December 9, 2020 519 PM
In our story, “Explosive COVID, tourism and the future of testing in the Big Bend,” from the December 3 issue of the newspaper, a health authority was quoted as saying cases had “gone up exponentially.”
A keen eyed reader, Dave Leet of Alpine, reached out following the story to let us know that the statement was mathematically inaccurate. Leet, a mechanical engineer, offered some data to us and our readership that hopefully will give a more in depth view of the stats behind the COVID-19 numbers in the area.
We certainly never aim to mislead our readers and apologize for using the quote without checking the case-rise’s exponentiality or, in this case, lack thereof. Thank you for reading.
The last issue of The Big Bend Sentinel had a very arresting graphic on the front page, showing how the epidemic has gone “exponential” in Presidio County. It certainly got my attention, mainly because the assertion is plainly wrong. This is not to discount the seriousness of the situation, but we still have to keep some basic principles in mind.
The first one is if you want to show something as being exponential, you really need to plot its data on a semi-log scale. If you do this with the Presidio data, you will immediately see it is not exponential. I am not an epidemiologist, but know enough math to know I can find the exponent of exponential data by measuring the slope of a straight line made by the logarithmic vertical axis data vs. the arithmetic horizontal axis data. This is one of the steps required to find the infamous Ro number, as it turns out.
The second point is our small population in the tri-county area naturally provides more variability than the larger populations people are accustomed to seeing data on, like COVID-19 infections and deaths in the U.S. or in Texas, for example. What this means for us is more dramatic jumps in data. This is just the nature of it, that Tversky and Kahneman famously (and humorously) labeled the Law of Small Numbers when they saw this principle ignored repeatedly by participants in their experiments, even by the statistically savvy.
I had a conversation with friends recently much along these lines, who mentioned it may be worth a bit of sensationalism in order to scare people into acting sensibly around this virus, if that’s what it takes. It looks like generally that is what the news media is trying to do. I replied that this is not a good tactic, since scared people generally do stupid things. If you treat them like children, they will have temper tantrums like children too. I am only pointing this out as a caution against using anything sensational or arresting to the eye that is not accurate; please keep up the good work at The Sentinel.
The reader can look at a demonstration of this on Github at /github.com/Dav909/Tri-County2/blob/master/Tri-County%20example.pdf. Just type that string into the URL field on your browser and it will come right up.