## Statistics Can Be Misleading

Faulty meaning adds to complexity and that is bad.

Statistics and statistical ideas pervade our society. Most people understand the basic ideas and some act on them.  The problem is that there is another whole class of folks who use their victim’s flawed intuition to make points that are not valid. Statistics and probability are fields of study where a little awareness is harmful.

Let’s take a look at some common mistakes that are used to game the system.

Survivor bias.

People look at Mark Zuckerberg, Jack Ma, Jeff Bezos, Bill Gates, Larry Ellison and Steve Jobs as being representative of the tech billionaire crowd. People can track their growth from inception to completion and by looking at the progress, draw the inference that it might not be that hard. An idea,  a break here and there, and we’re done.

Nothing could be further from the truth. Survivor bias narrows the field of study to only those that made it. There are thousands of others we have not heard of because they did not make it.  A study of their history might show nothing much different from the winners. All had an idea, all had opportunities they may have failed to address or more likely could not address.

Jerry Yang and David Filo did okay with their invention of Yahoo, but nothing close to what they might have done with better decisions. Market cap \$125 billion at one point in 2000 and sold for \$4.8 Billion last year. That observation is an example of another flaw.

End Point Bias

Peak to now will give different answers than something more representative of reality. Yahoo market cap in 1997 was 1.5 billion and in 2002 it was \$9 billion.  Cherry picking the beginning and end deceives people.

Comparing trends that are not comparable

You find this fairly commonly in the climate change debate. If the trend line of temperature from 1990 to 2000 is up at 2% a year and the trend line from 1960 to 1970 is up at 1.5% a year and the trend line from 1930 to 1940 is up at 1% a year it is not acceptable to assume that the average rate of change per decade is accelerating.  The average rate of change from 1930 to 2000 in this scenario could be zero. You need to know what happened in between too.

Averages mean nothing unless you know the nature of the population.

What would you think if the average said something, that while arithmetically accurate, did not correspond to any observation in the material reviewed.  In an opinion sample of 200 people, 100 rate a product 10 out of 10 and another 100 rate it 4 out of 10.  Average rating is 7, but useless.

Relating big changes to small occurrences.

If there is a disease that kills 10 people in a million and a treatment is found that reduces it to 5 in a million.  The change is a 50% reduction in the number of people who die.  At the same time it is a 5 ten thousandths of one percent increase in the number who don’t die.  50% sells better and that is what they report.

Most of the time reporters show faulty statistical inference because they do not know how to assess the data.  I sent an example to one of my math professors with the attachment,  “A pity journalists don’t understand math.” his reply,  “More’s the pity mathematicians can’t write.”

Look at statistics with a skeptical eye. Truth can exist in the number but the interpretation of it can lead you to believe things that are not true or that do not matter. Try to see the meaning.

Don Shaughnessy arranges life insurance for people who understand the value of a life insured estate. He can be reached at The Protectors Group, a large insurance, employee benefits, and investment agency in Peterborough, Ontario.  In previous careers, he has been a partner in a large international public accounting firm, CEO of a software start-up, a partner in an energy management system importer, and briefly in the restaurant business.

Please be in touch if I can help you.  don@moneyfyi.com  866-285-7772

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