This is certainly not any thorough test and may not prove anything, but I experimented between conventional motor oil and synthetic motor oil in a particular machine that seems to quickly dispatch it's engines. I'm talking about the little 4 cycle gas powered edger. I used to have a mowing business besides mowing a dozen or so acres around my house. Just around my house I edge about 2000 feet per week. When I did other jobs I edged quite a bit more. It didn't seem to matter what brand I'd buy, at best it seemed like I'd get a year out of an engine. After a year the 4 cycle engines would smoke so bad that they looked like you were running a 2 cycle with waaaay too much oil in the gas. Being that I toasted Toro, Stihl, Husqvarna and Troy Built pretty well equally, I ended up just buying the cheapest. Heck, I'm not even positive of the brand. I think it was the Troy Built from Lowes.
Anyway, a few years ago I dumped out the oil in the Troy Built when it started smoking and put in Royal Purple synthetic since I had a few ounces left in a quart bottle. Well, what do you know, it kept smoking some but never got any worse. I think it only takes something like 4 ounces of oil. I now change the oil in it a couple times a year with Royal Purple and I think this edger just finished it's 4th year. And, yes, I constantly clean and replace the air filter in them. After just one trimming at my property it seems like the air filter is practically clogged because it literally 'lives' in a cloud of dust that it kicks up when in use.
Like I said, this may not prove anything. All I know is that now an edger is lasting me for several years where I maybe got a year's use out of one. Again, I'm perfectly aware that the engine design may have been changed, maybe I just finally got a 'good one', maybe all the previous ones were defective, etc. Since I only go through about 8 ounces a year I don't really care that Royal Purple is expensive. As far as I can tell, Royal Purple stopped the gradual destruction of a small engine that I'd witnessed over and over again. Heck, I've even started using it in my 4 cycle weed eaters too. Maybe it's just in my mind, but they seem to have just a bit more power and seem to rev faster. The bottom line is that I'm convinced that, since the only thing I changed is the oil that I use and now my edger keeps on ticking, I'm actually saving money by using synthetic oil in my situation.