The following is quoted from "Instinctive Archery Insights" by Jay Kidwell. this ook is excellent reading for instinctive archers. this theory may not apply to other disciplines, but for the instinctive archer, its spot on.
"...The inference then would be that the dominant eye should be directly above the arrow, thus allowing for more accurate horizontal( windage) adjustments. .....there is no evidence that suggests that we should change our shooting style if we find that the wrong eye is dominant.
In theory, a right dominant eye for a RH shooter will allow the dominant eye to align itself directly over the arrow thus providing a clearer sight picture in the peripheral vision of the arrow aligned with the target.
In reality, very few instinctive archers actually align their dominant eye directly over the arrow. A quick look at your favorite videos,magazines etc will prove this point.
Some of the fundamental charactoristics of insteinctive archery serve to explain why the dominant eye has little or no bearing when shooting with the instinctive method. When aiming instinctively we try to concentrate completely on the target.We cannot focus on the target completely, and on the relationship of the arrow to our eye and the target. If you are aiming using the arrow as a reference point, then you are not shooting instinctively.
It is true that the dominant eye doiminates our sight picture in our primary field of vision( where you are focusing) and at closer distances. It loses much of its dominance in our secondar field of vision(peripheral) and at greater dstances.
...with instinctive shooting we cant (tilt) the bow and our head. A target archer that holds the bow straight up and down keeps his his head straight and can place his eye directly aboe the arrow. When we cant the bow however, it places the arrow between both eyes. When you cant the bow, a number of other changes must necessarily occur in order. When you cant the bow, the string also naturally must cant. A canted string causes a canted anchor. To keep your anchor consistent, you must cant your head. Therefore, as you leave the perfect vertical alignment...that the target archer strives for....the arrow moves away from your dominant eye and falls somewhere in between both eyes until finally in ends up under the opposite eye with extreme canting of the bow. Try it for yourself. Look inthe mirror and draw your ow with an arrow and hold it at full draw in a vertical position. The arrow will line up dirctly under your eye. Now cant the bow. Notice how your head must tilt to correctly anchor and that the arrow now falls directly under and between both eyes in its vertical position.
Which eye is dominant with you? It doesnt matter."