I am reminded of the problematic nature of statistics by the debate over what is going on in Wisconsin. Factcheck.org has a nice, well-documented article on claims about Wisconsin's budget that are being made by supporters and opponents of the Wisconsin governor.
The article leads to comments here on use, misuse, and manufacturing of that most plebian of descriptive statistics, the arithmetic mean. So, how much do teachers in Wisconsin make? Not, as Buchanan claimed, $100,000 ($56K in salary and $44K in benefits). That, apparently is a fairly good estimate for the pay of teachers in Milwaukee -- the largest city in the state. Is Milwaukee typical for Wisconsin? Is the mean for Milwaukee teachers a good point estimate for the state? No.
Or consider Rand Paul's more modest claim that
The average teacher in Wisconsin is making $89,000 a year to work nine months
That's not right either. It's not clear whether he's talking about plain salary or salary plus benefits. Even if he were referring to salary plus benefits, it is highly unlikely his number, as precise as it sounds, represents mean salary or salary plus benefits for Wisconsin K12 teachers.
Factcheck.org says:
The state Department of Public Instruction only calculates average teacher salary and benefits on a district by district basis. Of the 425 public school districts in Wisconsin, only one had a salary and benefits package in 2010 that exceeded $100,000; the Nicolet Unified School District average total compensation was $103,315. And only 22 school districts — about 5 percent of the total — paid average total compensation that topped $89,000.
A link, provided by Factcheck.org to the Wisconsin district-by-district averages can be found here. Note that this is an official government website. One thing immediately becomes obvious from the Factcheck.org article: The data are dirty. There are mistakes in the spreadsheet. The known problems are for the Kenosha Unified School District and the Niagara School District. There may be other errors. From what I've seen, we generally assume that reporting errors of this kind are not going to be biased: it's not that the numbers are systematically made too high or too low; it's just that someone typed in the wrong number, and wrong numbers are as likely to be high as low. But data like these are collected and reported by human beings. There will be mistakes.
Another thing to notice is that unless we have information about the number of teachers in each district, we can't use the information in the table to tell us anything about average teacher salaries in Wisconsin. Without the number of teachers per district, we can't compute a weighted mean.
And third is a question of interpretation. We can't judge salaries and fringe unless we have appropriate comparisons from Wisconsin. How much is the governor making? How much does a store manager at Walmart make? How much does a computer programmer make?
In addition to looking at how salaries and fringe vary by locale within Wisconsin, we still need to ask: How does teacher salary vary by seniority (alas, not a great metric), educational level achieved (more for teachers with graduate degrees?), and quality measures (Is there a fund for paying fabulous teachers more money so they keep teaching? There ought to be!). But if there is a superfund for superteachers, their salaries will skew the mean. (More on that below.)
Further the fringe numbers seem really scary, but how many people know exactly the value of their benefits packages? I don't. I know it's a lot of money, but I have no idea how much our Benevolent Patron pays in fringe. When I write a proposal for a grant that would allow me to spend some of my teaching time on research, the University asks me to request my salary + 33% of my salary for fringe benefits. I'm not sure how standard that amount is or the extent to which the cost for fringe benefits varies across different parts of the country. Moreover, I would expect K12 teachers to have a larger proportion of their salaries go to fringe than people who work all 12 months because teachers are specifically paid for 9 months in the classroom, but the fringe benefits (health insurance, most notably) have to be paid all year long.
A final point: the notion of "average" salaries. Everyone here is using arithmetic mean. Means have flaws: they are easily skewed by extreme values. If teacher salaries in Wisconsin are well represented by a normal distribution (a bell curve) or even by a flat distribution (for example: 1/3 of teachers get the same low pay, 1/3 get the same moderate pay, and 1/3 get the same high pay), the mean is reasonably informative as a point estimate, as one number that summarizes the central tendency of the data. But means tell you nothing about dispersion of the data: how stretched out the data are. An example: The numbers 99, 100, 101 have a mean of 100. The numbers 0, 100, 200 have a mean of 100. These are very different distributions! (Standard deviation is the usual statistic used to report the dispersion of the data, but it still doesn't tell you anything about the shape of the distribution.)
My bottom line: As citizens it's our job to be critical about the statistics that are presented to us and to question their accuracy and their meaning.
And a note on teachers:
It's too bad that as a society we don't want to pay our teachers at rates that would attract more excellent teachers. Don't get me wrong. I know many absolutely wonderful teachers out there, but in my experience (anecdote, not statistic, here!), those teachers teach because they love it. They could be earning more money doing something else, but they choose to be teachers because they have a calling. Other potentially wonderful teachers don't consider teaching because they have other concerns and priorities that work against being able to give up more remunerative pay in order to teach.
To paraphrase Rabbi Jonathan Maltzman, wouldn't it be wonderful if we paid our star teachers the way we pay our sports stars? What could be more important to us, our children, our country, and the world than to have highly qualified and competent teachers appropriately compensated for the difficult and critical job that they do?
