Dan Domenech is a highly educated man. The Executive Director of the American Association of School Administrators, Dr. Domenech was once Superintendent of the Fairfax County (Va.) Public schools (168,000 students) and holds a Ph.D from Hofstra University.
Domenech is also statistically illiterate. That’s a shame for one whose mission is to help school administrators advance the goals of public education and advocate for the children.
Statistical illiteracy is shockingly common in our society. As one wag observed, 8 out of 5 people suffer from it. More seriously, Gerd Gigerenzer, an eminent German psychologist, recently wrote that “Statistical literacy is a necessary precondition for an educated citizenship in a technological democracy.” He is absolutely correct. It is vital that voters, politicians, bureaucrats, journalists, health professionals, and all manner of businesspeople understand the numbers behind policy decisions that we must make.
What was Domenech’s statistical faux pas? In a recent interview with National Public Radio, Domenech weighed in on the case of an Ohio mother who sent her kids to another school district for a better education. She was found out, tried, convicted, and imprisoned (briefly) for lying about her residency. Domenech, decrying the disparity in education quality between districts, said: "The correlation between student achievement and zip code is 100 percent. The quality of education you receive is entirely predictable based on where you live."
First let’s review a brief definition of correlation. When two measurements tend to move together, they are said to be correlated. For instance, if you were to prepare a table of daily ice cream cone sales and daily high temperature, you would see that more ice cream is consumed at 90 degrees than at 30. Ice cream sales and temperature are said to be correlated. Similarly, a comparison of sunstroke incidents to temperature would show a kindred relationship. But one must be careful – correlation does not imply causation. If you looked only at sunstroke rates and ice cream cone sales, they would also be correlated, that is, high sunstroke rates occur with high ice cream sales and vice versa. But one cannot say that eating ice cream causes sunstroke. Behind the scenes, they are both correlated with a common variable – the temperature.
Correlation is represented by a number between zero and one that describes the degree of relationship between the two variables. A correlation of zero means that variables are completely unrelated, such as the cost of bubblegum and the distance between star clusters. A correlation of one, on the other hand, means that the variables are perfectly related, such as the number of pennies represented by various dollar amounts.
A discussion of direct vs. inverse and negative correlation will be postponed to a future topic.
So let’s return to Dr. Domenech. If the correlation between student achievement and zip code were indeed 100%, then all of the students in a given zip code must have the same grade. All students in 90210 must have a C grade, and all in 20511 a B, or the correlation is not 100%. But we know that that is untrue. Some students in 90210 get A grades, and some are awarded D grades. There is variation within the student body that is caused by will, ability, and parental expectation among other things. So it is patently untrue that “the correlation between student achievement and zip code is 100 percent.” Domenech should be made to sit in the corner with a dunce cap until he learns his lesson. (Perhaps the problem is that we no longer do such things).
As a responsible citizen and voter, the most important thing you can do to make informed decisions is to arm yourself with basic math skills and not be afraid to challenge those who appear to be speaking from a position of authority. Our intellectual and political elite are not always completely accurate, sometimes from ignorance and sometimes from calumniation. I’m sure that you are shocked.
