Can We Correlate WKCE Scores to ANYTHING?

It's time somebody looked (at least in the public eye) at some of the demographics and policy/practices and how they may or may not relate to achievement (in terms of WKCE scores).

First a very brief less in the art of correlation.  We can take any two pieces of information and mathematically determine whether or not there is a pattern...a correlation.   The mathematical tool is the correlation coefficient. It provides a number ranging from -1 (perfect inverse correlation, as X increases, Y decreases) to +1 (perfect correlation, as X increases/decreases, so does Y).  Then, all we need to do is apply some statistics based on the size of our data set to determine whether or not the correlation is significant (statistically speaking).  For this exercise we looked at the 95% level of confidence, which means that there would be 5% or less chance that the correlation observed resulted from chance alone.

Batting First:  Class Size

We had the benefit of the Elementary Task Force having provided the public with data on K-5 class sizes for all 16 Dane Co. school districts.  The correlation is a negative one, -0.356, meaning that as class size increases, WKCE scores actually IMPROVE.  The interesting thing is that if one removes Madison from the data set, the correlation suddenly becomes significant (-0.615), although not hugely so.   To be statistically significant with this small sample size (16), a correlation above 0.497 is required.  But every picture tells a story, and this one is interesting.   Note that for this exercise we focused on WKCE scores at grade 4, which is the only elementary grade at which all five subject areas are tested.

We can see that Sun Prairie, with an average class size of 20.3 kids in grades K-5, resides in the quadrant associated with lower WKCE scores, but also lower class sizes.  Granted, we'll stipulate that the range in class sizes is small to begin with (18-23), but look who resides in that cherry quadrant( higher class sizes, and best WKCE scores):  Waunakee, Middleton, Oregin, McFarland.  These are the schools that are whipping our butt in WKCE performance, yet their class sizes, on average, are larger than ours.


Batting Second:  District Diversity

We hear it all the time...unfortunately most of it is discussed in hushed tones.  Face it folks, this country...and this community with it...has become much more diverse.  We need to talk about it more and better embrace that which comes with diversity.  Not being shy, we correlated district diversity to district-wide WKCE rank for the 16 Dane County districts.  We found a correlation (0.486)just slightly below one significant at the 95% level.  Once again, however, if we take Madison out of the equation, the correlation changes substantially, dropping to 0.286.  This of course, also highlights one of the considerations with the correlation coefficient.  You have to look at the data!  One outlier data point can skew the resulting correlation.  Madison clearly is an outlier here.  But that's not surprising for a district that has nearly 4 times the enrollment of the next largest Dane Co. district.


So...we couldn't see a correlation between diversity and WKCE scores.  Slight, but insignificant.  Do the schools with lower diversity fare better on school testing? Certainly Waunakee, our overall number-1 ranked district for WKCE scores also haves the lowest diversity with "white" students comprising over 90% of the population.  But what about Middleton, with a diversity of over 20% and yet a WKCE rank of 2 out of 16?


Batting Third:  District Socioeconomics (Poverty)

Socio-economic Status.  We most often hear it expressed as the percentage of kids eligible for free or reduced price lunches. It means poverty, folks.  And over the past 3 years of this "blip" in the economy, the numbers have soared all across the state.  Interestingly enough, this is where we found the highest correlation to WKCE scores.  Imagine that...it might be that kids who just don't get enough to eat don't fare well in their learning.  We couldn't possibly imagine that just living in a home that struggles monthly to pay the mortgage or make rent might have some bearing on learning.  Could we?

The correlation here, 0.768, is definitely statistically significant.  And it remains pretty much the same (0.74) even if one excludes Madison. What's interesting about this data, however, is there seems to be a direct correlation from Waunakee to Sun Prairie, but from there, things fall to pieces.  First the correlation takes a downward turn, and then it rises meteorically for the districts with the lowest WKCE scores...and highest poverty levels.


The CleanUp spot
Sorry folks, all batters got left on base.  We looked at average teacher...excuse us..."professional educator"...salary and average years of teaching experience and we got bupkis.  The plots look like a shotgun blast.  Zero correlation.  We hoped to have something to wow you fro the Braun spot, but that's not the case.

All in all, some interesting data.  Wouldn't it be nice to see this from the board and hear them discuss it instead of that snoozefest "Monitoring Report" document?  Hell, this district could wrestle the Cherry-Picking title away from Door Co. what with the way our administration cherry picks the data to show the community.  If data supports what they want to do, we'll see it.  If it doesn't, it will never see the light of day.