This is the second part of my "presentation" on the topic of "Lies, ..."
Click here for the first part: http://tvpclub.blogspot.com/2007/06/lies-damned-lies-and-statistics-part-1.html
In this part, we will explore "truth and consequences" and "playing the percentages."
EXAMPLE #1: What did I say?
This year is 2007. If I told you I was born in the year 2000, how old am I?
Well, 2007 - 2000 = 7, so, I guess I am seven years old. Right?
All right, not necessarily. This is the month of June 2007, so, if a person was born before June 2000, he or she would be 7, but, if after June, he or she would only be 6. So the answer is six or seven years old. Right?
Sorry, nope! No matter what I told you, I am the age that I am. That happens to be 68 years old. I am sixty-eight years old!
LESSON: No matter what someone may say, that does not change the truth of the matter.
EXAMPLE #2: Let us move on to playing the percentages.
From now on in this posting, let us assume (for the sake of this discussion) anything in purple bold italic type font is a literal truth.
Poupon University has five academic departments. Four out of the five have more male than female professors. Thus, 80% of the departments at Poupon U. are male-dominated.
The percentages of Male/Female are as follows:
- Engineering: 90% male / 10% female.
- Physics: 80% male / 20% female.
- Philosophy: 65% male / 35% female.
- Foreign Languages: 60% male / 40% female.
- Humanities: 25% male / 75% female.
If you average the percentages of the five departments, you get 65% male / 35% female.
That would seem absolute proof that old PU is discriminating against female professors! Right?
Not necessarily! Here are the numbers for each department, and the sum of the numbers for Poupon U. as a whole:
Note that there are EXACTLY 200 female professors and 200 male professors at old PU! The genders are EXACTLY 50/50!
What happened to the discrimination? (The same thing that happens to your fist when you shake hands!)
THE LESSON: Beware of percentages, particularly when they are averaged.
EXAMPLE #3: Percentage Increase and Percentage Decrease
In 1980, gas in the US cost about $1.50 per gallon and now it is up to about $3.00 per gallon, which is a 100% increase.
If gas prices should drop back from $3.00 to $1.50 per gallon (I'm not predicting that, just suggesting it for the purposes of illustration), that would be a 50% decrease.
What is going on? When prices go up by $1.50 we get twice the percentage increase as when they go down by the exact same amount!
If we look at the historical record, US gas prices peaked in 1980 when they were about $1.50 per gallon. Considering inflation from 1980 to 2007, that is about $3.00 per gallon in constant dollars! If you calculate the gas price as the number of minutes the average US worker must devote to earn the price of a gallon of gas, the current price is less than the historical peak in the 1980's!
The same percentage increase and percentage decrease confusion holds for unemployment, crime rates and all things that are bad.
As an example, in the Orlando Sentinel for June 26th 2007, there is a report on the increase in Florida gun crimes, based on data for 2005 and 2006. Gun Murders in Florida went from 521 in 2005 to 740 in 2006, an increase of 42.0%
What if they happen to decrease in 2007 to the same number as in 2005. That is, if they went down from 740 in 2006 to 521 in 2007? That would be a decrease of only 29.6%, 12% less of a decrease than the increase reported above.
If the number of Gun Murders in Florida happened to be 521 in odd years and 740 in even years for a decade, and you averaged the percentages, that would show an average increase of 6.2% per year while, in truth, the rate was unchanged for the decade!
THE LESSON: Beware of percentages, particularly when percentage increase and percentage decrease are compared.
Please comment on this material. (Stay tuned: I plan to post yet another part of this "presentation" in a week or so.)