A week or so ago I published a blog post boldly stating that you could probably sort districts by their aid ratio from high to low and get a pretty accurate projection of how their PSSA reading and Math scores would look.   One of my loyal readers, Rogue Anthropologist, inquired about whether any such research was available.  Being interested in statistics and more so probabilities, I set out to determine how accurate my blurted out hypothesis had been.

What I found was not an exact, one to one correspondence but it is pretty telling. Using 2012 PSSA scores in reading and Math and district aid ratios (AR) for 2012 I was able to get a pretty good picture of district scores in relation to the economic status of the community.  I do want to go on record as saying this isn’t a statistical analysis.  It is a collection of facts based on the data.  I also want to clarify that when I talk about making Adequate Yearly Progress (AYP) I am talking about what we call in education “making the number.”  In other words I did not take into account whether districts made AYP using confidence interval, Safe Harbor, Growth Model or a combination of any of the above.  I simply used 78% for math and 81% in reading – “the numbers.”  Also, I will note that I used only district totals not individual schools.  For example, Central Dauphin School District is lumped together although it is made up of many different schools including two high schools.  As well, the Philadelphia and Pittsburgh school systems were grouped as one district.

I took all of the school districts in the state and order them from lowest AR (.1500) to the highest (.8814).  I then divided the entire lot into quartiles.  There are 500 school districts in the state of Pennsylvania.  I eliminated one, Bryn Athyn, because they don’t actually educate any students in their district.  Look it up!  It’s pretty interesting.  So, of the 499, since I was looking primarily at the top and bottom quartiles, there were 249 in the middle two quartiles and 125 in the top and bottom.

In the area of Math statewide 62% of the school districts made AYP.  That is important to know as a yardstick for the rest of the data.  School districts in the top quartile according to their AR made AYP 90% of the time.  Conversely, schools in the bottom quartile only made AYP 26% of the time.  That means that a rich school district is about three and a half times more likely to make AYP than a poor one.  To take it a step further, the schools in the top two quartiles – I gave them number 250 – made AYP 80% of the time while the schools in the bottom half made AYP only 42% of the time.

On the Reading PSSA only 28% of the school districts statewide made “the number.”  That seems to have really skewed the numbers based on AR.  In reading only 2% of the schools in the bottom quartile made AYP.  Of the top quartile school districts 70% made AYP.  Some of this in my professional opinion can be attributed to poor households being more apt to be language-poor and those students tend to come to school with fewer background experiences.  When you look at this information as a 50/50 split, the bottom half of school districts only made AYP 8% of the time and the top half made AYP 48% of the time.

There are of course exceptions to every rule.  Windber Area School District and Cambria Heights School District made AYP in both subjects despite ARs of .7324 and .7241 respectively.  Inversely, 14 school districts did not make AYP in either subject even though their ARs ranked in the top quartile.  Pequea Valley School District had the lowest AR of any school not to make either number; .2554.

In addition to economic indicators, I was also interested in determining other factors rather than the quality of teaching that may determine performance on the PSSA.  Research has been done about how the education of the mother impacts achievement.  When I look at that statistic I tend to think that it leads back to the affluence of the family.  Students in privileged circumstances would more likely have two highly educated parents than students living in poverty.

One thought that I have heard, and this is probably do to the poor performance of Pennsylvania’s urban areas, is that the percentage of minorities in a district has an impact on achievement and PSSA. The data on the percentage of minorities in a district is interesting but not very conclusive.  In the area of Math school district that have 10% or greater minorities were proficient 50% of the time (remember that the entire state only had an AYP rate of 62%).  On the opposite end, only 57% of the schools with 2.5% or fewer minorities achieved the 78% threshold.  In Reading the discrepancy is greater but weighted towards the districts with a higher number of minorities, with 33% of school districts with 10% or more minorities making the 81% necessary for AYP and the school districts with 2.5% or fewer minorities making AYP only 13% of the time.  Bear in mind that statewide only 28% of school districts made AYP in the area of Reading.

At the behest of my superintendent I also looked at scores based on the size of the school district.  This is a tough measure when used for measuring the entire district.  The reason being is that the statistic does not take into account the size of individual schools.  For instance the Pittsburgh Public School System, the second largest in the state, has nine high schools to serve 6000 students and the School District of Philadelphia, the largest school district in the state, has 55 high schools to serve roughly 38,000 students.  With those kinds of numbers it is possible to have some high school s doing very well and some high schools doing very poorly.  Anyway, here’s what the number say:  When broken down into quartiles, the top quartile – the largest schools – were proficient 45% of the time in Reading and 71% of the time in Math.  Thirteen percent of schools in the fourth quartile were proficient in Reading and 50% in Math; much to the chagrin of my superintendent.  I’ll have some good news though for him as our district broke many of the rules.

At this point it looks like rich, white – but not too white, large schools have a decided advantage in my personal; race to the top.  Let’s look a little closer though.  Where exactly are the schools that are making it and does that have any impact on their goal of Proficiency?  Well, I’m glad you asked.  There might just be a link.

The National Center for Educational Statistics breaks down districts into categories based on where they are located, how close they are located to a city and the size of the city within the nearest proximity.  Following is the data that I collected on those categories:

As you can see from the data, it is definitely a benefit to live in a suburb especially the suburb of a large or mid-size city.  Those two categories along with the All Suburb categories were the only categories to have a higher percentage of district proficient than the state averages listed previously.  The worst place to live and therefore go to school is obviously in the city with the lowest percentages of all groups.For more information on what each of these categories mean see the NCES website.

With a little dime store analysis you can determine why the suburbs do so well.  Or at least generate an additional hypothesis.

For the conclusion of my hypothesis, without formal statistical analyses, I would say that I was pretty close to accurate.  More affluent school districts are almost three and half times more probable to be proficient on the Math PSSA than their poorer counterparts and more than 35 times more probable to be proficient on the Reading PSSA.  Put another way:  if you live in the top quarter of the wealthiest district in the state your child’s school will have a 9 in 10 probability of being proficient in Math and a 7 in 10 probability of being proficient in Reading.  In opposition, districts that comprise the poorest quarter of all Pennsylvania districts will have a 1 in 4 probability of being proficient in Math and a 1 in 50 probability of being proficient in Reading.  As AYP expectations go up in 2013, to 91% in Reading and 89% in Math, look for those numbers to change.