Monday, February 13, 2012

Dr. Φ Does LAUSD

There are approximately 635 public and public charter elementary schools in the Los Angeles Unified School District. Of these, GreatSchools.org has both demographic and rating data on around 550.

image003*

Three quick observations:

  • Damn!  I mean, really, I don’t need any mathematics to recognize the implications of this graph.
  • It appears that my earlier observation, based on the schools in the Unnamed Metropolitan Area near which Φ resides, didn’t hold up.  If anything, school quality in LAUSD is relatively robust under 20% NAM; only at percentages above that does average school quality start to decline.  That said, there are differences between the two jurisdictions.  Hispanics don’t have much of a presence in UMA, whereas in LAUSD they outnumber blacks (though multiple regression on the LAUSD show blacks and Hispanics to be mostly interchangeable in terms of their impact on school quality).  Further, UMA is a slowly dying rust-belt city where nothing much happens demographically, whereas the population of LA has been in considerable turmoil over several decades because of immigration and white flight.  But I don’t have a testable hypothesis on why this might make a difference.
  • The data appear upper triangular.  They suggest that high NAM percentages and high GSRs are not inconsistent, although relatively unlikely.  But low NAM percentages seem to put a floor on the GSR.

On to the stats.  LINEST() yields:

LRA for GSR vs. NAM**

-0.069377883 10.64438456
0.002510365 0.212176384
0.58224699 1.503263987
763.7798947 548
1725.991803 1238.371833

Again, I have a killer coefficient of determination: R2 = 0.58, which means 58% of the variation in the data is accounted by the NAM percentage alone.  The slope of the regression, m = –0.07, is middling.  The implication is that every increase in NAM student body percentage  of 14.4% causes a drop of one GSR.  My intuition is that, given the bounds of the data (1 < GSR < 10, 0% < NAM < 100%), the largest slope I could expect would be m=0.1.

I will issue the usual caution to the HBDers (in which category I include myself):  most of what we are seeing here is self-sorting.  It doesn’t matter what the educability of NAMs or their effect on school quality actually are:  a generalized belief among parents of all races that NAMs adversely affect education will cause parents for whom education is a priority to flee to low NAM schools, leaving behind parents for whom it . . . isn’t.  This alone might generate patterns like we see here.

* As you can see, my Excel graphing skills have improved, although I still haven’t figured out how to set upper and lower bounds on the axes.

** For a full explanation of the LINEST() output, consult the Excel documentation or see my earlier post.

6 comments:

Dexter said...

Diversity Is Strength!

Professor Hale said...

This is what happens when you teach people math. Nothing good can come of it. Multiple regression should be illegal since its results are invariably non-progressive.

Peter said...

One thing I noted from the chart is that with one exception* minorities don't cause a significant drop in school ranking until they become an overwhelming presence. Even most of the schools in the 50% to 60% range score a 6 or better. You don't start seeing a noticeable dropoff until around the 70% mark, and almost all of the really low-ranked schools, those with a 3 or below, are past the 80% mark.

This being said, I am curious as to what effects the black/Hispanic mix of a particular school's minority population might have. It's my suspicion that white parents might be somewhat more willing to send their children to heavily Hispanic schools than to heavily black schools.

It also would be interesting to see a chart for LAUSD's high schools, though of course there would be fewer data points.

* = the exception being the fact that almost all the schools with 10's have few minorities.

Dr. Φ said...

This being said, I am curious as to what effects the black/Hispanic mix of a particular school's minority population might have.

Multiple regression shows identical black and hispanic effects on the GreatSchools rating.

Peter said...

It's strange that the two groups have identical effects on ratings. It's always been my impression that white people find one of the groups a lot more tolerable than the other. Maybe it's that the sheer numbers make things different in Los Angeles.

Professor Hale said...

Multiple regression be racis. Was invented by white people to oppress the blacks. Expecially the blacks in college, taking statistics classes.