New analysis of achievement gap: ½ x ½ = 1½
By David Berliner
The numbers referred to in the title are standard deviation units. I want people to understand a special set of circumstances in which two sociological variables, each producing approximately a one-half standard deviation difference in the achievement test scores of students, end up producing jointly a one and one-half standard deviation difference in the scores of those same students ( ½ x ½ = 1½ ).
For those who are not familiar with standard deviation units, just think of them as a convenient way to break up the normal curve that is so commonly found when we measure many human characteristics.
If IQ or the height of 16 year-olds are distributed normally, as they usually are, then the bell-shaped normal curve occurs. Whether the mean (average) score is in IQ units, inches, or millimeters, that score would be at the 50th percentile in the distribution of IQ scores or height.
A score about one half standard deviation above that average would be at about the 70th percentile, while a score about a half a standard deviation below the mean score would be at about the 30th percentile. That is, a score half of a standard deviation greater or lesser than that of another individual or group, represents a rather large difference between those individuals or groups. If a student or group of students were to be 1 ½ standard deviation units above or below the mean score of another individual or group, the difference between them would be considered huge, not just large.
It surprises no one to learn that poor students, on average, score approximately ½ of a standard deviation lower than do middle-class students on achievement tests, and that wealthy students, on average, often score around ½ a standard deviation higher than middle class students.
If a group of middle class students scored at about the 50th percentile on some test of achievement, it would not be uncommon to find that, on average, a poorer set of students would score at about the 30th percentile, while a wealthier set of students would score at about the 70th percentile. The gap between the average score of poor and wealthy students on a particular achievement test, then, might then be 40 percentile ranks, and often is more.
It also will surprise no one to learn that schools serving mostly wealthy students outperform schools that serve mostly poor students. The differences between the wealthy and middle class schools may be around ½ of a standard deviation and the differences between the middle class and the poor schools may also be about ½ of a standard deviation. Thus, the difference between average scores for the schools that serve the wealthy and the poor may be 40 percentile ranks, or even more.
But there is an impressive and depressing finding that is new and surprising. It is about the joint effects of being the poor students in the schools that serve the poor, or the wealthy students in the schools that serve the wealthy. This situation magnifies the effects of family poverty and wealth. The joint effects of family resources and school resources lead to differences that are about 1 ½ standard deviations apart, a huge difference in achievement! Thus ½ x ½ = 1 ½.
Perry and McConney of Australia collected data on family income for individual students, and they computed the average income for the families in the schools those students attended. They created a table in which one dimension represented family income broken into fifths. The other dimension was average income for schools, also broken into fifths. This yields the 5 x 5 table, presented below.
In Australia, there were enough poor students in very wealthy schools and enough wealthy students in very poor schools to fill all the cells of the table. Each cell of the table is filled with science scores from the PISA tests, the international comparison of 15 year-olds. Reading and mathematics show the same pattern as found with science.
The SES that predominates at the school
|Individual Student's SES||1st fifth (lowest)||2nd fifth||3rd fifth||4th fifth||5th fifth (highest)|
|1st fifth (lowest)||455||457||471||497||512|
|5th fifth (highest)||555||544||550||582||607|
Australia’s average score on this science test (525) hides incredible variation around that average based on the social class of the students, and the social class that predominates at the schools they attend. A poor student in a school serving the poor (cell 1, 1) scored, on average, 455 in the PISA exam.
But were that same student to get to a school that serves mostly upper class children (cell 1, 5), that student would likely have scored 512, over half a standard deviation higher. And were a wealthy student attending a school with mostly poor children (cell 5, 1), that student would score 555, rather than a score of 607 were he or she in a school that had mostly wealthy children (cell 5, 5). This also is a difference of about half a standard deviation.
Reading down the columns you see how family income, from the first fifth (the poorest students) to the highest fifth (the wealthiest students) produces differences in scores that are even greater than half a standard deviation.
