Before this thread descends into some rabble, lets clear up a point.
Clinton is pretty much on the money. The reason is a poor F/A ratio engine runs rough is usually because the cylinders are still firing, albeit at vastly different F/A ratios, and thus the HP per cylinder is vastly different.
On a fully instrumented carby engine this is easy to demonstrate, as the EGT and CHT data will prove the cylinder/s who are considerably leaner are still producing power. So the notion suggested above that they immediately shut down and caused rough running because the mixture is so lean it would not support combustion is not quite how it happens, or certainly in the vast majority of cases.
So
CM, chocky frog for you
Peter C...my medication is quite fine thank you for asking. Your comment about publications written by engineers would be correct, if only the manuals were written that way. It may pain you to learn that far too many sales and marketing and legal department folk are the reason for such poor manuals.
If I were to ask Walter for the fellows name it might lend more credibility, but one of the old timer Lycoming engineers attended the APS course a few years back in Ada and was over joyed that the truth was being told by someone. He told the class how the it was that these kind of publications were released, much to the horror and dismay of the engineers.