Fun With Statistics

Lies, Damned Lies and Statistics.  Statistical information is so easy to manipulate because so few people understand its important aspects.  People should develop a better awareness.

Some time ago I sent a copy of a newspaper column that dealt with statistical inference to one of my old professors.  My comment was, “Isn’t it a shame that so few newspaper writers understand statistics.”

His reply, “It is more the shame that so few mathematicians can write.”

Touche

Most statistical information makes sense if you understand how it was created and then how it was selected for use.

Example 1

In 1900, in wealthy countries, cancer accounted for 64 deaths per 100,000 of the population.  By 2010 it was 186.  Problem or not?

It depends on what story you want to tell.  Cancer is a terrible and growing problem, please send some money so we can combat it. Or.  In 1900 1100 people per 100,000 died.  Of those, pneumonia, tuberculosis, gastrointestinal disease and diphtheria killed 580.  Today those diseases are near invisible.  Cancer is a slow developing disease.  The longer you live the more likely you are to get it.  So from these statistics, all accurate, we can make no assessment of whether cancer is a bigger problem than it was in 1900.

Example 2

The Gini Co-efficient (a measure of how unequal incomes are over a population) is much higher than it was.

It depends on how you measure it.  If you measure income alone, then the story is true.  But, what if we measure it based on after tax income and include transfer payments like welfare or other government handouts to the low income side, it is only very slightly higher.

To use the unadjusted number is misleading.  Higher taxes for the high income earners is politically expedient, but the Gini Co-efficient would not change much if you did that by itself.  It makes some sense to determine what the effect of the change would be and to do that, transfers and taxes must be considered together. Plus the effect higher taxes have on the desire to, earn high incomes.

Example 3

Unemployment has fallen to 5% in the US.  True, but it requires that you know how the numbers arise.  Is it 5% of all the people of working age?  No!  It is 5% of the people who are working and/or looking for work.  It does not include those who have given up and it does not include those who are looking for a better job.  For example, if a software engineer loses their job and works as a barista at Starbucks, they are not among the unemployed, but they are seeking a better job.

Example 4

How much is the inflation rate.  If the price of bread doubles will it affect the number.  You would think so, but maybe not.  The current method assumes that people would substitute one good for another that had risen in price.  The substituted good forms the base.  That’s why you think your cost of living has gone up but the inflation number does not show it.  You have, foolishly, continued to buy the familiar good instead of substituting something cheaper.

To understand statistics, you must understand how the population of studied events is created and how the relevant event is defined.  Pay attention to the descriptors.  Percentage comparisons are usually meant to mislead.

Averages are worse because a single very different instance can distort it. The average wealth of the people in Bill Gates high school graduating class, is quite high.

You make better decisions when you know what the data means.

Don Shaughnessy is a retired partner in an international public accounting firm and is now with The Protectors Group, a large personal insurance, employee benefits and investment agency in Peterborough Ontario.

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