take your home defense shotgun somewhere you can pattern it at house ranges, 5 to 50ft? See what the pattern looks like. We know how they test handgun bullets for penetration but I have never read of shotgun pellets tested in the same media.
War stories tell us the close range scattergun is VERY effective, but again I have never read any study done on this.
One of the africa hunting writers tells of shooting a female lion out of the middle of her spring with a 20 ga. loaded with bird shot. Head shots count.