This is opening up all new avenues of thought in my head! So theoretically if we tested an astronaut on a simple mental recall test on Earth and timed then, then had them repeat the test on a trip to the Moon but timed them on the Earth the astronaut outside of Earth's gravity well should be observed completing the test faster (from Earth), but if they measured the test on the space craft, the results would be the same as when they completed the test on Earth.
Correct, but the effect would be too small to measure like that (human performance at tests is noisy).
If you made the difference in gravity more extreme the difference in measurement would be trivial to notice, but we don't have a way to achieve that in practice.
