You should reject the null hypothesis when the data provide strong enough evidence to conclude that it is likely incorrect. This typically happens when the p-value, which measures the probability of observing the data assuming the null hypothesis is true, is less than or equal to a predetermined significance level (commonly 0.05 or 0.01). A smaller p-value indicates stronger evidence against the null hypothesis, meaning the observed effect is statistically significant. In other words, reject the null hypothesis if:
- The p-value ≤ significance level (alpha, e.g., 0.05)
- The observed data is statistically unlikely under the null hypothesis
- The test statistic exceeds critical values set for the test
Failing to reject the null hypothesis means there is insufficient evidence to conclude that an effect or relationship exists. Be aware that rejecting the null hypothesis when it is true results in a Type I error, and failing to reject it when it is false results in a Type II error. In summary:
- Reject the null hypothesis if p-value ≤ significance level (e.g., 0.05)
- Do not reject if p-value > significance level
This is the standard procedure in hypothesis testing to decide when to reject the null hypothesis.
