I have two sea water temperature column from two different location and I want to test if they are significantly different. KS test and MANOVA test classify the water depth profile into different layers, which I don't want. on the other hand, kernel density estimate take the whole profile at once. What other statistics test could be used?
You have one profile from location A, and one profile from location B.
Each profile (please correct me if I am mistaken) comprises a serie of correlated temperatures, i.e. two temperatures close in the profile will be more similar than two more distant temperatures.
The bad news is that you have only one profile per location.
Each profile is considered as one individual, with the many increasingly deep measurements being correlated measures of the same serie. That's similar to measuring, for example, the height of someone from age 1 to 50. Or the concentration of free cadmium in soil from 0 to 100cm deep. You could perform a million measurements along the profile, it stays one profile.
So you can say that the two profiles you wish to compare are different, visually different.
However you can't test if these two profiles are significantly different. It is the same as asking : are these two guys significantly different based on their height ? They are different. Because these are two different people. The same conclusion holds for the two profiles of temperatures.
To test whether the two locations are significantly different by their profile of temperature, you need multiple independent profiles at each location.