Have to disagree here; barrel length and pattern have pretty much nothing to do with one another. The main reason 'sawed off shotguns' opened up was because the gun had a modified or some other choked barrel on it; only the last couple inches or so has the choke/restriction so when you remove that (saw off your barrel) then it becomes cylinder bore. That obviously makes a big difference but if you test a 30" barrel vs an 18" barrel with identical or no choke, your pattern is going to be pretty similar. (assuming the exact same gun, ammo, etc... different shotguns/ammo types can pattern much different from one to the next)
Here is an excerpt from the ballistics book I showed at the top of this page, concerning barrel length and pattern;
