Tolerance V

 

It Ain’t The Meat It’s The Motion

It ain't the meat, it's the motion
Makes your daddy wanna rock
It ain't the meat, it's the motion
It's the movement that gives it the sock

It ain’t the average, it’s the tolerance.

Engineers learn that you can’t achieve perfection. You have to accept tolerance around the ideal, what statisticians and other scientists call standard deviation, from perfection. That means that you have to report both the average AND the tolerance to determine if you have an acceptable batch. Reporting only the average is meaningless.

Many statistical agencies report only the average when they should also be reporting the variance, the square of the tolerance. You need both measures to judge a batch.

If the goal is to achieve growth then reporting the average is part, and only part, of the story.

·        If the average is increasing and the observations have a variance that is within acceptable limits then there is growth;

·        If the average is increasing but the observations have a variance that is NOT with acceptable limits then there is no growth;

·        If the average is decreasing but the observed variance is still within acceptable limits, there is growth; and

·        If the average is decreasing and the observed variance  is NOT within acceptable limits there is no growth.

Reporting the average without also reporting the variance does NOT establish whether there is growth. It is easy enough to report the variance in addition to the average. Most statistical packages can report both. Most statistical packages can also plot both, the average and error bars around the average. (the error is the standard deviation divided by the square root of the number of observations.)

Statistical reports should report variances, (aka Standard Deviation, tolerances) in addition to averages. Reporting only averages gives an incomplete and possibly misleading picture. It is reporting the meat without reporting the motion. You are actually reporting the growth which is a vector and matrix math applies. By only reporting the average,  you are reporting the change in position without reporting any change in direction. You want to report both the observed average AND the acceptable tolerances.