Precision, Accuracy and Absurdity

Have you ever calculated your pool’s volume precisely, right down to the nearest gallon? How about treating the water for that hair-splittin’ saturation index of 0.00 +/- 0 by adding a carefully calculated calcium chloride dose, figured to the closest half pound. Surely you remember referencing the handy-dandy tables offered to you by your equipment supplier (figured by a computer database, of course), with weights and measures like 466.531 pounds or 2.922 gallons? And for those of us really into math, we use 3.141593 for pi, of course, figuring that spa capacity. We want to be as accurate as possible, for sure, so we always use the “best” numbers we’ve got...

Ah, so you are one of those?? A precisenik! If you knew just how “wrong” you were, you might just change your calculatin’ ways... There IS a difference between accuracy and precision!

Just what is the difference between being “accurate” and “precise”? Quite different, these two words. We need to be accurate in our work, of course; but we have very little need, indeed even less opportunity, to be precise. Take pool volume as an example: Length and width, measurable to the nearest — what? Quarter inch? But depth — sectioned, guesstimated, averaged or read from as-build drawings — no matter how you cut it... pool depth is guesswork, weighted by coves, slopes, variations in contour, and the contractor’s deviation from the idealized drawings. We are, frankly, lucky to be correct within a foot for the real average depth. And that lack of true measure dominates the calculations. Volume cannot, therefore, ever be calculated “precisely”, that is, to the nearest, say, hundred gallons ? much less single gallon. And darn’ near every other calculation for your pool is based on that liquid volume calculation!

Now those engineers who design our pools regularly figure the capacity down to the nearest gallon. As engineers, of course, they feel a certain professional obligation... never mind that each tenth of an inch of actual depth variation in a typical fifty-meter pool represents about a thousand gallons of water, and more can evaporate while we have this discussion than the last two digits represent. It’s not a matter that he shouldn’t figure so close, it is that he can not and must not. Drawings for a fifty-meter pool design were recently annotated “854,621 gallons”. Isn’t that just a little ridiculous? Are we, as they say in the Air Force, “measuring with a micrometer, marking with chalk and cutting with an ax”? You bet we are.

The swimming-pool industry is particularly fraught with false precision, propagated as a habit by well-intended professionals. Just who else is contributing to this over-figuring that has perpetrated the pool-care world? Nice people, really. Teachers, writers, distributors, manufacturers... Pages and pages of tables have been provided thousands of pool operators by the makers of fine and popular equipment, loaded with columns full of “precise” numbers like those shown above. Textbooks, handouts, guidesheets and the like are offered by well-meaning trainers in this field, taking arithmetic to its ludicrous extreme.

How about a few more illustrations? Reviewing maintenance logs at a resort pool recently a consultant discovered that the pool’s saturation index had been calculated every single day, and minute corrections were performed almost as often. The C.S.I. had been carried out to hundredths of an index unit, with fractions of a pound of chemical added to the quarter-million-gallon pool. Frequency of occurrence, as well as the splitting of hairs, is not immune to ridiculous excesses in noble but misguided efforts to be “precise”!

See if you can follow this one: A health-department inspector checked a 25 yard by 25 meter pool whose rate of flow, based on an estimated/calculated pool volume of “234,720 gallons”, was supposed to be 652 gpm. The flow meter, sold as accurate within +/- 10%, persistently showed about 620 gpm, so the sanitarian closed the pool. But look — ten percent of this flow is 65 gpm, either way! The indicated flow was well within the manufacturer’s tolerance, and could not have been confirmed as non-conformity with the code. Now figure, to make things worse, that the guesstimated depth of the pool’s complex bottom could easily be off in either direction by, conservatively, one-half foot. In this case, that six-inch error could result in a difference of 23,000 gallons, or a range of possible error of 46,000 gallons! That’s another ten percent, each way! That means the pool could hold as little as 212,000 or as much as 258,000 gallons, with commensurate six-hour flows of 590 gpm through almost 720 gpm! Throw in the flowmeter’s tolerance, the acceptable flows for this pool lie between 530 and 790 gpm! These extremes are, of course, unlikely; errors tend to cancel each other out. Halfway values, however, near 5% instead of 10% as the deviation, are more than likely, they are inevitable. Not exactly “precise”, wouldn’t you agree? You cannot and must not make flow, volume, or dosage-rate judgments regarding your pool and its water any closer than about 5%! Now, would you have closed that pool?

