Yes, it does matter greatly yet most people don’t know which of their eyes is the more dominant. This last weekend I had one student, a friend, who was right handed yet left-eye dominant. He actually knew it, but we often test at the beginning of class because it will almost always affect how students approach key factors surrounding accurate presentation of the tools to the work. Accuracy starts with aligning everything surrounding the hand-eye coordination but between the eye and the hand is that upper mass of body linkage that allows the eye to sight exact alignment of a tool’s cutting edge to the line and then along that line. Normally people are predominantly right-hand AND right-eye dominant at the same time. If a person is right-hand dominant but left-eye dominant he or she must align their body differently to the work to achieve the best results. How about that! It’s of less concern for machine woodworking because the machines do the cutting and alignment is rarely using the freehand of the body but alignment by fences and jigs that actually guide the wood into the cutting edges. That’s not the case with hand work where the person guides and aligns the tool to the cut using only hand-eye coordination and all self-propelling energy.
I have not always been aware of the struggle people have with this problem, but those I have discovered have been at the bench when they seemed to have a problem aligning the saw to the cut line. Amazingly, after a few seconds reconciling a preexisting condition, new levels of accuracy become evident.
I have a clock 40 feet away from my bench hanging on a blank wall. I ask the students to find out which eye is dominant at the beginning of class. This can save time later. With both eyes open they extend their arm, form a circle with their thumb and first finger and place the clock in the circle. They then close one eye but keep the hand extended so. Which ever eye retains the clock in the circle determines which eye is dominant. Closing the dominant eye will show the clock missing as the circle seems to jump to the right.