How to tell if Acoustic Treatment is Needed?

Shadorne is 100% correct. You should move your listening chair away from the back wall. Try getting about 6 feet away from the speakers. So your ears might be 3 feet from the back wall and the front of the speakers 3 feet from that wall. Give that a try and let us know. It is cheaper than room acoustic treatments I believe.

If you move six feet from your speakers you will also, very likely have to bring the speakers together as well in order to keep the soundstage focused. This, in turn, may also reduce your soundstage and imaging abilities to a smaller space. This is based upon my own experience with various speakers in my own space. I can tell you that in my room of similar proportions, that arrangement also looks pretty ridiculous and closes the room off to a significant degree. You mentioned you have a coffee table which makes this proposition even more challenging. It rates extremely low in the WAF. Hell, I don't even like it, in every way imaginable (visually and acoustically). Diffusion on the back wall is a far more pleasing solution for me. BTW, speaking of the coffee table - you did mention that you'd tried moving it away from the chair. You might try two other things: eliminate the table all together and see what that sounds like. The second is to leave the table in the same place you use it and find the actual reflection points on the table. To do this place a mirror flat on the table surface. Sit in your listening position and move the mirror around the table until you can see the reflection of each speaker in the mirror (two separate spots on the table). As a test, in those spots place a pillow or a small plant or something that my otherwise absorb or diffuse the sound. See if that makes a difference for you.

Keep in mind, that none of this stuff may occur to you to make a difference at all, or perhaps it makes a difference, but one you'd really have to make an effort to hear yourself. There's no doubt the physical changes in the room do make a difference, and that treating a room can have a positive effect. The question really is do you hear it, is it worth it to you, and do you care about the differences it does make. If the answer is no after giving it a try, then keep on enjoying what you have!

i agree that long wall speaker positioning is the way to go (as it greatly ameliorates side wall reflections), but it does create its own problems:
1) bass articulation
2) staging
3) top end extension

IME you cannot overload the room w/ bass traps---put them in the corners to start (lots of DIY solutions for very little money--search Jon Risch). but you've also got to reduce standing waves between the walls that are 12' apart (check for slap echo; if its present, add wall panels--OC 703 is a nice product, put that covered w/ some polyester battling over top on the wall behind your head and see if you notice anything. its a $50 experiment).

Thank you for all the wonderful suggestions and links. With the speakers on the long wall I can't move my seating position or I'll be sitting on top of them, but it is something I will keep in mind for the future should I change the speakers' position. At present I think I'll try some diffusion on the wall behind my head.

What I think you'll need is, absorption on the wall behind your head.

Ken in Calgary - it's Kevin in Toronto here.

Some more thoughts for you:
(1) Get your hearing tested. Men, moreso than women, and especially after 50, lose our hearing quicker. Best to know if or at what frequencies you may be challenged by. If it's mid/high frequencies then all the diffusion and mid/high absorption won't mean a damn thing if you can't hear it to begin with. Sorry for the frankness.
(2) assuming (1) above is fine, in your case the first surface to deal with is the wall behind your head. DO NOT put diffusion there as you need to sit 6-10feet away from diffusion for it to work properly. I have both 1-dimensional GIK D1 diffusers and 2-dimensional Sklyine diffusers and you can sit closer to the 2-D because about half the sound is diffracted horizontally back towards you, but I digress. Instead, put some broadband absorption 4" to 8" thick sold by GIK or RealTraps, which means moving the picture to another wall. If you can't/won't move the picture, then try moving the bottom of the picture out away from the wall by putting a block of wood between the wall and the picture so that sound hitting the picture will be reflected upwards towards your slanted ceiling which will then be reflected down and toward your front wall (behind the speakers) which is fine.
(3) put a blanket overtop of your coffee table or move it during listening sessions so as to prevent high frequency reflections that interfere with the speaker's direct sound.
(4) try diffusion on your front wall behind the speakers.

No side wall treatments needed if your stereo is centered along the long wall.
No ceiling treatment needed unless by using a mirror you can see the tweeters from your listening chair in which case put up some diffusion (1D or 2D) if sufficent distance exists.

Generally speaking, think of your room in frequency bands and treat each one individually.
(A) Bass below the Schoeder frequency which in most rooms is about 300Hz: The clustering of bass nodes are less dense than upper frequencies which causes bass peaks and dips in SPL to be much easier to hear, so evening them out is the goal. Try to minimize the dips as best you can using absorption as the peaks can always be cut in volume with a little parametric EQ. Use 8" or more of absorption (diffusion would require well depths of several feet, clearly not an option) so to the extent you want or need better bass try putting bass traps in a variety of places, play some test tones and using a SPL meter graph the results. This is an iterative and time consuming exercise, so beware.
(B)Mid - Upper frequencies: for music you want to maintain the aliveness of the room to help create the "spaciousness" that is critical. Most domestic rooms are overly damped to begin with (i.e. furniture, draps, carpeting, people, pets etc)so I'd recommend diffusion over mid/high frequency absorption. Other main factors to consider are "timbre" and "location of instruments in space." All three factors will benefit from diffusion BUT only if you're sitting far enough away from it. This is why small room acoustics is so much more challenging than larger rooms due to more constraints. The deeper the well depths of the diffuser the lower the frequency it will work down to. The well depth is half the frequency wavelength distance and may in fact continue to work down one additional octave but less effectively.

So in summary, check your hearing, move the painting and replace it with 4"-8" absorption, move the coffee table or throw a blanket over it and pour yourself a libation. Enjoy and do report back to us how you made out.