Significance is a measure of how strong the evidence is against the null hypothesis, assuming the null hypothesis is true. It answers the question "How likely is it that I would observe this result by chance, if there was really no effect (i.e., the null is true) ?" Significance is typically measured using a p-value, and a small p-value indicates strong evidence against the null hypothesis.
Power, on the other hand, is a measure of how likely the test is to correctly detect an effect if one exists. It answers the question "How likely am I to correctly detect an effect if it really exists?" Power is influenced by factors such as the sample size, the effect size, and the variability of the data.
To illustrate the difference, consider a scenario where we want to test whether a new drug is effective in treating a certain disease. We conduct a study and obtain a p-value of 0.05, which is below our chosen level of significance (say, 0.10). This means we reject the null hypothesis and conclude that the drug is effective.
However, if the power of our test was low, we may have a high risk of making a Type II error, which is failing to detect a true effect when one exists. In this case, we may have falsely concluded that the drug is effective, when in fact it is not. So, while we may have found the result to be statistically significant (i.e., evidence against the null hypothesis), we may not have enough power to confidently detect a true effect.
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