Skewered by Skew and Castigated by Kurtosis: Did it ever make sense for 92% of Harvard undergrads to make the Dean's List?
Recently, April 30, was Carl Friedrich Gauss' birthday. (He would have been 241-years old.) Gauss is probably the greatest mathematician that ever lived. In my own field of mechanical engineering, Gauss - as an afterthought - developed the mathematical techniques required to break down complex vibration signals into the discrete frequencies that make up the vibration. This allows engineers to troubleshoot problems with rotating equipment. Gauss also made great contributions in the field of statistics, and is credited with identifying the normal distribution of a statistical sample. In his honor, this blog post will examine whether it made any statistical sense for 92% of Harvard undergraduates to have been on the Dean's List. (Spoiler alert - it didn't, and the financial crisis proves it!)
The "normal distribution" of data in a statistical sample gives us the classic bell curve. What the bell curve plots is a characteristic that is being measured - say weight - along the x-axis, and the number of times a particular measurement of that characteristic will occur in a sample along the y-axis. The technical term for the equation that is used to plot the normal distribution is a "probability density function" or PDF. While that is a mouthful, it does a good job of describing what the normal distribution is. For the characteristic being measured, the PDF tells us how likely any one value is to occur. Note that in Chart 1 below, the values closest to average of "0" are the values most likely to occur. As values move further from the average, they occur less frequently.
In the 1980s, the Japanese - capitalizing on statistical concepts developed in the 1920's at the greatest concentration of industrial genius in world history, Bell Labs - created manufacturing techniques that were focused on minimizing the variation between manufactured parts.1 For a Japanese automobile factory making engine shafts, the variation between shafts would be very small. In purely practical terms, all the shafts would have nearly the same diameter. The distribution curve - or probability density function - describing the diameter of these shafts would then be very narrow, see Chart 2 below.
However the statistics associated with people are much different than they are with auto parts. For any sample involving people that hopes to measure any behavioral or personality based characteristic, the variation between individuals will be far greater than it is between shafts in a Japanese factory. By virtue of this wider variation, the bell curve describing human characteristics will also be wide, and look far more like Chart 1 than Chart 2. Most people will be average and there will only be a handful of really exceptional people. With this being the case - and even without the glaring example provided by the financial crisis - the notion that 92% of Harvard undergrads were exceptional enough to merit a place on the Dean's List can be seen for what it clearly was - transparently bogus.
However, what of the notion that Ivy League schools have such a rigorous selection process? Isn't this bound to create a sample that includes a disproportionately large fraction of people who are then well-above average in any number of aspects? Sure, Harvard and the other Ivy League schools are very difficult to get into, but they are not much more difficult to get into than any of the service academies. I am completely confident that 92% of service academy cadets aren't constantly being told how great and smart they are are by their military officer instructors!
What of the many people who attend Ivy League colleges and go on to great things in mathematics, medicine and the physical sciences? Surely, the mere presence of all these Ivy League graduates succeeding in these fields proves it made perfect sense for 92% of Harvard students to be on the Dean's List. However, the most popular major at Harvard isn't mathematics, pre-med or any of the physical sciences. It is almost certainly economics - and by a large margin. Furthermore, the industry that employs more Harvard graduates than any other is likely Wall Street finance. Economics and Wall Street finance were at the epicenter of the financial crisis. If people on Harvard's Dean's List were really so smart, and 92% of Harvard undergrads were on the Dean's List, then how could an enormous crisis originate in two fields dominated by Harvard (and other elite university) graduates? The question answers itself - it never made any sense for 92% of Harvard undergrads to be on the Dean's List and the financial crisis proves it.
Harvard ultimately got rid of the Dean's List. However, if Harvard wants to do the country a real favor, they should get rid of their economics department. It remains a far bigger menace than their Dean's List ever was. While they are at it, they can also stop Wall Street banks from holding on-campus interviews. While this seems pretty draconian, Harvard - and all the other Ivy League schools for that matter - used to bar the military from conducting on-campus interviews.
The fact that Ivy League schools used to bar the military from recruiting at their schools brings up an interesting point. Few people doubt the military is the most successful organization in the US today. In contrast to the Ivy League dominated industries at the core of the financial crisis - the economic establishment, Wall Street finance, central banking and government - the Ivy League presence in the military is, (thankfully2), non-existent. There is no way to reconcile this contradiction other than to say that the military succeeds, not in spite of its dearth of Ivy League graduates, but because of it! This will be the topic of a future blog post.
Peter C. Schmidt
May 20, 2018
1. In addition to its role in the statistical process control (SPC) of industrial processes, the normal distribution can be useful in drawing conclusions from statistical data. A normal distribution allows conclusions to be drawn from very large samples of data when only a few sample characteristics are known. Because of this, the danger of incorrectly applying results, limited to a normal distribution of data, to data that is not "normal" is very real. History has repeatedly shown that the group most likely to commit this error is PhD economists, particularly MIT PhD economists. The classic example of this mistake was the 1998 collapse of the hedge fund Long Term Capital Management, (LTCM). LTCM, which boasted a huge number of MIT PhDs, attempted to use statistics - that could, at best, perhaps describe the past - to inerrantly predict the future. Unsurprisingly, it was a disaster. In spite of the enormity of the blunder and the financial panic it sparked, this same mistake continues to be made on Wall Street and in academia.
2. Because of how it captures the critical importance each individual - regardless of rank or responsibility - plays in the attainment of an objective, one of General Patton's favorite sayings was, "whoever thinks they're indispensable, ain't." Ivy League graduates - at least the huge fraction who end up on Wall Street - are apparently convinced they are better than everyone else. These people would constantly run afoul of Gen. Patton's injunction and the military is much better off without them.
20 MAY 2018