Thursday, March 27, 2008

   Statistics, Skepticism and Bias
Put on your thinking caps - it's time for a stastistics lesson. Try not to fall asleep, if this is not all review for you, I think it is very important.

I recently read an article from a conservative web site that throws around a lot of numbers. If you are really interested, I can send you the link or later post a URL to it. One important thing I noticed was there was no reference to the source of the statistics. This is an immediate red flag for me. I prefer to see the actual numbers referenced to verifiable sources, like the US census rather than tossed about with the assumption that they are trustworthy.

In general, I have been seeing more and more statistics being thrown around with the intent to pursuade. Unfortunately, I do not believe the american masses understand even some of the basic terminology that becomes very important when trying to understand what these statistics mean. The most important thing when trying to understand any statistic is understanding what is really being represented by those numbers. By making a slight change to the definition of what you are looking at can change the numbers and initial impact significantly.

The first terms I would like to address are Average and Median. These are both generally accepted as ways to measure the middle of a group of numbers, but they do so in very different ways. Depending on what you are looking at, this can be a huge difference.

Average: This takes the total sum of the numbers and divides by the number of items. So, if you have a shopping cart with 3 items in it priced $1, $2, and $3 your total cost is $6 for 3 items. $6 divided by 3 is $2. Your average cost per item is $2.

Median: This takes the middle number in a group. You should have an equal number of items greater than the median and less than the median. With the same shopping cart, the median price of the items you bought will still be $2, since that is the price in the middle.

If the numbers are evenly distributed, these numbers can be the same or very similar. They begin to represent very different things when the numbers are heavily weighted to one side.

Example: There are 10 people in a room. 4 people have $10 each in their pockets. 1 person has $15. 3 people have $20 each and 1 person has $785. The total money in the room is $900. You can then say, the average amount of money a person in the room has is $100. The median amount a person has in a room is $15.

So - for the above example, if someone said that the average person in the room can easily afford to buy a $50 book. That could be considered a true statement since the average amount of money each person has is $100. Unfortunately, the reality of it would be that only 1 of those 9 people could afford to buy the book with the money on hand.

The article I referenced earlier was trying to persuade people that the richest americans were paying more than their fair share of taxes. "The top 1% of american are paying 37% of the income tax". I have seen similar statistics referenced as a standalone statement trying to persuade people that it is unjust that 1% of the people should pay 20% or more of the taxes. The immediate question that should be asked is "How much of the income does the top 1% of americans make?" The answer according to the conservative web site was 19% - no reference given. According to the Tax Foundation for the year 2005, it was 21.2%.

The big question now - Is the conservative web site numbers wrong? Well... no way to tell. They don't say what year their statistics are determined, so we can't even go back to reliable sources to double check. The other item that should be noted in that statement is it is only referencing "income tax". So, other taxes - sales tax, property tax, city and county taxes - all not included. Would that make a significant difference in the amount of taxes paid? Probably, but this was a persuasive article, so, being a skeptic, I would assume that the income tax figures are going to be the most favorable to represent their point of view.

The other quote from that article I would like to analyze is this: "The upper income bound for the middle class is now roughly $68,000—some $23,000 higher than in 1967. Thus, a family in the 60th percentile has 50 percent more buying power than 30 years ago."

Sounds pretty good doesn't it? There is a slight of hand done here. The article was written in 2007. They give an income comparison to 1967 (40 years) and then follow it with a "buying power" comparison to 1977. Their use of the word "thus" implies that it is a logical conclusion when they do not provide any supporting data for their claim. They also do not provide a definition of "buying power". The other item I would note is that they chose the 60th percentile. I don't care for the use of the word percentile here. The percentile term could be for a family exactly AT the 60% mark similar to median, or I believe it is actually revferencing everybody at or above that level (the income most likely averaged) - including the top 1% of people making over 20% of the money.

Instead of researching both 1967 and 1977, I decided to find some statistics for just 1967. Was there a bias on my part to choose that year instad of 1977? Absolutely, the math is easier based on the stats I found for my definition of "buying power".

First off, to determine "buying power", I will use the Consumer Price Index (obtained from the US Dept of Labor) and compare that to the median income for 1967. The median income for 1967 was $7,143 (US Census). The median income for 2006 (most recent data I found) was $48,201 (US Census). This is an increase of about 575%. The consumer price index for the price of all goods in urban areas for 2006 (that's what dept of labor uses) was 603. That means you will need to spend 6 times as much to buy the same stuff as you would have had to pay in 1967. 1967 was the old standard for CPI, so it's CPI is 100 (which is where the easier math part comes in). So - to determine comparitive buying power, I will to compare the median income to the cost of stuff.

(insert nasty math stuff here)

So, when I did my comparison for median income compared to CPI, I did get an improvement of 11.9%. That is however, a far cry from the 50% improvement that they want you to believe. Is their number false? Possibly, but more likely just very misleading.

Be skeptical. Be informed. Be a force for good in the world.

If at least one reader get's something useful from this, I'll be a happy guy. Take care.

-bunraku
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