This is not correct. Light sockets must have correct polarity so the hot is on the center contact and neutral on the outside screw shell. This is required due to the risk of shock from the exposed screw shell when changing bulbs.
Look closely at your exposed lamp cord. One wire should have some kind of marking, either printing on the insulation, or a ribbed texture to the insulation. This is the neutral.
Failing that, get an ohmmeter or continuity tester, or find someone who has one. Check for continuity between each wire and the center contact of the light sockets. The wire which shows continuity is the hot.