Friday, October 4, 2013

Two Plus Two Equals Fish

"By all accounts, it just doesn't make sense!"

Hi, there!

Dave-El here and this is my blog, I'm So Glad My Suffering Amuses You, voted the Internet's Most Popular Blog by an overwhelming 92% of the voices in my head.

It's been a VERY busy day and it's very late right now so I'm really tired and pushed for time. But I've committed to consistently providing well crafted, original content. That's my promise to you, the reader. I'm not just going to slap something on this blog I happened to find in an old document file.


Here's something that I happened to find in an old document file, a speech I gave to my Toastmasters club back in the spring of 2010.



Two Plus Two Equals Fish
Here's some information for you:  83% of all statistics are made up.

Is that true? I don't know, I made it up.

It has been said there are lies, then damned lies and then there are statistics, a quote attributable to Mark Twain and Benjamin Disreali.  But they were not the only ones with a low opinion of statistics. English writer Rex Stout said, "There are two kinds of statistics: the kind you look up and the kind you make up”. British Prime Minister George Canning said "I can prove anything by statistics except the truth

Which is kind of odd in that statistics is a mathematical survey of events and trends. It involves actual numbers and rigid formulas.  Numbers represent facts.  Cold, hard facts. Two plus two equals four. 


Yet statistics are frequently greeted with skepticism.  Perhaps this is because too many people and organizations seek to use statistics to convince you two plus two equals five. Anyone can come up with statistics to prove anything.  14% of people know that. (That's from Homer Simpson so you know it must be true.) 

Now there is a methodology in the collecting of statistical data.  First of all, when applying statistics to a scientific, industrial, or societal problem, it is necessary to begin with a population or process to be studied. Populations can be any group from "all persons living in a country" to "every atom composing a crystal".

Let's consider this potential problem: 

The American Pie Producers Association are concerned about a decline in the sale of pies. What's going on? Are the pies the wrong flavors? Are they not flaky enough? Is there another sweet treat distracting American from eating pies? Has part of the population been replaced by pie hating aliens from Alpha Centauri?  APPA needs to find out.  They need a survey! 

So it's time to start asking some questions.  You can gather data from every single member of the population.  This is called a census.  Asking each person in one room what their favorite kind of pie, that wouldn't be a big deal.  Asking all of 300 million plus citizens of the United States the same question, that is a bit impractical, it would take waaaaaay too long and those pies are just sitting there.  You need a subset of the population to study.  This is called a sample.  And it is  important  that the sample cannot be too small.

Suppose I'm doing a survey on who likes pie and the first person I approach is a woman. Wow! 100% of the people who like pie are female.  Which comes as a surprise to myself and any other guys who likes pie.

Obviously, this sample is too small.  

But even if you were to survey a sample of just 1% of the United States population, that's still 3 million people to ask and that's a lot of people. (Statistically, what this means is if you are a 1 in a million kind of person, there's 300 more out there just like you.)  The actual number may vary depending on the study and established parameters but a national survey may rely on a sample of the population of ranging from as few as 1,000 to 10,000 participants with segments of this sample coming from different regions of the country to insure a wider cross section of the population sample. 

For a sample to be used as a guide to an entire population, it is important that it is truly a representative of that overall population. Representative sampling assures that the inferences and conclusions can be safely extended from the sample to the population as a whole.

A major problem lies in determining the extent to which the sample chosen is actually representative. Just as the sample can't be too small, it is also important to make sure the survey doesn't cast too large a net.  If I were to survey 10 people, half men and half women and ask if they've ever had their prostate checked, right off the bat, half of the respondents are going to say never and if 1 out of 5 men said never, then my survey says 60% of those surveyed are at risk of prostate cancer when the reality is 20% of the relevant population has not had a prostate exam. 

This why during presidential election years, you here the parties surveyed as "likely voters".  If you surveyed everyone including children, the statistical analysis would determine the next president of the United State will be...Spongebob Squarepants!*

*"Who lives in a White House under the sea?  President Squarepants! Defend the Constitution will he.  President Squarepants!" 

So back to the problem of pies, APPA would survey those who buy groceries and are likely to make a decision whether or not to buy pies. 

Misuse of statistics can produce errors in description and interpretation that can lead to devastating decision errors. For instance, social policy, medical practice, and the reliability of structures like bridges all rely on the proper use of statistics.


For example, there have been 72 Postmasters General of the United States.  That's a fact.  Of those 72, all but 2 are dead.  That's a fact.  That's a 97.2% mortality rate.  Therefore, I can make the conclusion that the Postmaster General is a very dangerous position.  


Of course, this an absurd conclusion.  I am counting every Postmaster General who ever lived.  I've going back to the first one, Benjamin Franklin.   The conclusion is mathematically correct but it doesn't make sense. 


Or consider this:  If I put your feet in the boiling water and your head in the freezer, on average, you'd be comfortable.

Or this:  One out of every four people is suffering from some form of mental illness. Check three friends. If they're OK, then it's you. Yes, I've used statistics to convince 1 in 4 of you that you're insane. 


Statistical data can unintentionally or deliberately misused.  And now we've moved beyond the realm of two plus two equals four or even five.  That's two plus two equals fish. 

Like almost anything, statistics are not inherently good or bad but are tools to be used and they can be used wisely but can be misused as well.  So when someone quotes something happens 80% of time or 2 of 5 people think this or that, consider the source and look at the whole picture, not just the numbers.  Just trust me, I would not lie to you about that.

At least 67% of the time.

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