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.
