Based on 3 different tests, I estimated the following return period values* and their 95% confidence intervals from the test measurements. As an example, imagine that we are testing different engine oils and measuring the engine temperature, and we want to know which oil results in the lowest engine temperature. The confidence intervals from the first 2 tests contain the return period value from the other tests. Does that mean that we can't actually distinguish the 3 return period values, i.e. the difference between the values is not statistically significant? If that interpretation is incorrect, what is the right interpretation of overlapping confidence intervals?
Value (Lower 95% CI, Upper 95% CI)
3.36 (3.09, 4.61)
3.50 (3.02, 7.33)
4.35 (4.06, 5.50)
*The return period value is just the value associated with a certain probability level. An example is the wind speed associated with a 100-year storm.