Accuracy is the Enemy of Precision: Part II

Error is a pervasive concept in our lives. Either consciously or subconsciously we seek to eliminate error or to manage error.  When we as a species were roaming the savannahs, error was a life and death concept.  We either ate or we were eaten.  Now, possibly, we balance error versus convenience.  You might even say that error determines the magnitude of risk versus reward.  In many ways, we choose the amount of error that is acceptable to our lives, and for the most part this choice is relative.  When setting the standards for the passage of time, acceptable error is in the millionths of a second.  For firing a rocket for a Moon landing, error might be in milliseconds.  For boiling an egg, it is in seconds.  For managing our airplane flights across the country, acceptable error could be in minutes or hours.

In a somewhat humorous vein, one might say that the woodworking population could be divided into two groups: those who assume that errors only accumulate (the fatalists) and those who assume that in the end errors will cancel out (the magical thinkers). This might be an existential divide.

You cannot talk about either precision or accuracy without talking about the concept of error. In fact, accuracy and precision are literally defined by error.  You might say that striving for accuracy is the attempt to eliminate error, while striving for precision is the attempt to manage error.  You might also define error as “acceptable variation” because it is impossible to eliminate error from any process.  In everything we do, we strive to understand and to reduce the effects of error.  The more we accept error in our work, the more likely we are to have an “acceptable” result.  This defines the concept of “confidence”.  While we have high confidence in our work if error is managed tightly, the rate of acceptable outcomes may be low.   On the other hand, if we accept error, then the outcome is more liable to be acceptable, but the confidence in the result may be low.

There are basically three types of error: random error, consistent or fixed error, and allowed error. You are aware of error when your achieved result does not match your intended result, and the achieved result is outside of some predetermined acceptable variation.  For example, you cut four sides for a square box, stack the pieces together, and test the lengths with your fingertips.  Your acceptable error may be higher if the box is meant to be free standing, and much lower if the box is meant to slide into a carcase.

Random error arises from not thinking through, understanding, or controlling variables in a process. Generally, there is an expected end result (the diagonals on a box are the same length—is that accurate or is that precise?). You have to evaluate the magnitude or effects of error for each step in a process.  For example, you use a square to lay out joinery but you have never tested the square to see that is in fact square.  The inside of the bar might be square and the outside of the bar might not be square.  You sometimes mark with a knife (sometimes on the bevel, sometimes not so), sometimes with a pencil which is sometimes sharp and sometimes not sharp; and finally when you saw, you might split the line or saw to one side or to the other.  Ideally, you want the only variable to be your accumulated skill level, and all else to be as defined as carefully as possible.  The expected result is both precision and (assuming your layout is not random) accuracy.  If you do not achieve this result, you examine the process, understand the limits for each step, and work to be consistent.  The way to reduce random error, is to break down a process into its constituent steps, define a standard method for each step, and be consistent in the implementation of these steps in the future (the learning curve!).

Consistent or fixed error is means that the achieved result is always (precisely and accurately) different from your expected result. It is error in one direction.  Usually this means that all variables but one have been controlled for.  Or that there is an error that cannot be controlled, but is in fact a constant effect.  For example, you use a knife to make a tick mark to set a length.  When you square across, you set the square to the tick mark.  When you scribe the line however, you do not tilt the knife to have the bevel rest tight against the bar of the square.  You are consistently (and precisely) overlong in your cut pieces.  You may not recognize what that uncontrolled variable is, but you see the effects in the end result (consistently).  Again, isolating or understanding this variable is a process of looking carefully at each step of the process, being aware of the acceptable variation.

Allowed error is consistent error that you build into (or allow into) your project because you know from experience that your achieved result will still match the expected result. For example, you always cut the panel in a frame and panel smaller than it needs to be, to allow for seasonal expansion and contraction.  You never cut the panel to match, but how small you make it is variable within some limits.

Error is a moving target. There is never one standard for acceptable error that can be applied to all projects.  You have to recognize that error will occur, understand the impact of the magnitude of the error, and be able to accommodate error.

Throughout this discussion, you can see that the concepts of accuracy and precision are somewhat fluid, impacted by the effect of error, and by what we define as acceptable limits of variation. The titular aphorism embodies many of these concepts, but only makes sense if you take the time to delve more deeply into what the underlying message is.

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