The ground wire is a mystery, though, as it only came out of the old light fixture itself and was not inside the square electrical ceiling box (not sure if that's the correct term).

The old light had a ground wire that ran from the ground screw in the metal hanging bracket (mounting strap? plate?) to a metal part of the old light.

There is no ground wire coming out of the ceiling electrical box! Is that normal? It just has the black wire and the white wire. Anyway, we removed that old ground wire.

Then, we attached the new round hanging bracket (mounting strap? plate?) that came with the new light, matched white to white, put one of those plastic twisty cap things to merge the bare wires and then covered it with elec tape, and did the same with the black wire to "black" wire.

Hmmmm, where is the ground wire? I see the green ground screw. Well, the ground wire comes out of the tippy top of the light fixture, along with the black wire and the white wire, all of which are INSIDE the part of the canopy/glass/lamp that we attached to the plate.

Is this the right way to do things? Is it safe?

I thought the ground wire was supposed to come out of the electrical ceiling box along with the black wire and the white wire.

Did we do this right, or are we in trouble?? If it's not right because we don't have a house ground wire, how do we fix it? I guess we haven't had a house ground wire since 1987 ...

Thanks for any help!

Only if it is actually grounded.