However, it is one of the diagonals that is of most interest. The diagonal in this table represented by cell 1,1 versus cell 5, 5 shows that the difference between poor students in poor schools and wealthy students in wealthy schools is much greater than the effects of either family income or school resources alone.
The joint effects are huge, in this case a difference of over one and one-half standard deviations! That is, sometimes ½ x ½ = 1 ½.
Famously, that report found quite small school effects on student achievement, finding instead, quite large family effects. The conclusion was that family poverty and wealth mattered much more than did schools in determining the life chances of America’s youth.
Schools, it seemed, had little power to affect the destinies of children because family overwhelmingly determined life’s outcomes.
But this new analysis refutes that conclusion quite convincingly. Using newer statistical models unavailable to the earlier investigators, the recent conclusion is that the effects of a school’s average level of family resources was more than 3 times that of the effect of family resources.
Although using different data sets and different statistical models for analysis, the American data and the Australian data reach similar conclusions. Family resources are important, school resources are important and have quite dramatic effects, and the joint effect of the social and fiscal resources found in families and schools appears to be much greater than either alone!
The United States has a great deal of housing segregation by income. It also has many small school districts serving relatively homogenous populations of middle class, or poor, or wealthy students.
Because of these two factors, it is more likely that in the United States of America, compared to some of our competitor nations, poor children go to school with other poor children and wealthy children go to school with other wealthy children.
Thus the approximately ½ standard deviation difference we might expect to see on indicators of achievement for upper and lower social class students, and the approximately ½ standard deviation difference we might expect to see between schools that serve either poor or wealthy students, actually gets magnified by the school and housing policies we promote in our nation.
Already substantial differences in achievement because of school and family resources become huge, almost insurmountable differences, as an achievement gap of 1 ½ standard deviations opens up between poor students in schools that serve poor students and wealthy students in schools that serve wealthy students.
It is not pleasant to contemplate, but when poor children go to public schools that serve the poor, and wealthy children go to public schools that serve the wealthy, then the huge gaps in achievement that we see bring us closer to establishing an apartheid public school system. We create through our housing, school attendance, and school districting policies a system designed to encourage castes—a system promoting a greater likelihood of a privileged class and an under class.
These are, of course, harbingers of demise for our fragile democracy.
See: Borman, G. D. & Dowling, M. Schools and Inequality: A Multilevel Analysis of Coleman’s Equality of Educational Opportunity Data. Teachers College Record, 112, 5, 1201–1246.
Perry, L. B. & McConney, A. (2010).Does the SES of the School Matter? An Examination of Socioeconomic Status and Student Achievement Using PISA 2003. Teachers College Record, 112, 4, 1137–1162.
Follow my blog all day, every day by bookmarking washingtonpost.com/answersheet. And for admissions advice, college news and links to campus papers, please check out our Higher Education page at washingtonpost.com/higher-ed Bookmark it!
| June 29, 2010; 6:30 AM ET
Categories: David Berliner, Guest Bloggers, Learning, Research | Tags: arizona state university, coleman report, coleman report and 1960s, david berliner, educational research, effects on student achievement, how much does school affect student achievement?, parental influence and student achievement, standard deviations
Save & Share: Previous: Willingham: Newsweek story on single-sex ed research misses mark
Next: Two new studies on charter schools
Posted by: Brooklander | June 29, 2010 7:24 AM | Report abuse
Posted by: someguy100 | June 29, 2010 8:28 AM | Report abuse
Posted by: Wyrm1 | June 29, 2010 8:40 AM | Report abuse
Posted by: WashingtonDame | June 29, 2010 9:39 AM | Report abuse
Posted by: chuanhe20878 | June 29, 2010 9:59 AM | Report abuse
Posted by: shadwell1 | June 29, 2010 11:07 AM | Report abuse
Posted by: Nikki1231 | June 29, 2010 3:52 PM | Report abuse
Posted by: clevin | June 30, 2010 9:47 AM | Report abuse
Posted by: AGAAIA | July 1, 2010 6:56 AM | Report abuse
The comments to this entry are closed.