The affliction for “precision” is widespread. Cooks make level cups with a straight edge. Pilots plan flights into assumed winds to the nearest half minute. Weather folks say we’ve received 21.63 inches of rain so far, and it’ll rain again at noon next Wednesday. Doctors tell you to take that medication at 5:30 each evening, and that you should weigh 122 pounds. Your banker says there’s $55,003.21 left to pay on your mortgage. And just look at this one: A guide at a historical site was overheard telling the crowd that the fossils displayed were “one million and three years old...”. Asked where that number came from, he said with all seriousness, “I was told that these bones were a million years old when I got this job, and I’ve been working here for three years”.

Here’s an even better example of accuracy verses precision, considering the reading of directions of travel. In an airplane, there’s always a magnetic compass and a directional gyroscope in the instrument panel. The “old reliable “mag compass is always bouncing around the plane’s correct direction, plus or minus as much as five degrees. But it is always “accurate” within the confines of turbulent motion, variation between true north and the earth’s magnetic north, and so forth. The gyro, on the other hand, is stable and hair-splittin’ precise, to the nearest half degree or so. However, the gyro is set by hand, usually during ground taxi, using the mag compass as a reference! You can set the darn’ thing anywhere! North can be west... In other words, it can be “precisely inaccurate” if it is set wrong or if it wanders later in the flight. And it is never more accurate than the original calibration. Give me the accurate compass, not the precise gyro, any cloudy day.

Pool-controller calibration (called “standardization”) is an extension of this reasoning. Some of these digital machines have three clearly “significant” digits; that is, with pH values looking like 7.34 and ORP numbers like 726 mV or residual readings, 3.21 ppm. (More often now the pH values are, appropriately, “truncated” or rounded to two digits like 7.3.) Nonetheless, the only way most operators can standardize the machine is with a manually operated pool-water test kit, using color comparisons or a titration technique. These methods are much less “precise” than the controller; however test-kit values, when properly taken, are reliably accurate and within the tolerance needs of a well-maintained pool. Like the airplane’s directional gyro, that hair-splitting controller could easily be misset to be precisely inaccurate!

We don’t need that kind of precise silliness in our lives, say statisticians, mathematicians, and philosophers. And, most especially, we don’t need it in the world of swimming-pool maintenance.

Not only is it wasteful of time, energy and attention, it is MATHEMATICALLY INCORRECT to carry out calculations to the extremes described here. There’s this thing called the rule of significant digits that must not be broken. Oh, you can break it, all right – most of us do – but we are not more precise, we are simply incorrect. A significant digit is a number that means something, that has been measured or referenced and is established as “significant”. Trailing zeros are generally not significant digits. “100” has one significant digit, although 100.0 represents at least three. “121” has three; .002 normally has one; .109 has three; 15,000 has two while 15,002 has five, and so on. Sometimes the numeral “5” is significant, sometimes not quite; like somewhere between 40 ppm and 50 ppm is 45 ppm a rounded average. It can get complicated, but it doesn’t have to be. That’s why the rule exists – to avoid excesses in numerical work. The intention is to allow the person performing calculations to assign levels of precision to the various elements of her or his work, thus allowing the element of least precision to determine that of the result.

So the rule states, somewhat simplified, that the resultant of a calculation must be expressed using no more than one significant digit greater than the least significant of all the numbers used in the work. In figuring a 20-foot circle’s area, 3.1416 times a radius of 10 feet squared is not 314.16 square feet. It is 310 square feet. 1000 plus 55 plus 226 plus 3 doesn’t equal 1284, it equals 1300! The last example may not, however, hold valid with money, where the $1000 would generally be quite specific and fully “significant” (it would be to this editor...). Of course if the example were truly an estimate, e.g.: “about a thousand dollars”, the value might be plus or minus a few bucks.

You now have completed a pool-guy’s course in statistics and math management. This “scientific rounding” makes sense, doesn’t it? It is clearly reasonable as well as convenient when figuring pounds or gallons of chemical to add to your pool. It might even make your job a little easier, and a little less worrisome. When you’re trying to pass this rather academic concept to your boss, however, it can be expressed in simpler terms. Besides the micrometer quote, try these: As a chain is no stronger than it’s weakest link, a calculation no more precise than its weakest numerical element. One cannot read seconds on a sundial, nor inches with an odometer.

And you don’t need postal scales to measure chemicals in the pump room!

~kw