What are the major differences between pratical and statistical significance?
Statistical significance means the oberved mean differences are not likely due to dimpling error.
Practical significance looks at wether the difference is large enough to be of value in a practical sence.
For example, it is like adding an ingredient to a car's oil to improve the efficiency of the fuel. There is a need to have a careful controlled experiment by measuring the efficiency of the fuel before and afer introducing the additive. The findings of the experiment is that the difference is that the difference before and after has a statistcally significatly better, and come to the conclusion that the additive does improve the deficiency of the fuel. In the other hand the ingrdient has a cost of $100 a bottle, which effectives the savings in the efficiency of the fel. The diver does not really drive very much, so the conclusion is there is not much practically significant.
Does this sound like I am on the right path?
Yes, you are on the right path! Your explanation accurately captures the differences between statistical significance and practical significance.
To elaborate further, statistical significance is a measure used to determine if the observed differences in a study or experiment are likely to have occurred by chance or due to sampling variability. It helps in evaluating if the results are reliable and can be generalized to the larger population. In other words, statistical significance tells us whether the observed differences are unlikely to be solely due to random fluctuation in the data.
On the other hand, practical significance focuses on the real-world importance or meaningfulness of the observed differences. It asks the question, "even if the differences are statistically significant, does it actually make a practical difference?" Practical significance considers factors such as the magnitude of the difference, the costs and benefits associated with it, and the context or application of the findings.
In your example, you correctly illustrate the concept of practical significance. While the experiment showed a statistically significant improvement in fuel efficiency after adding the additive, the practical significance is low because the cost of the additive outweighs the savings in fuel efficiency. This highlights the importance of considering both statistical and practical significance when interpreting study results.