Lighting, Light Fixtures, Ceiling and Exhaust Fans - replacing light w/outlet with one without

I removed the old wall light (vanity bar) from my bathroom. It had a light and an outlet. The replacement light does not have an outlet. I can't tell which 2 of the 4 wires coming from the box I should use for the new light. Either of the 2 blacks will light up the tester with either of the 2 whites even when the switch is in the off position. It is lit more brightly with one than with the other. The old light worked fine, but I'm replacing it for cosmetic reasons. I already put in a new switch. Thanks. :confused:

Was the receptacle switched or permanent hot on old light? Tell us all the wires going to the light and the switch.

I was able to do it using a suggestion posted for someone else's question. There were 2 black wires and the white wire was split into 2. I assumed the black that made the tester light up the brightest was the power from the old receptacle, so I capped it and left it. I attached to the new light the other black, which lit up the tester dimly, and one of the whites. I capped and left the extra white. The suggestion I followed said to connect the power wire to the extra white wire and tuck them away, but the breaker wouldn't hold with them connected, so I separated them. It works the way I have it now. Is it safe?

Were the black and whites you connected to the light in the same cable?