Can a hypothesis test yield a statistically significant (say p<=0.05), yet practically meaningless result? Give an example of how this might happen.
Yes, it is possible for a hypothesis test to yield a statistically significant result (p≤0.05) but still have a practically meaningless outcome. This situation can occur when the sample size is large enough to detect even the smallest differences, making the result statistically significant, but the observed effect is so minor that it has no practical significance.
For example, let's consider a study on the effects of a new drug on insomnia. The hypothesis test is conducted to determine if the drug leads to improved sleep quality compared to a placebo. The null hypothesis states that there is no difference between the drug and placebo, while the alternative hypothesis suggests that the drug does have an effect.
Suppose the study involves a large sample size and the statistical analysis reveals a p-value of 0.001, which is below the conventional significance level of 0.05. Based on this result, we reject the null hypothesis and conclude that the drug has a statistically significant impact on sleep quality.
However, upon further investigation, we find that the difference in sleep quality between the drug and placebo group is negligible. While the difference is statistically significant due to the large sample size, it may not have any meaningful impact on real-world situations. In other words, although statistically significant, the practical significance of the effect is so small that it may not be relevant or useful in practical terms.
Therefore, in such cases, it is important to interpret and consider the practical implications of the results alongside the statistical significance to avoid drawing misleading or irrelevant conclusions.