You are not actually measuring the accuracy of the clock, rather you are measuring the magnitude of the noise. The clock source itself is something physically f

You are not actually measuring the accuracy of the clock, rather you are measuring the magnitude of the noise. The clock source itself is something physically fundamental and unchanging, but it gets mixed with noise. For example even very small magnetic fields will change the clock speed, thermal changes will as well (so will lots of other things). So you try to shield from that, and keep the temperature stable (and of course you need to figure out every other things that could add noise). Then you measure all those influences that you just are unable to control, and calculate what affect they have on the clock, and that's your accuracy number. One way to directly measure that, instead of calculate it, is to have two identical clocks, synchronize them, and let them run. Then compare them, and see if they differ. (Watch out for relativity messing with time.)