How do I know if I need a sub woofer?

Oh dear. To address your apparent complete misunderstanding would take too long so I won't bother. You do you.

I provided you with the names of some extremely well informed people to read up. If somebody writes their thesis on this subject then I think it's fair to assume they know what they are talking about. 

Have you read anything from those authors? No I didn't think so.

I will not respond to anymore of posts.

sounds_real_audio OP, I hope you did not suffer too much with all the above. I attempted to explain that all rooms regardless of the speakers' size will benefit greatly from a pair of subs however it seems to have ruffled some feathers.

Good luck in your quest.

Two Blue Jeans 45' Canare L-4E6S shielded star quad XLR stereo pairs to Velodyne DD Plus through put to a second DD Plus. Approximately $230. 

Oops, wrong thread! 

If you listen to interments you should easily be able hear the distinct timbre of plucked bass, or bass guitar - telling them apart for one, but also the tonality of a particular instrument.

Cheap subs don't do a good job with is - they give an impressive but tonally mushy bass extension.  They can also transit floor vibrations that further muddy things

I like Dynaudio...