# Overstating Precision

#### (Guaranteed to be 97.306847% accurate!)

## A Ham’s Bedtime Story

Once upon a time there was a Ham that tended to overstate the precision of his numbers. This is not a sole, Ham-related problem, but a bigger problem in the general population. People often don’t have their facts straight, and, even then, aren’t aware of how precision is determined. How many times have you heard the bilge that “ya’ know, day say we only use 10% of our brain’s ability?” Well, aside from the fact that this is just nonsense, how would you measure a “brain’s ability” and what units of measurements would you use (the μEinstein, with the inverse units being the μMook, perhaps)?

“Your antenna system determines 80% of your station’s ability”??? What the hell does that actually mean? Is it 80% or 80.0% or 80.0000000% or is it closer to 74.38953725%??? In fact, it is none of these. A station’s ability is not a repeatable, measurable quantity, it is an arbitrary assumption of differing individuals (i.e. what’s the best flavor ice cream?). When cornered these people rationalize that the 80% is an approximation, or a “ballpark estimate” that is more easily understood than the vaguer “your antenna can be the most important aspect of your shack”. But it strikes me as roughly 85% hyperbole on the adviser’s part.

Precision is a REAL thing in the world of science and engineering. It does not mean that you arbitrarily extend the number of significant digits out to infinity to impress the other guy. Everyone has heard about Bird meters. They have developed a reputation as a “gold standard” by which all other RF power meters are compared, and yet like any other piece of test equipment, they have their built in limitations of precision. Very often their slug-meter combinations are rated as ±5% of the meter’s full scale. This would mean that if the full scale of a given meter is 100 watts, then, although the meter says 100 watts, it might be 95 watts or 105 watts. Most people have no problem with this, but if you try to explain that this also means that if the same meter is reading 5 watts of power it can in reality be anywhere from 0 watts to 10 watts. To me that doesn’t seem very precise, but that’s how all test equipment actually works! Error rates of these types of measuring devices are all relative to full deflection.

Another problem that people seem to have is that when you calculate a value from more than one initial measured value, the final result has the precision of the lowest value used to calculate it. As an example Power equals Current times voltage. 13.8 volts times 4.7 amps equals how many watts? Well, 13.8 x 4.7 = 64.86 right? But I only gave you the current to two places 4.7 amps. Not 4.70 or 4.700, but just a two digit 4.7, so the lowest precision number is two digits long – that means that 13.8 volts x 4.7 amps = 65 watts ± the error range introduced by the two devices that measured the volts and the amps (we will spare you how to determine the calculated error range for another day). Most people will erroneously offer the answer of 64.86 because that’s what their calculator tells them, real chuckleheads will tell you its 64.8600000000 because, apparently that’s how many trailing zero’s their calculator displays!

It’s not only a matter of ability or inability to measure something, or the accuracy and precision of a given measurement (no, accuracy and precision are two different things – look them up if you don’t believe me)! Accuracy is random errors in a measuring device and precision is repeatable errors in a device. It’s also a matter of knowing what (watt?) you actually want to measure. A Watt is a Watt is a Watt? Hell, no. There are devices that measure your “Peak” Watts, others that measure your “Average Watts” and still others that measure something called “RMS” (Root Mean Square) Watts. They are all useful but they all tell you something different about the device you are measuring!

Some values we play with every day in this hobby have no real fixed measurable value. This is unfortunately true of your “S” meter numbers. There is a recommended value for S9 being 50 microvolts of radio signal with each lower unit being 6 dB or 1/4^{th} the power of the previous unit. Most manufacturers don’t seem to care about this accepted value. Each manufacturer determines his own parameters from model to model and rarely calibrates all of one model to any precision. The bottom line is that you should consider your S” meter values as relative numbers (i.e. S9 is much stronger than S5) but not rely too much on what the numbers are supposed to actually mean!

So, the moral of tonights story is that you should use your head more and your calculators less.

So if the next guy on the radio gives you a hard time when you don’t tell him what your power output is to the nearest micro Watt tell him to read this article!

Pleasant dreams…

-Your [Cranky] Editor –