I've read in places that these type devices "increase" arrow speed and "tighten" your groups. Is this true and how does it accomplish this if so?

They will not increase your speed unless you take your string silencers off, which you can do and that will result in an increase in speed. Tighten groups? I didn't notice a change in mine, but that may depend on form, etc. A string Suppressor also decreases hand shock

Dan

It got rid of all the hand shock for me

Actually Dan, you might not be giving your product enough credit...

Various studies have shown that a product like yours can in fact add a few fps to an arrow. It's widely thought that the cleaner release provided by a string suppressor is the cause, as it stops the string at brace. It doesn't allow thestring to "pull" ever so slightly on the nock as a bowstring without a suppressor travels extremely far past brace, and that's where some have surmised that the string returning to brace isactually counter-productive at that point.