Direct comparison
Null Vs Alternative Hypothesis: Key Differences & Comparison | CASRAI
The null and alternative hypotheses are the two competing statements at the heart of a statistical test. The null hypothesis (H0) states that there is no effect or no difference; the alternative hypothesis (H1 or Ha) states that there is one. A test gathers evidence to decide whether the null can be rejected in favour of the alternative.
Side-by-side comparison
| Dimension | Null hypothesis | Alternative hypothesis |
|---|---|---|
| What it is | A statement of no effect, no difference, or no relationship | A statement that an effect, difference, or relationship exists |
| Symbol | H0 | H1 or Ha |
| Role in the test | The default assumed true until evidence challenges it | The research claim the study aims to support |
| What is tested | The hypothesis directly evaluated against the data | Accepted only indirectly, if the null is rejected |
| Possible outcome | Rejected, or not rejected — never "proven" | Supported when the null is rejected |
| Direction | Always an equality (e.g. no difference) | One-sided (greater/less) or two-sided (different) |
| Error if wrong | Type I error — rejecting a true null (false positive) | Type II error — failing to detect a true effect |
| Decision rule | Reject if the p-value is below the significance level | Favoured when that threshold is crossed |
| Common pitfall | "Not rejected" does not mean proven true | Statistical significance is not the same as importance |
Common questions
FAQ
Why do we test the null rather than the alternative?+
Because the null specifies an exact value (such as "no difference"), it gives a precise model from which we can calculate how likely the observed data would be by chance. The alternative is usually broad ("there is some difference"), so it cannot be tested directly — instead we see whether the data are too unlikely under the null to be credible, and reject the null if so.
Can you ever prove the null hypothesis true?+
No. Failing to reject the null only means the evidence was not strong enough to overturn it — absence of evidence is not evidence of absence. A non-significant result is consistent with the null, but also with a real but small effect the study lacked the power to detect.
What is the difference between one-sided and two-sided?+
A two-sided (two-tailed) alternative says the value differs from the null in either direction. A one-sided (one-tailed) alternative specifies a direction — that the effect is greater than, or less than, the null value. The choice should be made before seeing the data, as a one-sided test is more powerful but only in the pre-specified direction.
Going deeper
