Standard Deviation and Stable Genius

About three thoughts came together and gelled last week.  One was a headline that explained voter turnout in Wisconsin was 5 standard deviations from the mean.  The other was looking at Trump assessing himself as a “stable genius” and Biden’s frequent challenge of having a high IQ.  I realized that I don’t have to explain how to calculate a standard deviation – there is a chart that shows it all in terms of IQ, and it really simplifies matters. 

If you look at the linked table, on the scale that accepts 15 points as the standard deviation, an IQ score of 175 is 5 standard deviations above the norm.  To make that statement understandable, that’s one person out of 3,483,046.  Chances are that I have never met one, despite a career in science and the academy. 

Nasim Taleb writes “IQ” is a stale test meant to measure mental capacity but in fact mostly measures extreme unintelligence”, so let’s look at the IQ 25 – whom I also haven’t met.  0.0000287105% of the population would score below this mark.

Tierman’s classification for genius (based on a standard deviation of 16) was 140 and over – so if you check the chart, that’s one out of every 161 people.  Statistically, we should have four or five living within the Trego school district boundaries.  I don’t know what it takes to be a stable genius – maybe a horse?

IQ RangeClassification
140 and overGenius or near genius
120-140Very superior intelligence
110-120Superior intelligence
90-110Normal or average intelligence
70-80Borderline deficiency
Below 70Definite feeble-mindedness
Table developed by Tierman, source: IQ Comparison

When we look at Biden’s quote, “I think I probably have a much higher IQ than you do, I suspect.” and look at the chart in Talib’s paper, toward the bottom we see the range for “legal professions”.  Talib’s comment at the bottom is just as valid for attorneys as college professors.  It does add a bit of perspective.

Community, Demography

Covid’s Mask and Pascal’s Wager

According to the Internet Encyclopedia of Philosophy, “Blaise Pascal (1623-1662) offers a pragmatic reason for believing in God: even under the assumption that God’s existence is unlikely, the potential benefits of believing are so vast as to make betting on theism rational.” As a stats guy, I could write this from memory, as a scientist, I need to cite a source.

Pascal’s statistical argument is a gambler’s view of the universe – the cost of believing, of the ante, is so small compared to the infinite reward (the size of the pot).  I worked with an accountant who had a system for buying lottery tickets – his break from understanding Pascal was that both cost and reward in the statistics of lottery cards are finite – the odds really can be calculated.  Lotteries are a tax on people who don’t want to do the math.

Covid is also a game for statisticians.  It’s still at a point where we have a bunch of unknowns, but there are fewer unknowns than there were 6 months ago.  Then the Diamond Princess was a horrifying news story – now it is data, as taken from “A total of 712 people were infected with COVID-19 on the Diamond Princess cruise ship – 567 passengers and 145 crew members. The cruise ship, which had more than 3,500 people on board, was quarantined for around two weeks. All passengers and crew members had finally disembarked the ship by March 1, 2020.”

Wikipedia shows 14 deaths among the 712 infected people on the Diamond Princess.  Somewhere right around 2%.  About the same as Texas and California, and lower than New York, New Jersey, and Massachusetts.

We’re still looking at less than perfect representative numbers – but Diamond Princess has provided some data:  roughly 20% of those exposed between January 20 and February 19 wound up infected.  In March, we had estimated R0 values from 1.5 to 3.5.  Now, we have Rt values (Average number of people who become infected by an infectious person with COVID-19 in the U.S. as of October 17, 2020).  Those numbers vary from 0.91 in Mississippi to 1.31 in New Mexico.  Montana scored 1.2. 

Generally speaking, in the absence of data, we have a tendency to assume the worst.  We have data now.  The actual infectivity is lower than the initial data – perhaps because the precautions have been effective, perhaps it is related to the fact that 80% of the people on Diamond Princess did not catch covid.  Correlation is not causation.  Causation is inferred from statistics, not proven.

This week, an article from the American Society of Hematology stated: “Blood type O may offer some protection against COVID-19 infection, according to a retrospective study. Researchers compared Danish health registry data from more than 473,000 individuals tested for COVID-19 to data from a control group of more than 2.2 million people from the general population. Among the COVID-19 positive, they found fewer people with blood type O and more people with A, B, and AB types.

Making statistics personal is a challenge – data suggests that my risk factors are increased by age (70), height (6’3”), asthma, and diabetes.  How much we don’t know – for neither my asthma nor the diabetes scores particularly high.  My risk factors are reduced by my blood type.  So let’s look at masking.

My mask is like Pascal’s wager – it seems logical that any level of masking will reduce transmission.  The question is: “How much?”  I don’t have that answer.  Does my mask protect me significantly?  When I have been in surgery, the surgeons and medical staff were masked to protect me.  Similarly, is my mask to protect others?   Business Insider offers an article comparing mask effectiveness, but cautions that “Mask studies should be taken with a grain of salt.”  My mask is like Pascal’s wager – and I hope wearing it adds a sense of security. It costs me little to wear it.


Talking about Risk

A headline read, “What if we could live for a million years?”  My casual answer was “not a chance.”  Even if we could eliminate aging and disease, we still have to consider risk.  The National Safety Council reports 1.25 deaths for every 100 million miles of highway travel.  Assume 10,000 miles per year of highway travel, in the first thousand years of life, you’re up to 10 million miles.  That turns out to be a 1 out of 8 chance of dying – just from highway transportation.  The National Geographic gives odds of being struck by lightning as 1 in 700,000 each year, and one in 3,000 over a lifetime.  Increase the lifetime to that same 1,000 years, and the odds go up.  We live in a risk society, and often ignore that fact. 

I know a guy who survived a grizzly mauling, and I’ve known one who died from wasp stings.  Even in Trego, I encounter more wasps than bears.  CDC stats show 89 people who died from bee stings in 2017.  It isn’t a large risk – but 80% of the fatalities are male.  Bee stings are a greater risk to the male half of the population. 

Just about every endeavor includes misunderstood risks.  In 2018, the police fatality rate was 13.7 per 100,000 (bureau of labor and statistics).  CDC shows the 2017 fatality rate for farmers was 20.4 per 100,000.  BLS shows a rate of 132.7 per 100,000 loggers in 2015.  CDC shows bartenders have a higher on job fatality rate than police.  In some places policing is a relatively risky job – but in farm country and logging country it seems fairly safe.  Here’s the link to more data if this interests you.

When we started looking a Covid-19, we didn’t have the statistical data to calculate risk.  Now, we do have some data – and we’re seeing disagreements, mostly because folks see risks differently.  As I write, RealClearPolitics shows 5,746,272 confirmed cases in the US, and 177,424 deaths, yielding a 3.09% confirmed case fatality rate.  Still, that number goes from 8.25% in New Jersey to 0.79% in Utah.  We have solid numbers – but not numbers that allow us to calculate risk.  When we look at the charts that include age, we can begin to calculate risk – 70 is higher risk than 40.  80 is even higher.  New York numbers suggest that dense populations and public transportation increase risk – but not enough to calculate. 

The numbers let us develop ordinal data about covid risk – ranking things as more or less, rather than develop statistical data.  At 70, I’m at more risk than someone who is 50. The age data is good enough to develop some statistics – but the comorbidities that make it covid fatal mask that. Riding mass transportation is more dangerous than driving a car alone.  The virus doesn’t differentiate between bars and churches – open spaces are safer than crowded enclosed spaces.  So far we know that Covid is a bit more infectious than flu, and less infectious than measles.  Ordinal data. Buzz Hollander, a physician in Hawaii, has a good, readable article on covid at this site