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Why the Achievement Gap Matters

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skoolboy has explained, much more eloquently than I can, why achievement gaps matter even if the scores of white, African-American, Hispanic, and Asian students are all rising equally:

There are a great many social institutions that sort and rank individuals on the basis of test scores and the competencies they represent. Most of these institutions don’t have an unlimited number of positions or slots—rather, individuals are competing against one another for access. When these institutions rely on test scores, and there is an achievement gap among racial/ethnic groups on these tests, the lower-scoring group will be underrepresented. Raising everybody’s scores doesn’t change the rankings of individuals, which is the only way to change the representation of minority groups among those who are selected. Only by reducing the achievement gap can we increase the chances that members of racial/ethnic minority groups can get ahead in society via selective social institutions.

In K-12 and postsecondary education, examples of these selective processes abound. Kindergarteners are often placed in reading groups when they first arrive at school, students are selected to be part of gifted and talented or magnet programs, and even less selective colleges have limited capacity. The same processes apply in the workplace. Whether you are looking for a job at Walmart or Goldman-Sachs, there are usually more applicants than positions.

Taking inspiration from the conclusion of skoolboy’s earlier analysis, I performed a basic simulation to demonstrate how black and Hispanic students fare in selection processes given existing NYC achievement gaps. I randomly generated 100,000 student scores, which roughly represents the size of a NYC cohort. In NYC schools, approximately 15% of students are Asian, 15% are white, 39% are Hispanic, and 31% are African-American. I generated these data to mirror the achievement gaps that exist in 8th grade math NAEP scores in NYC: the average African-American and Hispanic student scores .83 and .72 standard deviations below the average white score, respectively, and the average Asian student scores .28 standard deviations above it. I then asked what the racial composition of selected students would look like if we selected 5% of students, 10% of students, and so on.

Let’s start with a relatively selective process. Imagine that we choose the top 10% of students in NYC for a gifted and talented program based solely on their test scores. The graph below shows the difference in the percentage of students that would be selected in each racial group compared to their representation in the NYC student population. Though NYC schools are only 30 percent white and Asian, 66 percent of selected students would be white or Asian under this scenario. Only 17% would be Hispanic and 10% would be black.

race_simulation2.jpg

Because of the achievement gap, black and Hispanic children are left behind in many selection processes that potentially - and significantly - affect their life chances. When we make these processes even more selective - think, for example, about admission to schools like Stuyvesant or Bronx Science - white and Asian students will be even more overrepresented, as the table below demonstrates.

And this is not only relevant to very selective institutions. Below, I move the cutoff point for our selective program progressively up. Even if 50% of students would be given a slot, white and Asian students still represent 44% of selected students, though they are only 30% of the population.

race_simulation.jpg

In short, the achievement gap has real implications for black and Hispanic kids as they move through their educational careers: they are more likely to be placed in low ability groups in integrated schools, less likely to be selected for gifted and talented programs, and less likely to attend the college of their choice. And, I stress again, this applies to both very selective and relatively non-selective institutions. Gains in proficiency that do not also close achievement gaps on continuous measures do little to help black and Hispanic kids get ahead.

See previous takes from Mike Petrilli and Jay Mathews here.

A few notes: To keep this simple, I assumed that the scores of all groups follow a normal distribution with equal variances. Since achievement gaps are often larger at the top of the distribution than in the middle and bottom, white and Asian students have an even larger advantage than they appear to based on this simulation.

10 Comments

Eduwonkette: I'm not sure what your point is here. Your first point appears to be that in modern day America, a student's actual test score may not be as important as his or her ranking among other student test takers, based on the limited number of slots for higher education and jobs.

But what's your second point? It seems to be that unless each racial group's scores are exactly the same, there is a problem in society. What problem is that? And what is the solution?

If much of the score difference is due to different average income and SES levels between the races, will we be satisfied when students of different races but the same income level perform equally, or will we only be satisfied when all children perform exactly the same?


