I have a raw EEG signal of length 2,50,000 samples. I band passed it from 0.05-10Hz (sampling frequency=500). Then I down sampled it at 20Hz. Now question is: What will be effect if I vary down sampling from 20Hz to say 5Hz or 60Hz? And why 20Hz is appropriate?
Given that you have removed all signal content above 10 Hz, your 20 Hz sample rate will be identical to the minimum sample rate based on the Nyquist sampling criterion.
If you instead use 5 Hz, you can only represent a bandwidth of 2.5 Hz and, e.g., a signal appearing to be at 2 Hz might have been a 3, 7 or 8 Hz signal as well (meaning that you can not distinguish between a signal at any of those frequencies after the downsampling). This is caused by aliasing.
Using 60 Hz would be clearly feasible but will consume more storage of the signal. The possible benefit might be that later processing may be simpler as the signal does not cover the whole signal band. However, this depends on which processing is required later. Also, while the processing in itself may be simpler, there are more samples to operate on so the total complexity may not be reduced.
By saying you sample your signal,you actually convolve it with a train of impulses spaced apart by Ts (1/f).That results in MULTIPLE COPIES of your signal in the frequency domain. That multiple copies could possibly create problems,resulting of that change in the sampling frequency (you may dont care about that but you may be asked in the future).If the sampling rate is reduced (downsampling) then this copies will EXPAND,(and may overlap with each other) if the sampling rate is increased (up sampling) this will shrink. Now,the limit where you will not have them overlapping is the fundamental frequency range (+-fs/2).That is derived by the Niquist criterion,for sampling and that is why it "should" be kept the frequency range within this limits.