What is the difference between the null and alternative hypothesis?
The null hypothesis (H0) is the default claim of no effect or no difference, while the alternative hypothesis (H1) is what you are trying to find evidence for. Hypothesis testing asks whether the observed data is surprising enough under H0 to justify rejecting it in favor of H1.
How to think about it
Every hypothesis test begins with two competing statements about the world. The framing you choose determines exactly what your test can and cannot conclude.
The null hypothesis (H0)
H0 is a precise, falsifiable claim — almost always “no effect,” “no difference,” or a specific parameter value. Examples:
- “The new drug has the same mean response time as the placebo.”
- “The conversion rate of variant B equals that of variant A.”
- “The population mean is 50.”
H0 must be stated sharply enough that you can compute the probability of your data under it.
The alternative hypothesis (H1)
H1 is what you suspect is actually true and hope the data will support. It can be directional (one-tailed: mu > 50) or non-directional (two-tailed: mu ≠ 50).
The logic of the test
You never test H1 directly. Instead, you assume H0 is true, compute how likely your observed data (or something more extreme) would be, and decide whether that likelihood is too low to be believable. If it is, you reject H0 — not because you proved H1, but because H0 became implausible.
| H0 | H1 | |
|---|---|---|
| Role | Default / skeptic | Research claim |
| Testable directly? | Yes — probabilities are computed under it | No — only indirectly supported |
| Outcome on rejection | H0 rejected | Evidence for H1 |