October 5, 2007

The Achievement Gap and 100% Proficiency

Many in the edusphere have been saying that NCLB's 100% proficiency target is unrealistic and should, therefore, be lowered.

Sounds good in theory. But, I don't think these edu-pundits have thought through the ramifications of lowering the bar. Because when you lower the bar by an amount that seems reasonable, say to 85%, you wind up with a whopper of a problem. By lowering the bar you essentially foil the primary purpose of NCLB which is to "clos[e] the achievement gap between high- and low-performing children, especially the achievement gaps between minority and nonminority students, and between disadvantaged children and their more advantaged peers."

White students tend to outperform black students by about a standard deviation. But because these two populations are distributed normally, the percentile achievement gap between the two groups differs depending upon the difficulty of the testing instrument. Here is what the achievement gap looks like plotted against white pass rate.

As you can see, if we make the test sufficiently difficult such that no white students pass the exam, then we see that no black students will pass the exam either and the white/black gap is zero. We can achieve the same thing by making the exam so easy that all students pass it. This is shown at the white passing rate of 100%.

Setting the pass rate at zero would be political suicide. Setting the pass rate at 100% is NCLB--if all students pass the test the achievement gap is zero. (Of course, we'd like to see student achievement actually rise to the 100% level as opposed to merely decreasing the difficulty or cut score of the test, but I suppose in the real world we're going to get a little of both.)

Let's simply the issue and stipulate that it is politically feasible to set the the white pass rate at 50% or higher.

Looking at the graph, you quickly see that we have a big problem in that the achievement gap stays at a high level until we reach a 95% white pass rate, and even then the achievement gap is still likely to be at a politically unacceptable level.

Let's say we exclude all students in special education, about 13%, and require all non-special education students to pass the test. You can see from the graph that we're are still going to wind up with about a 25% gap which isn't exactly an improvement over the status quo.

The point of all this is that we have almost no room to play with NCLB's 100% pass rate before we negate the reason why we allow the feds any role in education in the first place--to address civil rights issues. Once we lower the pass rate a hair, the achievement gap will skyrocket which is an outcome the edupundits don't seem to appreciate.

Update: Here's another graph to help you visualize the achievement gap.

The top distribution is white distribution, while the bottom distribution is black distribution. You can picture how the gap increases as you hit the fat part of each distribution.


Anonymous said...

Was there meant to be more graphs?

How about one showing the overlap of white and blacks, to make it easier to visualize.

I think Murray had some nice graphs on this issue last year.

Anonymous said...


shouldn't you at least try to send some of your better posts to the nytimes and washpost as letters to the editor?

or do those papers have any ed reporters who understand statistics well enough to comprehend your blog?

This is great, topical stuff... It really should get in the major dailies somehow.

Unknown said...

While you make an excellent point, I must disagree about the 100% pass goal. It's laudable, but it isn't realistic. Setting the goal at a minimum of 75% passing for all groups, however, is realistic, and it reflects the normal grade curve distribution.

KDeRosa said...

RWP, I agree that 75% is a more realistic target and that 100% isn't going to happen, at least if we maintain relatively high standards.

The bottom 25% should then be tested at some lower standard, say "basic." We'd rather have them undereducated than uneducated.

The rub is that under this saner scheme we are still going to have a giant achievement gap for the high performers and a disproportionate amount of blacks/hispanics in the low group.

Anonymous said...

What about the fact that "proficiency" has no agreed-upon definition? States are free to define it however they wish and change criteria at will. Do statistics on such an imprecise variable really mean anything at all?

Chester Finn has an article about this in today's Wall Street Journal but I'm not a subsriber so I don't know what he said about it.

I know in my own jurisdiction the tests change every year and so do the marking criteria; the scores are very much manipulated. Getting rid of tests is certainly not the answer but I'm not convinced that this type of holistic "peformance assessment" (which is what most states use) is the answer either.

There is some evidence that these "performance assessments" favor white and middle class students even more than norm-referenced tests do, but I don't remember the source of my data on that.

And what about aboriginal/native kids? Isn't anyone concerned about them? Seems you never hear much about how they are doing.

KDeRosa said...

Native Americans get lost in the shuffle because they only represent about 2% of the pop. As a group, they tend to perform like hispanics on these tests.

Anonymous said...

'The bottom 25% should then be tested at some lower standard, say "basic."'

I think all testing should be tiered. We should have a national level of proficiency for fourth, 8th, and 10th grade in reading, writing, and math. Then at the higher levels, we should also have mastery of individual subjects.

And yes, blacks and hispanics will be disproportionately represented in the lower tiers, and take longer to reach each tier.

But so what? At least we'd know what students knew how much.

Anonymous said...

I'd still say setting slow learners up to be achievers would be a better way to go to address the achievement gap.

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