If the ends of the wires are too far apart, the nut won’t go on properly. Be sure the ends match up before twisting them together. If necessary, snip off a bit at the tip to get them even before attaching the connector.
Household wiring in the US is color coded as follows: Black and red are hot, meaning the electricity come through these wires first. The white is the neutral wire, it carries the electricity back to the service panel to complete the circuit. The green, and in the case of NM cable, the bare wire, is the ground. This is a safety wire that carries electricity immediately to ground in case of a short.
Working through the channel, measure the distance between the joists and cut a 2x4 to this length. Attach a fan-rated outlet box to the midpoint of the 2x4 where you want the fixture to be. Attach a joist hanger to each end of the 2x4, keeping them flush, not protruding past the end of the wood. Butting the 2x4 against a flat surface while assembling can help to keep the bracket set properly. Insert the support assembly between the joists and set it so the outlet box is flush with the ceiling surface.
With the 2x4 and box assembled, hold them between the joists so the outlet box presses against the back of the ceiling. Trace the outline of the box with a pencil to mark the hole. Remove the assembly and cut a hole along the trace line using a drywall saw for drywall or gypsum board plaster and a reciprocating saw for wood lath plaster.
A circuit breaker or fuse box. Electricity enters the household circuitry through the service panel and is distributed from there through circuit breakers or fuses to branch circuits.
Mark a straight line along the wall a few inches from the floor just below the top of the baseboard. Cut the wallboard along this line using a drywall saw for the hollow parts between the studs and a drywall knife to cut over the studs.
Run the new cable from the source electrical box, through the notches and into the new outlet box. Pull an extra 8-10 inches of cable into each outlet box to allow for stripping and connecting the wires.
To install a fixture using a coupler, thread the rod into the center hole in the mounting strap and set the rod depth so the fixture base will fit snuggly against the ceiling when it’s installed. Measure the depth of the cover plate to estimate placement, precision isn’t necessary here, small adjustments can be made to the position after the installation by turning the coupler nut. Be sure all the wires are stripped for splicing, hold the fixture up and feed them through the threaded rod into the outlet box.