes past a threshold, hypothesis testing presumes the null until the data are sufficiently unlikely under it. The test never proves the null; at best it either rejects the null or fails to do so, leaving open the possibility that the effect exists but was simply not detected.
Why it matters
How it works
A hypothesis test asks: assuming the null is true, how likely is the observed sample? The analyst computes a test statistic — a z, t, chi-square, or F value depending on the design — that summarises how far the data lie from what the null would predict. That statistic is then mapped to a p-value: the probability of seeing data this extreme, or more extreme, under the null. If the p-value falls below a pre-chosen significance threshold (commonly 0.05), the null is rejected in favour of the alternative.
What makes this framework rigorous is that the rules are set before the data are seen. You commit to the null, the alternative, the test statistic, and the significance level in advance. Otherwise it is too easy to redraw the target around wherever the arrow landed. The framework also explicitly carves out two error types: Type I error is the false alarm — rejecting a true null — and Type II error is the missed detection — failing to reject a false one. The significance level controls the rate of Type I errors directly; controlling Type II errors requires planning sample size so that the test has adequate power to detect a real effect when one exists. Holding both error rates in mind protects against treating a single p-value as a final verdict.