How Can You be Sure?

A statistician once said to me, “Being a statistician means never having to say you’re sure!”  I don’t know if he is the author of that sentence, but it sure sums up the subject.

I, like many of you, never liked the statistics course I took in college.  It’s like chemistry, you never understand it until you actually have to work with it.

Over the years, I have run into a few simple instances where statistical variation was quite important.  So, leaving out words like “normal”, “standard deviation”, “mean”, “mode”, etc., here’s the situation.

You have designed and built something that has to perform within a given tolerance.  However, you can’t sell it to a customer without some reassurance that it meets that standard.  So, you test it.  And right away, you’re in trouble.  The means of measuring the unit’s performance also lacks accuracy.  And, if you were a typical person, you ignore that nagging doubt and proceed.

But wait!  How if you had to show that the temperature drop through a cooling unit was no less than 2 degrees F, and the means of measuring that is only accurate to plus or minus one and one half degrees F?

For now, let’s ignore the nitpicking details and take the simple minded view.

OK, so it looks like this.  If a particular cooler actually only cools the fluid by one half of a degree F, and your measuring instrument reads high by one and one half degrees F, you would think that the cooler was working just fine, and you would sell it to a customer — a customer who would soon be back pounding on your door wanting a full refund plus damages.

Or, it could be that the cooler cools the fluid by more than necessary, say two and one half degrees F, but your test instrument says that it only cooled the fluid one degree F.  So, you throw the cooler into the dumpster, even though it is perfectly good.

Both of these possibilities are going to cost you money, or something much worse.  On the other hand, your temperature measuring device was probably cheap, if that makes you feel better.

Although there are a number of technical issues left out of the story, things like this do happen in practice.  I have been involved in at least two cases like this.  Sad to say, I lost the argument both times.

As someone once said, “We never have the time to do it right, but we always have the time to do it over.”

Well, hold onto your hat, there are more stories on statistics in the queue.  Next time, The Three Way Duel.  (I can’t call it a Truel, can I?)