If much of the score difference is due to different average income and SES levels between the races,

That's not likely to be the cause:

Black students from families with incomes above $70,000 a year score lower on the SAT than white students from families with incomes of less than $10,000 a year. When the University of California was forced to drop race-based affirmative action, a study was done to see if a needs-based policy would bring in a similar number of blacks. What they quickly discovered is that the needs-based approach only brought in more high-achieving but poor whites and Asians. In other words, the top quartile of black American students—often from two-parent families with six-figure incomes and private school educations—is frequently not competitive with whites and Asians even from lower quartiles. But it is precisely this top quartile of black students that has been most aggressively pursued for the last 30 years with affirmative action preferences.

will we be satisfied when students of different races but the same income level perform equally,

That may satisfy some people, but whether this will ever come to be is a very open question.

(No link provided to avoid sending comment to moderation queue.) From the New York Times:


Yet whites and blacks taking similar level courses report that they spend the same time on homework. It is just that the results are different: 38 percent of whites who spend two hours on homework nightly get all their work done; only 20 percent of blacks spending two hours finish their homework � the Gap.
[ . . . . ]
It would be politically convenient for Professor Ferguson, a black man raising his two children plus a nephew in a Boston suburb, if the Gap could be explained away by economics.
[ . . . . ]
It cannot. When he controls for income, half the Gap persists. Among the richest families, blacks average B+, whites A-. How to explain it?

Add to this the lack of satisfaction we see on other fronts even though equality has been achieved long ago. Consider wage inequality.

The Myth of Racial Discrimination in Pay in the United States
Satoshi Kanazawa
MANAGERIAL AND DECISION ECONOMICS
26: 285–294 (2005)

The analyses of the General Social Survey data from 1974 to 2000 replicate earlier findings from the National Longitudinal Survey of Youth that racial disparity in earnings disappears once cognitive ability is controlled for. The results are robust across many alternative specifications, and further show that blacks receive significantly greater returns to their cognitive ability than nonblacks. The trend data show that there was no sign of racial discrimination in the United States as early as 1970s. The analyses call into question the necessity of and justification for preferential treatment of ethnic minorities.

or will we only be satisfied when all children perform exactly the same?

What do you think was the main impetus behind, and appeal of, NCLB?

But what's your second point? It seems to be that unless each racial group's scores are exactly the same, there is a problem in society. What problem is that? And what is the solution?

Very good questions.

Clearly, the achievement gap matters. But what do you propose to do about it?

I am uneasy about TangoMan's comments. He seems to be suggesting that minorities are inherently inferior so that they deserve to receive low wages. His suggestion that racial discrimination ended in the 1970's is absurd.

The large racial and SEC achievement gaps found in the United States are unacceptable and can be narrowed. The integration of schools by SEC rather than by race shows promise as an effective way to increase student achievement. Student funding should reflect the level of student need, with high risk students being funded more generously. Districts should identify those teachers most skilled at raising student achievement levels and deploy these teachers strategically in the schools with the highest need. It wouldn't hurt to pay these teachers more. Students with the most severe needs should receive targeted interventions. In Finland, one in seven teachers is a special education teacher. Struggling students are identified quickly and given the help that they need. This needs to happen in the US. In countries with smaller achievement gaps, the poorest children do not suffer the level of deprivation that is found in the United States. At a minimum, all children deserve access to nutritious food, adequate health care, and safe housing.

I am uneasy about TangoMan's comments. He seems to be suggesting that minorities are inherently inferior so that they deserve to receive low wages. His suggestion that racial discrimination ended in the 1970's is absurd.

I'm suggesting nothing of the sort. I'm pointing to evidence of reality, not passing judgment on how things should be. If you have evidence that contradicts that income, with cognitive ability controlled, is not race neutral then present your case.

The large racial and SEC achievement gaps found in the United States are unacceptable and can be narrowed.

