The Sinister Left Hand or Damn Lies and Statistics

Analysis at the crime scene in Villisca by special agent and "fingerprint expert" M. W. McClaughry of Leavenworth Prison indicated the killer was left handed.  Later, upon observing George Kelly chop wood, it was found that the reverend was left handed as well.  I bring this up because the investigators on both the Ardenwald and Rainier crimes scenes came to the conclusion the killer (or killers) was left handed.  There are many things you have to worry about as a lefty.  Manual can openers are an affront to your existence, golf clubs cost double and you're only allowed to play 1st base or pitcher in baseball.  But those are minor complaints really.
Lefties are also more likely to die in a car accident.  But the biggest kick in the pants is this; 20% of schizophrenics are left-handed.  Now you might be thinking that isn't such a big deal.  That leaves the other 80% of schizophrenics being right-handed.  It's a fair cop until you realize only 10% of the world is left-handed which means a lefty is far more likely to suffer from schizophrenia than a righty.  But really what does it all mean?  It's hard to say.  If 10% of the U.S. population was left handed in 1911-12 then that means (roughly) over nine million people qualify as a suspect based on that single characteristic.  If you subtract the unknown numbers of persons who would be disqualified due to age or other limitation (I would guess) you might still be looking at over five million suspects.  I can whittle that number down using blind stats (please note, these figures are guesses based on current percentages).  Currently about 1.1% of the U.S. population is schizophrenic (= a little over 1 million people in 1912) and then 20% of those individuals might be left handed which comes out to about 203,000 suspects in 1912.  But that is only if the suspect was in fact schizophrenic.  What if our axe murderer merely suffered from psychopathy?  That's starts me out with a number of around 3.6 million people in 1912 (about 4% of the population).  There have been some recent criminal studies suggesting a greater dependence on the left hand among psychopaths but nothing definitive has been published and it needs to be pointed out that left-handedness should not be used as a marker for either psychopathy or schizophrenia.  Now if there were only statistics available for left handed, psychopathic axe murderers I might be able to get somewhere with all these numbers.