In December 2004 the Seattle Post Intelligencer ran an article titled “State slips behind in school spending” subtitled “Administrators release study, call for Legislature to act.” In previous articles we examined two of the statistics quoted in that article, specifically, class size and per-student spending. The big problem of the originally quoted statistics was that it merely compared them to similar statistics from other states. When we examined these statistics we looked at similar statistics from all the states. But state-by-state comparisons only go so far; we also examined what the ideal should be and how Washington state fares in comparison to the ideal. In this final article in the series we’ll examine the state’s school education system not by comparing how much money was spend or by how large the classes are, but by how well they are performing. Specifically, what their graduation rate is.

Graduation Rate

The implication in these statistics, large class size and low per student spending, is they adversely affect the students’ education, but is this the case? What was missing from the original newspaper article (and indeed in many discussions on this topic) is an objective measure of effectiveness. How do we know that our children are getting a good education? Are we solely relying on class size and spending? “My child is getting an excellent education because there are only 9 other children in his class”, “My child is getting an excellent education because my state is spending $13,000 per year on her education.” These aren’t metrics for performance, if anything they’re metrics for effort. What we’re really interested in is whether that effort is effective.

One such metric is graduation rate. If you have small class sizes and spend lots of money on your students you’d hope that almost all of your students would graduate. Or, in our case, despite having the fifth largest class size and below average spending per student, Washington’s high school graduation rate is slightly ahead of the national average.

It seems as if Washington is doing the best in a bad situation; above average graduation rate despite below average class size and below average per student spending. But the cited statistic is that the national average graduation rate is 69.7%. Are we really satisfied with this number?

Surprisingly that’s harder to say and a full answer to this is beyond the scope of this series. One complicating factor is that it is hard to find any 2 reports that will agree on what the graduation rate is. If no one moved or changed schools then determining how many 9^th graders actually completed 12^th grade would be fairly easy, but people move so statistical methods are used to account for this, but those methods don’t agree on how to handle students who are held back a grade. Some will capture them while others will treat them as drop outs, even if they graduate from high school in 5 years instead of 4. Because of this, I’ve adopted the policy of treating graduation rates as a relative measure; those near the national average are good, those well above it are excellent and those well below it are poor. Washington state’s graduation rate is good despite having a significantly larger than normal class size.

But before we leave this, let’s briefly consider one final assumption, that is, whether there should be a correlation between class size, per-student spending and graduation rate. On the surface it seems plausible, but if you dig deeper into the data you’ll find the state of Utah is a remarkable state. It ranks last in spending per student but 2^nd in graduation rate for the 2004 academic year.

References

Seattle Post Intelligencer article available online at: http://seattlepi.nwsource.com/local/204608_schoolfunding21.html

Spending per student and class size information was obtained from the National Education Association’s reports:

National Education Association, “Rankings & Estimates, Rankings of the States 2004 and Estimates of School Statistics 2005”, June 2005. Available at: http://www.nea.org/edstats/images/05rankings.pdf

National Education Association, “Rankings & Estimates, A Report of School Statistics UPDATE”, Fall 2005. Available at: http://www.nea.org/edstats/images/05rankings-update.pdf

A study that recommends a class size of 13 to 17 students is:

American Educational Research Association, “Class Size: Counting Students Can Count”, Fall 2003 Research Points. Available at: http://www.aera.net/uploadedFiles/Journals_and_Publications/Research_Points/RP_Fall03.pdf

High School graduation rate information came from:

NCHEMS Information Center for State Higher Education Policymaking and Analysis, “Public High School Graduation Rates” for year 2004. Available at: http://www.higheredinfo.org/dbrowser/index.php?measure=23

In December 2004 the Seattle Post Intelligencer ran an article titled “State slips behind in school spending” subtitled “Administrators release study, call for Legislature to act.” The article notes:

Washington ranked 34^th in the nation for per pupil spending during the 2002-03 school year, spending $7579 per pupil compared with the national average of $8428

In an earlier article we noted that Washington is also concerned about their student/teacher ratio, and that upon closer inspection of the data it appears that this concern may be warranted. The original Seattle P-I article cited several statistics to sell the case that more money is needed for Washington state schools. Is the per-student spending as dire as the class size issue?

The actual data for all 50 states for the 2003-2004 school year is shown at right. It too looks vaguely reminiscent of a bell curve, albeit somewhat less reminiscent than the class size chart. One key difference that people who regularly examine these types of curves will note is that the bell is lop-sided. That is, one end is further from the middle than the other end. When this happens the use of the phrase “average” can be misleading. Most of the time the average and “middle value” or median mean the same thing. That is, the average also implies that ½ of the states spend more than average and ½ of the states spend less than average. But when the bell is lop-sided then the outliers can skew the average away from the middle value. This is one reason why the original article mentioned both rank (34^th in the nation; a sense of the median) and average spending.

