Proportional Thinking
We humans grow up on stories, not numbers. For most of us, language and literacy (the ability to read and write) comes fairly early. Numeracy (the ability to understand and work with numbers) comes later and to a lesser degree. We speak, tell stories, and read frequently, but how often are we called upon (or bother) to work out a percentage or think proportionally. Discomfort and unfamiliarity with numbers and math is corrosive, because it leaves us susceptible to people who lace their stories with numbers meant to impress, to shut down rational inquiry, but which are total BS. (For an example see the P.P.S. below.)
In the Saturday, November 6, Spokesman the front page article, “VANDALISM DOWN IN DOWNTOWN BUT BROKEN WINDOWS PERSIST” featured a dramatic photo of a shop-owner seen through a vandalized window. It is an odd juxtaposition, dramatic photography to tell us about a decrease in police calls downtown for “malicious mischief”. Here’s the article’s presentation of the numbers:
There were 491 malicious mischief incidents reported to police in 2020 between Jan. 1 and Sept. 13 and 448 during the same period this year, according to information provided by Spokane Police Department Officer Stephen Anderson, a department spokesperson.
There were 565 calls for service downtown related to malicious mischief in the entirety of 2019.
What shall we make of those numbers? In the eight and a half months (minus two days) between January 1 and September 13, 2020, for the downtown area there were 491 malicious mischief incidents reported to police. This year, 2021, during exactly the same 8.5 month period there were only 448 such reports. Let’s rejoice! But wait a minute. Let’s look at a monthly rate:
2020 491 / 8.5 = 57.8/month
2021 448 / 8.5 = 52.7/month
Now look at 2019’s 12 months of data (which, to make a comparison, assumes that the monthly frequency of malicious mischief reports is relatively constant within a given year—possibly an invalid assumption):
2019 565 / 12 = 47/month
Whoa! Malicious mischief crime reports from downtown Spokane soared from a low of 47/month in 2019 to 58/month 2020 and only came down by half to 53/month in 2021! Panic!
What the reader ought to take away is this: the treatment of numbers in this Spokesman article is shallow reporting. The counts presented are all relatively small numbers with a lot of variation. Extracting valid statistical meaning from such raw information requires looking for a trend in ten or twenty years of comparable data. Without such comprehensive analysis these numbers are of marginal use and are readily twisted to confirm whatever bias the reader already possesses.
A current national example of misuse of numbers is the incessant harping of the media on “President Biden’s 3.5 trillion dollar infrastructure bill” rather than calling it the “Build Back Better Act,” its official name. (A 1.2 trillion dollar piece of the Build Back Better Act was signed into law this week. The fate of the broader bill remains to be seen.) Oh my! 3.5 trillion! OMG, that’s a huge number! Panic! The media focuses us on that giant, incomprehensible number rather than on what the bill would do. Hardly ever are we reminded by the same media that blares “3.5 trillion dollar spending package” that the quoted number is the authorized spending played out over 10 years, or, on average, 350 billion dollars per year. Still a large number? Consider that number in the context of the entire U.S. economy quoted on a per year basis, the Gross National Product, the “total domestic and foreign output claimed by residents.” In round figures the GNP of the U.S. is 20 trillion dollars. In a given year the entire Biden proposal is 0.35 trillion/20 trillion = 0.0175, just 1.75% of the U.S. economy. Put in the context of the wages of an hourly employee making $15/hour (~$30,000/yr), 1.75% of the annual salary is $525. That’s still a significant number but it offers perspective. Biden’s full infrastructure bill would cover a host of initiatives that would help out the families of that hourly worker.
When you see a large number quoted without contextual reference you ought to suspect a political agenda aimed at convincing voters of something. Republicans are great at this. For any bill that actually might help the common man the focus is on a large number cost, not what the bill does. When Republicans added trillions to the national debt with the 2017 “Tax Cuts and Jobs Act”, you rarely heard of those trillions—and when you did they were lost in dry discussions of “net economic effect”. The talking point that emerged from every Republican mouth around the “Tax Cuts and Jobs Act” spoke of “money in your pocket,” trusting that neither the media nor the general public would see the other side of the budget: a dollar given away in a tax cut is budgetarily equivalent to a dollar spent.
News articles and politicians rarely offer context for incomprehensible numbers. Enhance your numeracy by looking up and memorizing a few relevant numbers for context. Think in proportions. Every weekday the Spokesman’s Covid page in the main section tells us the number of new cases of Covid reported in two counties, Spokane County, Washington, and Kootenai County, Idaho. Comparing the two numbers is meaningless without population numbers. Spokane County’s population (2020 estimate) is 528,000; Kootenai’s is 171,000. To compare case numbers sensibly, multiply Kootenai’s cases by 3. Last Friday, for instance, the raw numbers were Spokane 179, Kootenai 88. Multiply Kootenai’s 88 by 3 to get 264, the number of new cases Kootenai would have if it had the same population in which to spread. After adjusting for population the story is more in line with the prevalence of vaccination in these two adjacent counties.
Dust off your numeracy.
Jerry
P.S. Looking up population figures in wikipedia is enlightening. The population of the island nation of New Zealand, for instance, a nation that looms quite large in the minds of many English speakers, is only a little over 5 million, about the same as the population of South Carolina. The population of Canada is around 38 million, about the same as the population of California, our most populous state. The U.S. population is around 330 million, nearly ten times that of our northern neighbor. Memorizing a few numbers and comparisons like these provides a useful perspective in reading numbers in the news.
P.P.S. Some presentations of numbers should set off alarm bells. “Sustainable Minimalists” is a moderately interesting podcast associated with a rather glitzy-looking website. The podcaster covers a variety of topics, but the episode that caught my ear was an interview with a very sincere and apparently well-informed man, Mr. R Blank, talking of the many dangers of human exposure to “EMF” (electromotive force) from all manner things in the modern world, for example, wifi, cell phones, and 5G. Had Mr. Blank assembled solid scientific evidence of this threat, evidence I had not yet heard of or was this another advertising rabbit hole? I had to know.
The podcast linked to R Blank’s website, “Shield Your Body (SYB).” On the website R Blank declares: “There are literally thousands of high-quality, peer-reviewed scientific studies linking EMF exposure with many negative health effects— cancer, infertility, melatonin suppression, blood brain barrier leakage, and many more.” Tellingly, Mr. Blank offers not a single a link to any study. There is no space limitation (as in a newspaper or a print ad) on a website, so why not offer links to some of the most convincing evidence? In another spot on the SYB website, apparently “thousands” didn’t sound impressive enough to Mr. Blank, so he makes it “TENS of thousands of different scientific studies demonstrating negative health effects from EMF radiation.” If a reader has dug into such a website and run onto this level of misuse of numbers, one’s bullshit alarm should be screaming. By then, the even mildly skeptical website visitor might have noticed that R Blank’s company is selling EMF-blocking Faraday cages and even EMF-blocking underwear to protect the believer from the supposed scary threat of EMF (electromotive force) pervading homes and offices.
Anyone who has listened to the radio programs of conservative commentators like Rush Limbaugh or Dennis Prager or watched late night TV should be familiar with this infomercial style of advertising meant to gain the consumer’s confidence by posing as the possessor of special knowledge or insight, ramp up diffuse worry in the listener, and then sell something of dubious value to those taken in.