The Unmuddled Mathematician

The Margin of Error

By Chris S. Coray, The Unmuddled Mathematician

It is very likely that you will find this month’s column a little strange and in some ways hard to understand.  Nevertheless, I can no longer hold back and either I write these words or I will explode and die, leaving a widow, my fly rods, my best marbles (the flints), and things equivalent to the Muddled Male’s cell phone, also known as his “Precious”.

It is not possible to enumerate the number of times I have heard talking heads on all news presentations, when describing poll results, say the following phrase or its equivalent, “According to our latest “Ask the nearest living Frog” poll, the difference between the results for Candidate A and Candidate B is within (or outside of) the “margin of error”.  

OK, what do you think that means?  For example, if Candidate A is polling at 30% and Candidate B is polling at 24% and you hear a beautiful (but it turns out to be a know-nothing) CNN anchor say that the poll results are outside the margin of error, which the talking head claims is 4%, what have you learned?  I promise you that it is not what you think, in fact it is nothing at all.

Without the addition of a significant and content loaded phrase that is almost never uttered, and is not understood by the talking head, you have actually learned nothing.  Zip, nada, and certainly not the location of El Chapo.  The needed phrase involves mathematical probability and hence is equivalent to the plague for pretty much everybody.  But for me this extra phrase is the essential and beautiful kernel of information that is the key to the gates of understanding.  You can understand it.  All you have to do is ask.

I remember a trip Bobbie and I took many years ago.  To this day I cannot remember where we were or why we were on the trip.  In those days we sometimes stayed in a motel.  The only memory I have is that the bed was not the same as in my home so it was not comfortable, it was noisy in the city, and I could not sleep.  So while Bobbie dozed as best she could I turned on the TV, low volume, and at 2 a.m. was greeted by an educational program covering the Central Limit Theorem and its proof.  

Yaay!  This show would not get high national ratings but it sure got my joyous attention as I listened to some guy trying to explain this really important math result to a TV audience.  I’ll bet there were 2 or 3 people watching nationwide.  It was pure joy for me until Bobbie woke up due to my in-room cheering and asked me what the heck I was doing.  

I was a truth teller so I told her which produced the question, “Are you even more nuts than I thought?”  That I was nuts was already well known to her but this data did not need to be repeatedly reinforced in the middle of the night.  Off with the TV.

All of which brings me to a slightly different phrase, namely, the margin for error.  This is especially important when that margin is zero.  For example, wearing a navy blue blazer with brown pants has a zero margin for error in this house.  It is graded with the virtual red pen and words used when marking incorrect answers to important test questions.  When in my bungling way I mismatch my clothes , an event that often occurs (I claim innocence here because I have no idea what things actually do match), our kids often asked, “Who dressed dad today?”  

Another example is driving a car in any city in the Middle East.  There is no margin for error.  One mistake and you’re dead.  Or making a bad mistake when you get an occasional question from your married children, the kind of question that has two possible responses.  You can get into serious trouble with the wrong answer, which becomes advice, which is actually not wanted, and has only a potential downside.  Bobbie taught me long ago that in this example the only correct response is “Mmmmmm”.  The tone, volume, and pronunciation have to be perfect so as to convey no information, no preference, only patience and loving, approving interest.  

Again, no margin for error. There, I’ve cleansed my pent up emotions about the margin of error.  Thank you for making me feel better.