Sunday, October 16, 2011

"Figures don't lie but liars figure."

An old saying by mathematicians and statisticians

Scripture says we should test for truth everything we are told. Thomas Sowell makes the same argument in his book "Economic Facts and Fallacies." A large segment of the book demonstrates how the mass media manipulates statistics in ways that misstate the true situation.

The example that most caught my eye was the one in which we are told that income for "average household" has declined during the past ten years. Here's a simple description of how that "statistic" can lead us away from the true state of affairs.

We must start with the reminder that an average is an artificial mathematical construct to explain the range between high and low within a given set. For the purposes of simplification, we'll illustrate by starting with a single household. In this household are four people: two parents and two teenagers. The two parents are employed full time, the teens each have part time jobs.

Dad earns $30,000 a year

Mom earns $30,000 a year

Teen 1 earns $ 6,000 a year

Teen 2 earns $ 6,000 a year

Total $72,000 a year

The total earnings are then divided by the number of households: 1. Thus the average household earnings for this set are $72,000.00.

Ten years pass by. Now, Mom and Dad have gotten increases in pay and both teens are grown up, fully employed and are on their own. Having gotten a place of their own, each of the teens now becomes a household of their own.

In household 1: Dad earns $40,000

Mom earns $40,000

Total $80,000

In household 2: T1 earns $30,000

In household 3: T2 earns $30,000

Total earnings for all three households is $140,000.

To find the average income of the three households, we divide $140,000 by 3.

Answer: $36,666.67.

Even though all four members of the original household are each earning more than they did ten years prior, the average household earnings are smaller because there are more households and thus a larger divisor when the average is calculated.

The more accurate and honest comparison would have been the average income for each of the individuals rather than comparing by households. BUT, to compare individual incomes would have revealed the fact that incomes within households have increased during the past ten years.

The same media that brought you this odious fraudulent comparison also told you that the "average worker" has not had a pay increase in ten years. That, too, is a fallacious statement. There is no single "average worker." Remember that an "average worker" is a mathematical construct. It's not a person.

Dr. Sowell also points out that when elitists talk about the differences between the poor and the rich, they use some subtlety there as well. Usually, they will compare the "income" of the poor to the "wealth" of the rich: like comparing eggs and onions and calling them eggions. The income of the poor does not take into account any government subsidies like food stamps, WICK programs, subsidized housing or Medicaid, all of which provide value to their daily lives. Certainly, there are differences between the incomes of each but if one group's cash income is being compared to the other's assets, we have eggions.

All this is to say we need to guard our minds against deceptions whether they deceiver intends to mislead or is simply too ignorant of basic mathematics to make mathematically correct comparisons.

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