## Statistical Uncertainty

Despite having developed a strong mathematical aptitude, I entered the final year of my undergraduate education in electrical engineering with great trepidation.  My nemesis was a final unmet graduation requirement to complete a course in statistics.  I excelled in solving math problems that had a single, unambiguous answer.  Unfortunately, I simply could not wrap my head around the idea that some problems had infinite, fuzzy solutions.  In the end, I satisfied the requirement with a difficult sounding class that thankfully had very little pure statistics.  That course was called “Introduction to Probability and Random Signals.”

A funny thing sometimes happens when you face and conquer your greatest fear.  In my case, I rapidly developed a passion for statistics and went on to major in econometrics and statistics.  To my great surprise, I was granted a statistics scholarship that covered a healthy chunk of my tuition.  Apparently, there are not a lot of statistics geeks, even in a very quantitatively focused business school like Booth.

I offer that background merely to acknowledge my statistics bias.  But, though you certainly do not need to excel in statistics to succeed in business or in life, knowing a few rudimentary concepts is extremely valuable.

Embrace Uncertainty

The greatest epiphany that I had was to embrace rather than fear variability.  Uncertainty surrounds us in nature, at home, and in business.  Absolute randomness is rare.  Rather, seek to understand the expected outcome and the range around it (usually wider than you think)

This concept has worked its way into the professional world in the form of the very useful 80-20 rule.  In 1941, management scholar Joseph Juran studied the work of Italian economist Vilfredo Pareto.  Pareto had observed that 80% of the land in Italy was owned by 20% of the population.  Juran honored the economist by formally coining the concept as the Pareto Principle.  (Not much has changed; the top 20% of households in the United States hold 85% of the wealth.  In fact, the top 1% command nearly 35% of private wealth all by themselves.)

The amazing thing about the 80-20 rule is that it allows you to stop digging when you can account for 80 percent of virtually anything.  It only gets better, because you can get to that level of understanding by doing only 20 percent of the work that you would need to do to get to a total and complete answer.  Unless you are a brain surgeon or a civil engineer, this rule of thumb is an risk-free and immense productivity booster.  To be able to stop when you only have eighty percent of the answer requires that you embrace uncertainty; switch from thinking in terms of yes or no and instead merely accept that an outcome is likely or unlikely.

Take calculated risks

The only way to excel in business and in life is to take calculated risks.  In fact, the more risks you take the better, since you will not only learn from your mistakes but will also have better odds of securing at least one big win.  Nothing ventured, nothing gained.

As you venture forth, it is critical to understand that people systematically overestimate risk.  Factors you should correct for that magnify perceived risk include: limited control, human made rather than natural phenomena, limited information, dreadful outcomes, lack of familiarity, and direct awareness.  Moreover, we ascribe greater risk to children than to adults engaged in the exact same activity.

Indulge me in one very personal example.  As a father, I am deathly concerned that one or both of my children will experience a severe spinal cord injury.  This fear nearly caused me to quash my daughter’s love of participating in recreational gymnastics.  But, consider a few facts and figures.  In the United States, there are estimated to be 40 cases of spinal cord injury per million people per year.  Of these, only 16% are caused by sports and recreation accidents.  Researchers in Japan provide the final piece of the puzzle.  Among Japanese spinal cord injuries associated with sporting activities, 6.6% result from gymnastics.  That means that the annual chance of a person experiencing a spinal cord injury in gymnastics is less than 1 in a million.  To put this into perspective, the odds of dying in a motor vehicle accident in the United States are fully 340 times greater at 144 in a million.  Based on the data, my fear of recreational gymnastics was completely overblown.  In fact, it is really my daughter that should be worried about me.

Beware of assuming that correlation implies causality

In May 1999, a study published in the popular scientific journal Nature nearly put the night light industry out of business, much to the chagrin of frightened infants and toddlers everywhere.  In the article, University of Pennsylvania Medical Center researchers studied the amount of ambient light that 479 subjects were exposed to during their nighttime sleep.  For children from birth to two years of age, myopia – or nearsightedness – was far more prevalent in children who slept with a night light rather than in darkness.  Moreover, those children whose parents left the room’s light fixture on were even more likely to have eye problems later on.  Parents of children with glasses must have been feeling extremely guilty for having used nightlights.

The researchers cited similar findings in studies with young chickens and outlined the likely developmental processes impacted by excessive light exposure at an early age.  Though they carefully hedged their bets, the researchers teetered on the brink of implying causality when they reported: “Although it does not establish a causal link, the statistical strength of the association of night-time light exposure and childhood myopia does suggest that the absence of a daily period of darkness during early childhood is a potential precipitating factor in the development of myopia.”

Fortunately, a year later, Ohio State University researchers spared millions of innocent children from the boogie man.  In a larger study of 1,220 children, Karla Zadnik and her co-authors determined that ambient light during sleep does not cause nearsightedness.  Instead, it turns out that nearsighted kids simply have nearsighted parents who are more likely to leave a light on than parents without vision problems, to light their own path in the middle of the night.  The cause is genetic.  In other words, the researchers of the initial study had found simply a correlation between ambient light and myopia, but not a causality, and thus had engendered needless guilt in many myopic parents.

Even very smart and well-meaning people fall into the trap of assuming that correlation implies causality.  To contend against this, in each instance look for three other explanations.  The first is an external cause.  This is what was at play with the genetic cause that explained the relationship between night lights and nearsightedness.  The second is known as reverse causation.  For example, you might notice there are more police at larger crime scenes and incorrectly conclude that police cause crime.  The third explanation is mere coincidence.  Some humorous examples of this are concluding that the growth of social networking websites or hybrid automobile sales fueled the 2009 economic recession.

Recap

Here are the concepts you can immediately apply to  take charge of statistical concepts :

• Embrace uncertainty
• Take calculated risks
• Beware of assuming that correlation implies causality

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