This is a brilliant essay written by Stephen J. Gould, an evolutionary biologist in 1991 about the limitations of statistics, something very relevant in today’s world where popular opinion is manipulated using statistics something that the common man struggles to comprehend properly. Gould drives home this point using his personal encounter with cancer.
He begins with a quote often attributed to Mark Twain, that “identifies three species of mendacity, each worse than the one before—lies, damned lies, and statistics.”
He gives a simple example of how those in power might use statistics to make a point that would favour their stance: “A politician in power might say with pride, “The mean income of our citizens is $15,000 per year.” The leader of the opposition might retort, “But half our citizens make less than $10,000 per year.” Both are right, but neither cites a statistic with impassive objectivity. The first invokes a mean, the second a median. (Means are higher than medians in such cases because one millionaire may outweigh hundreds of poor people in setting a mean but can balance only one mendicant in calculating a median.)”
When after he was treated for a rare case of cancer, he looked up the medical literature on the subject to find that “Mesothelioma is incurable, with a median mortality of only eight months after discovery”.
“I suspect that most people, without training in statistics, would read such a statement as “I will probably be dead in eight months”—the very conclusion that must be avoided, both because this formulation is false, and because attitude matters so much.
…When I learned about the eight-month median, my first intellectual reaction was: Fine, half the people will live longer; now what are my chances of being in that half? I read for a furious and nervous hour and concluded, with relief: damned good. I possessed every one of the characteristics conferring a probability of longer life: I was young; my disease had been recognized in a relatively early stage; I would receive the nation’s best medical treatment; I had the world to live for; I knew how to read the data properly and not despair.
Another technical point then added even more solace. I immediately recognized that the distribution of variation about the eight-month median would almost surely be what statisticians call “right skewed.” (In a symmetrical distribution, the profile of variation to the left of the central tendency is a mirror image of variation to the right. Skewed distributions are asymmetrical, with variation stretching out more in one direction than the other—left skewed if extended to the left, right skewed if stretched out to the right.) The distribution of variation had to be right skewed, I reasoned. After all, the left of the distribution contains an irrevocable lower boundary of zero (since mesothelioma can only be identified at death or before). Thus, little space exists for the distribution’s lower (or left) half—it must be scrunched up between zero and eight months. But the upper (or right) half can extend out for years and years, even if nobody ultimately survives. The distribution must be right skewed, and I needed to know how long the extended tail ran—for I had already concluded that my favorable profile made me a good candidate for the right half of the curve.
The distribution was, indeed, strongly right skewed, with a long tail (however small) that extended for several years above the eight-month median.”
But Stephen Gould possessed the intellectual capability to interpret the statistic unlike the rest of us. Gould then goes on to argue why we as a human race are vulnerable to this:
“We still carry the historical baggage of a Platonic heritage that seeks sharp essences and definite boundaries. (Thus we hope to find an unambiguous “beginning of life” or “definition of death,” although nature often comes to us as irreducible continua.) This Platonic heritage, with its emphasis on clear distinctions and separated immutable entities, leads us to view statistical measures of central tendency wrongly, indeed opposite to the appropriate interpretation in our actual world of variation, shadings, and continua. In short, we view means and medians as hard “realities,” and the variation that permits their calculation as a set of transient and imperfect measurements of this hidden essence. If the median is the reality and variation around the median just a device for calculation, then “I will probably be dead in eight months” may pass as a reasonable interpretation.”
If you want to read our other published material, please visit https://marcellus.in/blog/
Note: The above material is neither investment research, nor financial advice. Marcellus does not seek payment for or business from this publication in any shape or form. The information provided is intended for educational purposes only. Marcellus Investment Managers is regulated by the Securities and Exchange Board of India (SEBI) and is also an FME (Non-Retail) with the International Financial Services Centres Authority (IFSCA) as a provider of Portfolio Management Services. Additionally, Marcellus is also registered with US Securities and Exchange Commission (“US SEC”) as an Investment Advisor.
