Clinical significance refers to the size of an effect. An effect is considered of clinical significance if it is both statistically significant and the “magnitude” of the effect is large enough clinically.
Suppose a study was conducted to examine the efficacy of a new drug in reducing blood pressure (BP). A number of patients received the new drug and a number of other patients received the conventional treatment. The new drug reduced BP by 0.5 mmHg more than the conventional treatment with a p-value = 0.012. The difference is of statistical significance but the magnitude is deemed to be not of clinical significance.
In the same setting as in Example 1, suppose the new drug reduced BP by 10 mmHg more than the conventional treatment but the p-value was 0.420. Although the magnitude of the difference looks large but it did not reach statistical significance. Therefore, it is not considered of clinical significance.