Yet more biased sampling
There is a story that during WWII Allied Bomber Command noticed they were losing too many bombers over germany. They set up a team to study the problem. The team requisitioned a collection of squads of soldiers who went all over southern britain looking at shot-down bombers. They recorded every bullet-hole and flak-hole in the shot-up airplanes, and eventually produced a map of the bomber showing where the planes were hit the most. They recommended armor at those spots. The armor would make the planes heavier so they would have shorter range or less payload or less speed, but it was agreed that this price was worth paying if fewer bombers were lost. The recommendations were followed.
Another team kept track of bomber losses. The missions changed, and there were more missions, so it was complicated, but this other team eventually concluded that losses were at least as high as before and maybe higher. The armor was useless or worse than useless. So the first team was assigned to repeat their work and if possible find out what had gone wrong.
While the repeat study was in progress, one of the soldiers they had counting holes in aircraft pointed out to them, "You're only making me count the holes in the planes that made it back." Sure enough, when they looked at the data they found that the spots that were shot up the most often were spots that had no vital function. The most vital spots (like the pilot's seat) were hardly shot up at all. Because those planes didn't make it back across the channel to get measured.
Another team kept track of bomber losses. The missions changed, and there were more missions, so it was complicated, but this other team eventually concluded that losses were at least as high as before and maybe higher. The armor was useless or worse than useless. So the first team was assigned to repeat their work and if possible find out what had gone wrong.
While the repeat study was in progress, one of the soldiers they had counting holes in aircraft pointed out to them, "You're only making me count the holes in the planes that made it back." Sure enough, when they looked at the data they found that the spots that were shot up the most often were spots that had no vital function. The most vital spots (like the pilot's seat) were hardly shot up at all. Because those planes didn't make it back across the channel to get measured.
