### Achievement GAP Grows with Achievement

The NAEP Reading results are out. There's lots of disappointment over the lack of progress despite the sure-to-work involvement of the federal government. I've looked at NAEP data before and been put off by the seeming lack of standard deviations (sigmas) to make sense of the differences. So I decided to dive back in to see if I could find it, and sure enough there are indeed sigmas available. Now I could try to make some sense (with my limited statistical skills) of some of the state and race differences.

The results of the reading and math follow basically the same patterns, though there are some important differences. The racial gap for math consistently hovers around 1 (in standard deviations) with an average of 0.97, while the reading gaps are more widespread and average 0.84. The standard deviations themselves are fairly variable from state-to-state and between groups. One aspect of the racial gap both sets of scores share is that the higher the white scores, the larger the gap. Now this would seem obvious is you based it only on the raw scores, but the effect remains even after normalizing them with standard deviation units (I used the std. dev. for white scores for each state to measure the state-by-state gap).

Here's the scatterplot for the 8th grade reading score gaps by state:

As Steve Sailer pointed out, Wisconsin appears to be the worst offender by having a large gap without high scores overall. Note that while Wisconsin has the widest gap in scores, it's not the widest in terms of the standard deviation units.

And for math:

But while the higher the white scores the bigger the gap, black scores still trend higher with the white scores, just not as much. The black/white correlation for 8th grade math is 0.5. While I hope no one is stupid enough to think closing this gap would be easy, it may be even harder than some think if the white scores appear to increase faster.

I have ignored Asian scores in this analysis. I'm also interested in how the gap might have grown or shrank over time. I'll take a look at that tomorrow. Capturing and organizing this NAEP data may not exactly be like cracking the Rosetta stone, but it's also not exactly a push-button process either.

Data on reading scores here. Math scores here.

Update 3/26/10 7:11am EDT: Oh well - the kids wouldn't let me near the computer:) So I'll do some more looking this weekend.

Update 7/1/2010: Reading gap by state within region:

The results of the reading and math follow basically the same patterns, though there are some important differences. The racial gap for math consistently hovers around 1 (in standard deviations) with an average of 0.97, while the reading gaps are more widespread and average 0.84. The standard deviations themselves are fairly variable from state-to-state and between groups. One aspect of the racial gap both sets of scores share is that the higher the white scores, the larger the gap. Now this would seem obvious is you based it only on the raw scores, but the effect remains even after normalizing them with standard deviation units (I used the std. dev. for white scores for each state to measure the state-by-state gap).

Here's the scatterplot for the 8th grade reading score gaps by state:

As Steve Sailer pointed out, Wisconsin appears to be the worst offender by having a large gap without high scores overall. Note that while Wisconsin has the widest gap in scores, it's not the widest in terms of the standard deviation units.

And for math:

But while the higher the white scores the bigger the gap, black scores still trend higher with the white scores, just not as much. The black/white correlation for 8th grade math is 0.5. While I hope no one is stupid enough to think closing this gap would be easy, it may be even harder than some think if the white scores appear to increase faster.

I have ignored Asian scores in this analysis. I'm also interested in how the gap might have grown or shrank over time. I'll take a look at that tomorrow. Capturing and organizing this NAEP data may not exactly be like cracking the Rosetta stone, but it's also not exactly a push-button process either.

Data on reading scores here. Math scores here.

Update 3/26/10 7:11am EDT: Oh well - the kids wouldn't let me near the computer:) So I'll do some more looking this weekend.

Update 7/1/2010: Reading gap by state within region:

## 9 Comments:

Texas's math scores are just all-around impressive -- whites do well, Hispanics, blacks, everybody does well.

Maybe they just make a bigger deal out of getting kids to work hard on the NAEP?

Or maybe there is less public assistance in Texas so that low IQ types are more inclined to move to states with more generous welfare programs.

There are so many confounding variables. Texas teaching more to the fundamentals and maybe not so much B.S. could explain it. Lower welfare maybe. But unless someone explicitly tries Texas's approach and sees an improvement, we'll never know.

Could you take the time to fit a least squares line to this? I perfectly vertical line would be strong evidence of a strong and likely irremediable achievement gap and, just eyeballing it, I'd say this one is somewhere between 1 and 2 o'clock. I'd be interested to see this over time.

Deckin - yes, I could do that. I'll give it a shot.

Boy was I wrong about the line! Never forget the importance of outliers. Super interesting way of seeing the data, but so little clear indication of what is at work here. Let's hope the WV solution to the achievement gap isn't the new preferred

de juresolution, because CA seems to bede factoadopting it.Deckin - yes, it looks pretty grim. But the National results over time appear much less dire. I'll be posting that shortly.

Why ignore Asian scores?

Because everyone else ignores them. It's only the White/Black gap that gets discussed. The fact that the Asian/Black gap is even greater never seems to enter the conversation.

However, the Asian gap is tougher to look at because there are few enough Asians, and as population rather heterogenous, that there isn't as much good information. There were a handful of states (Mountain, upper New England) where there were not enough black students to score. There are a lot of states that come up empty with Asians.

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