Can a hypothesis test yield a statistically significant (say p<=0.05), yet practically meaningless result? Give an example of how this might happen.
Could someone please explain this to me so I will understand it in simple terms.
Yes, it is possible for a hypothesis test to yield a statistically significant result (p-value <= 0.05) but still have a practically meaningless or insignificant finding. This situation can occur when the sample size used in the study is large enough to detect even the smallest differences or effects, but these differences are so minor in practice that they are not of practical significance or importance.
To understand this concept in simple terms, let's consider an example: Imagine a study that investigates the effect of a new drug on reducing the duration of a common cold. The researchers conduct a randomized controlled trial with a large sample size and find that the new drug is statistically significant in reducing the duration of a cold compared to the control group (p-value <= 0.05).
However, upon closer examination, the difference in duration between the drug group and the control group turns out to be very small - let's say it is just a matter of a few minutes or hours. While this small difference may be statistically significant, in practical terms, it may not have any meaningful impact on individuals' everyday lives. Therefore, despite the statistically significant result, the finding would be considered practically or clinically insignificant.
It is important to consider both statistical significance and practical significance when interpreting the results of a hypothesis test. Just because a result is statistically significant does not necessarily mean it has a meaningful impact in real-world scenarios.