I have a chess.com 3-days-per-move rating of ~1400 and recently I played someone offline with a national ELO rating of ~1530 which was a surprisingly equal game (even according to the computer) until I eventually got a slightly worse position, blundered and subsequently resigned. I assume my national ELO rating (although I don't have one) would be between 1400 and 1500.
I found this website http://elometer.net, claiming to approximate your ELO strength (ostensibly with a 95% confidence interval of 250 points) by asking you which move you would play in 76 different positions (including, but certainly not limited to, tactical puzzles), and took the test.
Unfortunately for the authors of the test their estimation was about 500 (?!) points too high: I was estimated having a playing strength of ~1950 ELO with the "95% confidence interval" of [1829, 2079].
On the other hand, I remember taking this test one or two years ago, getting an estimation which was lower. IIRC (big if), the estimation then was around 1700. This correlates with my chess.com rating, which has improved by about 200 points since then.
The test appears to have some serious theoretical foundation and was made by people associated with a university in a major city in Germany, so I assume the people who made this are quite knowledgeable in their fields and knew what they were doing. Yet the test is quite inaccurate. Why did the authors publish this test? Do they actually believe the test is accurate? Why is it off by so much?