(RE)Ranking New Jersey’s Achievement Gap

New Jersey’s current commissioner of education seems to stake much of his arguments for the urgency of implementing reform strategies on the argument that while New Jersey ranks high on average performance, New Jersey ranks 47th in achievement gap between low-income and non-low income children (video here: http://livestre.am/M3YZ). To be fair, this is classic political rhetoric with few or no partisan boundaries.

As I have been discussing on this blog, comparisons of achievement gaps across states between children in families above the arbitrary 185% income level and below that income level are very problematic.  In my last post on this topic, I showed that states where there is a larger gap in income between these two groups (the above and below the line groups), there is also a larger gap in achievement.  That is, the size of the achievement gap is largely a function of the income distribution in each state.

Let’s take this all one more, last step and ask – If we correct for the differences in income between low and higher income families – how do the achievement gap rankings change? And, let’s do this with an average achievement gap for 2009 across NAEP Reading and Math for Grades 4 and 8.

First, here are the differences in income for lower and higher income children, with states ranked by the income gap between these groups:

Massachusetts, Connecticut and New Jersey have the largest income gaps between families above and below the arbitrary Free or Reduced Price Lunch income cut off.

Now, let’s take a look at the raw achievement gaps averaged across the four tests:

New Jersey has a pretty large gap, coming in 5th among the lower 48 states (note there are other difficulties in comparing the income distributions in Alaska and Hawaii, in relation to free/reduced lunch cut points). Connecticut and Massachusetts also have very large achievement gaps.

One can see here, anecdotally that states with larger income gaps in the first figure are generally those with larger achievement gaps.

Here’s the relationship between the two:

In this graph, a state that falls ON THE LINE, is a state where the achievement gap is right on target for the expected achievement gap, given the difference in income for those above and below the arbitrary free or reduced price lunch cut-off. New Jersey falls right on that line. States falling on the line have relatively “average” (or expected) achievement gaps.

One can take  this the next step to rank the “adjusted” achievement gaps based on how far above or below the line a state falls. States below the line have achievement gaps smaller than expected and above the line have achievement gaps larger than expected. At this point, I’m not totally convinced that this adjustment is capturing enough about the differences in income distributions and their effects on achievement gaps. But it makes for some fun adjustments/comparisons nonetheless. In any case, the raw achievement gap comparisons typically used in political debate are pretty meaningless.

Here are adjusted achievement gap rankings:

Here, if I counted my bars right, NJ comes in 27th in achievement gap. That is 27th from largest. That is, New Jersey’s adjusted achievement gap between higher and lower-income students, when correcting for the size of the income gap between those students, is smaller than the gap in the average state.