Keep the signal at a low amplitude otherwise you will be measuring the slew rate. I would expect to see the input square wave have a rise time of , say ten nanoseconds (from 10-> 90%) and the output having a rise time of, say one microsecond, so what is the propagation delay?. It might be 50 nS at the 10% point and 1.1 microsecs at the 90% point.
With a video (wideband analogue ) signal, a carrier sweeps across the band with a low frequency amplitude modulation. The output of the video device then is connected to the input of the test set, where the phase of the low frequency modulation is compared to the original signal. So the output on an oscilloscope is a graph plotting delay time against carrier frequency. This test is done so that all frequency components of a complex wave form take the same time to get through a system, its called group delay.
Frank