Don said some good stuff. I quote:
"Ground loops between signal generators, a scope, and an amplifier can destroy an amplifier including the P/L's. It's essential that the amplifier input and output are not both grounded to the scope via the ground on the generator. Since I use the external trigger from the signal generator which grounds the scope to the generator, I lift the ground lead between the speaker cables and the scope input. The dual banana jacks on the speaker cables make this easy. I also lift the ground wire on power cord for the scope."
115VAC
For the reasons mentioned above, the amplifier input and output should never be grounded together (this may create a ground loop that acts like an antenna for noise). The 115VAC power ground from the wall should be connected to the chassis of the amplifier. This is simple and straightforward. In the olden days, house wall plates did not have a third wire ground connector. My condolences to you if you live in one of those houses. Homes built properly after 1959 had grounded wall outlets and it became a NEC requirement between 1965-1969 (phased in). Unfortunately, appliances and stereo equipment designed for 2-prong outlets were not eager to change their designs for "house builders". In plain terms, your amplifier (at least; and all other components, at most) should have a 3-prong plug and cable with a green wire, the longest of the internal connections firmly (toothed lock washers) bonded to the metal chassis. This is so that if the power cord gets pulled out of the equipment, the ground wire is the last broken connection.
This does not create a ground loop, all of the devices plugged into your home are grounded together at the electrical box and that line is grounded by a rod buried 4-6 feet in the Earth, or should be.
For the o'scope, most modern o'scopes have a switch mode power supply and operate on 48-72 volts. Defeating the grounded isolated power supply should not make any difference in the display. Older (tube) o'scopes can operate at high voltages and the CRT nominally takes 6-9KV from a separate power supply. Some o'scopes feature a 'ground lift' to isolate the circuitry from the supply voltage; that is not the same as cutting off the ground pin from the plug or using a 2-3 prong adapter. If your o'scope has any accessible metal parts, ground the scope for safety.
Amplifier Inputs
The input connections should go straight to Joe's board, isolate them from the chassis and each other (remove the copper plate between them), and connect them, tightly twisted or bu Coaxial cable, to nothing else except the volume controls, if desired. Check the pots to ensure none of the connections are common to the shaft or body of the pot (they should not be). In other words, input common is not connected to chassis ground.
Amplifier Outputs
The amplifier output common or black wires, like the input commons, should not touch the chassis - anywhere. They are properly terminated at the black speaker jacks and originate at the "Star Ground," the common ground for the circuitry, not the chassis ground. This will keep the o'scope and the outputs from sharing a ground. The "Star Ground" for our Phase Linear amps is the bus bar between the two power supply capacitors. In these amps, I place a 2.2 Ohm 1 Watt resistor between the "Star Ground" and the chassis ground (one of the short terminal strips on the back wall between the rows of output transistors). This allows the "Star Ground" to 'float' above the chassis ground and send noise or hum to ground (Earth).