Whether the gaps are acceptable or not is a normative question. Whether they can be narrowed is prescriptive. The fact that trillions of dollars have been spent on this effort over the last 50+ years and the gaps haven't closed is very suggestive that despite your wishful thinking to the contrary, that they're never going to be closed.

The integration of schools by SEC rather than by race shows promise as an effective way to increase student achievement.

No, it doesn't show promise. If it did show promise that upper middle class blacks wouldn't be showing lower scores on SATs than lower class whites and asians.

Student funding should reflect the level of student need, with high risk students being funded more generously.

Peak under the hood of the New Jersey education system. Pay particular attention to the Abbott Schools. All of the necessary data is online.

Districts should identify those teachers most skilled at raising student achievement levels and deploy these teachers strategically in the schools with the highest need.

That's a normative position which privileges the closing of the gap as being more important than creating the greatest good for the greatest number of students. The value added by a good teacher has more effect on good students than on poor students. Depriving these students of these teachers causes the students more harm than the good that is created for the underperforming students.

In countries with smaller achievement gaps, the poorest children do not suffer the level of deprivation that is found in the United States.

Evidence please.

Re whether achievement gaps can be narrowed - it is worth looking at the long term NAEP trends, where there has been meaningful progress over time.

For example, in 1975 there was a 35 point black-white gap in 4th grade reading - in 2004 there was a 26 point gap. In 1978 there was a 32 point black-white gap in 4th grade math - in 2005 there was a 23 point gap.

For example, in 1975 there was a 35 point black-white gap in 4th grade reading - in 2004 there was a 26 point gap. In 1978 there was a 32 point black-white gap in 4th grade math - in 2005 there was a 23 point gap.

4th grade results are mere curiousities. Let's look at data for 16 and 18 years olds, where the education actually counts and has life consequences associated with it. Efforts that are concentrated at young children have a nasty habit of vanishing into the ether as that child ages. After the Great Society era, when it was thought that gains would be easy to achieve the efforts to close the gap intensified and racism abated. The gains that have been achieved show no promise of being extended with current methods, other than with increased time on task, but seeing how that will likely involve de facto segregation, that's not really a politically viable alternative, in other words, the low hanging fruit of educational reform has already been picked.

Hi TangoMan, Re data for 16 and 18 year olds, the NAEP long-term trend data for 17 year olds are even more promising than those for younger students (though complicated by the fact that student retention through 17 has changed over time):

- In 1975, there was a 52 point gap in reading; by 2004, there was a 29 point gap.

- In 1978, there was a 38 point gap in math; by 2005, there was a 28 point gap.

Let's put that long term data into some perspective. The standard deviation for the reading test hovers around 40 points. Blacks went from performing at about -1.29 sd to about -0.70 sd. Or, from about six grades behind to about 4 grades behind. White 13 yr olds scores are 266; 9 yr olds - 226. Compare this to black 17 yr olds - 294 in 2004 and 239 in 1971.

All of the achievement gap reduction took place between 1980 and 1988, and hasn't improved since.

Also, the exclusion rate for blacks is higher than it is for whites which also complicates the analysis, along with, as E (or is it SB?) points out, the higher drop out rate.

Hi Ken,

I'm not going to pooh-pooh a reduction from -1.29 to -.70 SDs - that's substantial! In terms of how/how much such a reduction matters, I can rerun the same analysis above when I get back to demonstrate how a reduction of that size changes the racial distribution of the "selected."

For others who are interested, I will post figures on the NAEP data trends over time when I return.

You are right to point out that the gap stopped closing in the 1990s; there is a new book coming out (published by Russell Sage) that tries to make sense of why.

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  • eduwonkette: Hi Ken, I'm not going to pooh-pooh a reduction from read more
  • KDeRosa: Let's put that long term data into some perspective. The read more
  • eduwonkette: Hi TangoMan, Re data for 16 and 18 year olds, read more
  • TangoMan: For example, in 1975 there was a 35 point black-white read more
  • eduwonkette: Re whether achievement gaps can be narrowed - it is read more

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