Numbers game and potentially misleading statistics

Not too long ago, I was told the following joke which involves a mathematician and an accountant.

A mathematician and an accountant are in the same room for a job interview.  The interviewer’s first question to the mathematician is:  “How much is $500 plus $500?”

The mathematician replies:  “$1,000, of course.”

The interviewer then turns to the accountant and asks the same question:  “How much is $500 plus $500?”

The accountant replies:  “Whatever you want it to be.”

The interviewer then tells the accountant:  “You’re hired!”

I have nothing against accountants here.  My point is that there are dishonest people (they don’t necessarily have to be accountants) who fudge numbers and “cook the books” to exaggerate sales reports, company returns, scientific data, and much more.  Even advertising and marketing campaigns can include misleading statistical data.

Some try to use statistics to imply a cause and effect relationship between two items.  For example, when there were arguments that were being made against legalizing marijuana, the following statistic came up:  85% of marijuana users went on to become heroine addicts.

Someone else replied to this with another statistic:  “Yeah, well 99.8% of heroine addicts drank milk.”

The first statistic might lead you to believe that marijuana usage leads to a heroine addiction.  However, are you also to believe that drinking milk is worse and results in a greater chance of heroine addiction?

This example shows that statistics don’t always imply causality … there’s not always a direct cause and effect relationship between two things.

Also, charts can be very misleading, depending on the scale that is used.  There are other things that can be done to create a misleading graph, but scale manipulation is one of the most visually deceiving.  Here is one such example below.

With smaller vertical scaling, it appears that there is a massive increase in house pricing (the same principle can be applied to exaggerating tax increases, sales returns, etc.).  In addition, the vertical scale does not start at zero!  When the vertical scaling is done in increments of 10,000 instead of 1,000 and starts at zero, the price increase does not appear as drastic.

Also, some will attempt to make their mathematical calculations and algorithms appear so complex and complicated to give the impression that they know what they’re doing.  For example, Madoff sent out a monthly statement to investors which showed a list of companies that he had traded using a “complex” formula.

There are many other ways to play around with numbers in a misleading or deceptive manner.  Feel free to share your thoughts and comments below.

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