We love comments. (From real people, that is. Spambots, you can stop any time.)
We love comments like, “Great blog!” We even love comments like, “You are wrong about every single thing related to medical editing, your mother was a hamster and your father smelled of elderberries, goodbye.” Both of those require simple responses—I like “Thanks!” for both, to be honest. For the latter, I would be charitable and not even comment on the comma usage.
Every once in a while someone will leave a critical comment that requires a longer response, and sometimes the consultation of outside experts. That was the case with this Quiz Bowl post on units of measure. A reader wrote:
A big problem with the AMA manual is a lack of consideration significant figures. The conversion factor listed in the online “SI Conversion Tables” section from feet to centimeters is 30. That’s wrong. Let’s say I try to convert my height (6.0000 feet) into centimeters. The “.0000″ means that my measurement has 5 significant figures. Significant figures are important in science and health care.
I start with the only unit conversion between customary and metric that matters: 2.54 centimeters equals exactly 1 inch. This is the only conversion that matters because it is a definition. There are infinite significant figures.
Here is what happens if I use the “SI Conversion Tables” section of the AMA manual of style:
6.0000 feet * 30 = 180 centimeters
Here is what happens if I use math and pay attention to significant figures:
6.0000 feet * (12 inches/1 foot) * (2.54 cm)/(1 inch) = 182.88
Where did those extra 2.88 centimeters come from? They came from a a conversion factor that was wrong.
For the same reason as above, your answer to the first problem is wrong.
7.2 inches^2 * (((2.54 cm)^2)/((1 in)^2)) = 46.45 (assuming 4 significant figures, to demonstrate the inaccuracy of your conversion factor)
This isn’t just an academic exercise. A text for editors shouldn’t have errors like this.
We made “hmmm” noises for a while but finally drafted a response to post here, since a shameful amount of time has gone by since the original comment.
You raise an important point about the significance of significant digits. The Manual addresses this in section 20.8.1 and, in chapter 18, where the conversion table is embedded that shows conversions for inches to centimeters, there is a caution that results should not be reported beyond the appropriate level of precision. It is critical to ascertain the precision needed for the clinical context of the conversion. If you only need significance to 1 place beyond the decimal (7.2 inches) to accurately describe tumor size, then the 2 significant digits of the result should be fine and the clinical difference between 46.8 and 46.5 is probably not important.
It’s entirely possible that the final 3 words of that paragraph are the equivalent of a thrown gauntlet to someone out there—if so, we’re willing to continue the conversation in the comments to this post.—Brenda Gregoline, ELS
There is an old joke about a man who worked in a museum. When asked about the age of a dinosaur skeleton, he quoted the age as 70 million and 6 years because, 6 years before, a naturalist told him the dinosaur was 70 million years old.
Have you ever been on an international flight? The altimeter alternates between 8,839 and 9,144 meters. These readings correspond to 29,000 and 30,000 feet, respectively. There are 2 significant digits in the actual reading, so the altimeter should really read 8,800 meters and 9,100 meters–this is due to significant figures.
The error we see in both of the above examples is false precision. It is similar to the error that you have in your manual, only the conversion factors listed are wrong, too.
This should really be remedied. Sure, the clinical difference between 46.8 and 46.5 may not be all that significant–unless it is. Some treatment guidelines for cancer use tumor volume to guide changes in therapy. An error of a third of a cubic centimeter may not seem like a lot, but the cause of the error is an incorrect conversion factor.
This isn’t the first time errors like this have occurred. I’ll provide an everyday example. You are sick, and have a fever. What is the normal body temperature? Common wisdom says that the answer is 98.6°F, but actually that measurement comes from a classic German study that estimated a normal body temperature at 36.6°C. The German study had 3 significant figures. Converting the result of the study carried out in Germany–and accounting for significant figures–common wisdom would (correctly) be that a normal body temperature is 97.9°F. Unfortunately, whoever did the calculation originally rounded the data from the study carried out in Germany to 37°C, converted to Fahrenheit, and got our current (incorrect) result of 98.6°F (3 significant figures, converted from a measurement with only 2).
Even the normal human body temperature that everyone knows to be correct is wrong because calculation errors–like the ones present in the AMA Manual of Style– are ignored.