Need advice on changing socket in light on ceiling fan
A lightbulb is a two wire device. *There is _no_ ground on a lightbulb
to connect to.
Unless its a socket for a three-way bulb.
Check the bottom of your old socket, if there is a center contact and
then another contact ring (in addition to the shell, obviously), then
its a three-way. If so, then you can either get a replacement three-
way socket, or else just wire up a new two-wire socket using on the
fixture neutral (to the shell) and one of the fixture's switched hot
wires to the center contact.