If one of the wires is still hot at the light fixture with the switch in the off position then you most likely have the light switch on the neutral wire. You gounded the fixture itself not the socket which wouldnt be grounded anyway that i know of.
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What happens if you wire a light backwards. Then attach the black leg to the side of the switchlabeled black or the side with the brass screw. Be sure to attach the white leg to the side of the switchlabeled white or the side with the silver screw. And be sure to attach the green or bare wireto the green colored groundscrew. Led light will not turn on if the polarity is reversed. There is a tester that plugs into a wall plug an. If you put a white wire and a black wire on the switch poles the best case is that you get a dead short and you trip the breaker.
With this method you will be able to tell which wire is positive and negative. If there is a light switch controlling the light it is because they ran romex wire wich has black white and a ground usually to the switch so common on power coming to fixture goes to common on light hot wire ties to either black or white going to switch the other one is hooked to other side of switch and going to hot on the light. This is a standard wiring practice. If you find more than one wire connected to an outlet or switch correct the problem by joining the wires with a wire connector and include a pigtail a short length of the same type of wire. Just remember that the side of the socket is hot now not the bottom tip. The easiest way to tell which wire is the positive and which is the negative is to test the wires with a 12v battery.
You may find some clues on the wires but if not you can do a simple test. A few homes have some of their wires reversed on a circuit. In all cases you have to determine which of the wires are hot and neutral to wire it safely. And loose wires are a very bad thing. There is a possibility that the switchwill be damaged. The worst case is the switch explodes and creates a fire.
In which case you will need to turn the power back off and unwire the switch and the other wire thats twisted together in the wire nut. This usually results in a loose connection.