The average and the median for the actual data are shown above, but to illustrate this point let’s swap a pair of values, the 9-10 bar with the 13-14 bar. The hypothetical data that would support this swap would be 2 states spending between $9,000 and $10,000 per student and 9 states spending between $13,000 and $14,000 per student. This hypothetical situation is shown at the right. Because of this change the average spending per student has increased by $600 but the median hasn’t changed at all, both groups of states were already above the median, and swapping them didn’t change that, but more states are now below the average than before.

Back to our real example, the national average spending per student was $8300, but there was a relatively large number of states that spent more than $13,000 per student. This pushes the average higher than it otherwise would be. The intelligent question should be “how much should we spend per student on education?” But neither the newspaper article nor the quoted school administrator pursued this question, instead they merely compared Washington state’s per-student spending to other states’ and the national average. While Washington is below the national average, it is in the median range and perhaps the national average would be closer to the median if it weren’t for this large number of higher spending states. Why did these states spend so much more than the others and, more importantly, did they get their moneys’ worth?

We’ll examine that question in our next and final article.

Washington ranks 34^th in the nation when it comes to funding K-12 public education, according to a study spearheaded by school administrators.

State and federal support for education is so insufficient here, the study said, that many school districts must rely heavily on voter-approved levies to meet basic needs – even though the state Supreme Court has deemed that approach unconstitutional.

and closes by quoting the administrator:

“You’ve got to keep the lights on, you’ve got to keep the heat on, but you have to stop doing some things.”

“And that’s hard, because whatever we stop doing affects programs for children.”

That’s right, the administrator pulled the “think of the children” card which should immediately raise a red flag, so let’s look a little more deeply at their complaint. Among the numbers quoted in the article are these:

• Washington (State) is #5 in the nation for class size. (5th largest)
  
• Washington ranked 34th in the nation for per pupil spending during the 2002-03 school year.
• Washington teachers rank 18th in the nation for wages. (Average teacher pay is more than $10,000 below the pay in California)
• Spending per pupil was $7597 compared to a national average of $8428

In summary, Washington is significantly below average in spending per pupil, Washington has very large class sizes and Washington’s teacher pay isn’t commensurate with the class size. The implied conclusion is that student education will suffer. Let’s examine whether this conclusion is valid when put into context for the rest of the country.

Class Size

Some people, when reading the first bullet point above probably created a mental picture assuming that class size followed a nice smooth curve, such as the one shown at right, with most class sizes being moderately sized, some being large and some being small.

Statisticians call this the “bell curve” because it looks like a bell. There are a variety of bells, illustrated below, ranging from short and wide to tall and thin.

Of course, other people may simply have read that bullet and not drawn any sort of mental picture at all. Regardless, lacking additional information, most people would rely on the “ranked fifth in largest class size” quote and exclaimed “Ranked fifth!?! Oh my gosh then your state has classes far larger than the average (assuming average to be 25^th place), how awful for you.” But in truth, without knowing anything more it’s hard to make any accurate conclusion.

Ideally the class size would be exactly the same for every student in the US. Each state would be tied for first place as well as 50^th place in size.

In such a world, discussions would center around the actual number of students in a class not on the rank in the list; on whether the class size, 15 students per teacher in this example, was too big not whether it was the largest in the nation; and on what the ideal class size should be.

Studies show the ideal class size is in the 13 to 17 students per teacher range. These studies also indicate that smaller class sizes are more important in elementary school than in middle and high school, however there are only a few studies on this topic and the results can not yet be considered conclusive. But if we accept these results then we should also be content with a more realistic but somewhat less ideal class size distribution such as the one shown below. If every state is within the acceptable range, then does it really matter if your state or your school is above or below average?

What does the real data indicate? The actual data for all 50 states for the 2003-2004 school year is shown below. It does indeed appear to follow a bell shaped curve. Some details may be odd, such as the fact that none of the 50 states have an average class size in the 18-19 students/teacher range, but in broad terms the curve is bell shaped as discussed earlier. Thirty-four states fall in the ideal range of 13 to 17 students/teacher. Washington, with an average of 19.3 students per teacher in the 2003-04 academic year resides in the hashed box. The height of that box is 2, meaning that 2 states have average class sizes in the 19-20 students/teacher range. Here the other state is Nevada with an average class size of 19.2. It appears Washington does indeed have a problem. Not only is it nearly last in the nation, but Washington’s average class sizes are well outside the optimal range.

To Be Continued

Next time we’ll look at the spending per student statistic.