Huge difference between elometer.net approximation and other rating 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?
I recently took the test and the result was reasonable (around 2100), so it is not complete bogus.

However I am rather skeptical about such tests, since I believe that playing strength/Elo rating depends on more factors than finding the best move in a certain position; such as the following which are not really tested at elometer as far as I can see: 


Can you concentrate for 4-6 hours that a game can last?
Do you blunder often?
Can you come up with good long time plans in the middlegame?
How good is your opening knowledge?
Can you spot the point in a game where you need to find a good/special move, i.e. the point where you have to invest some time thinking vs following a certain plan more or less automatically?


Regarding your comparison of online rating (1400), expected Elo of 1400-1500 and the elometer estimate of 1950, a few thoughts:


Any rating system is only relative to the pool of people playing. You cannot compare online ratings from one website with online ratings from another website or with the FIDE Elo.
You say your online rating is from 3 days/move game, which is a big difference to the Elo which is from normal games with hour long time scale.
In my experience players of your strength, particularly if they are beginning with chess, are not very stable in their playing strength. One game they might play like a grandmaster ;-) and in the next game, well...
There is a small (but finite) probability for you to score any Elo rating in the elometer test, so having just one outlier like yours does not mean that the test is bad.