I ran three regressions for household income versus low-SES student performance. For trial one, I used the percentage of households with incomes greater than $75,000. For trial two, I used the percentage of households with incomes greater than $100,000. And, for trial three, I used the percentage of households with incomes greater than $150,000. All the regressions showed nearly identical results, so I'm only going to discuss the middle trial, trial two.
The theory is that low-SES students will perform better in high-SES school districts. Apparently, these high-SES districts attract better teachers, have better students with better motivation, have more resources, can pay more attention to the small number of low-SES students, and the like.
For this example I'm using community household income as a proxy for high-SES. Specifically, I used the percentage of households having incomes greater than $100,0000 as my measure of high-SES. The greater the percentage of higher income households, the higher the SES of the school district. Let's compare the performance of low-SES students to the percentage of high income households.
Here's the regression results:
- R = 0.13 (there is a weak association between high household income school districts and the performance of low-SES students)
- R2 = 0.016 (there is a poor fit between the data)
- P = 0.007 (the results are statistically significant)
I added a trend line (black line) to the graph, but with a correlation this low, the trend is not reliable. I also added a horizontal line showing the mean of the performance for all school districts in Pennsylvania (mean = 60.7). As you can see, few school districts had low-SES student performance that exceeds the mean score. Low-SES students tend to be underperformers. RWP found that this underperformance was statistically significant.
The mean school district contains about 11% high-income households. This means that if we were to bus all the low-SES students from school districts with less than 11% high-income households to school districts with greater than 11% high-income households, most students would be sent to high-SES school districts having between 11% to about 25% high-income households. That's not much of an improvement and the regression suggests that low-SES student won't improve much anyway. Even if you were to believe the slightly positively sloping trend line, the expected gains in student performance would be minimal.
But there is good reason to question the trend line. Take a look at this graph:
This is a graph comparing high-income households to the fraction of moderately poor households in the school district. I've defined moderately poor households as households with between $15k and $29k of household income. The graph gives the percentage of moderately poor households relative to all poor households (household income less than $29k). As you can see from the graph as the percentage of wealthy households increases so does the fraction of moderately poor households. In other words, the higher-SES school districts have more low-SES students falling in the lower middle class as opposed to the lower or under class.
This is an important finding. The disaggregated data for low-SES (or "economically disadvantaged" under NCLB) students includes students receiving free or reduced lunches. A student can be from a family having a household income approaching $50k and still be included in the low-SES group. But, as the graph above indicates, not all low-SES kids are created equally. The low-SES kids in wealthier school districts tend to have higher household incomes. And, we already know that SES is positively correlated with student achievement.
Many books have been sold by the Kozol/Rothstein clique of SES hustlers who claim that our education woes can be cured if only we could send these kids to high-SES school districts. These claims are founded on the error of ascribing causation to a weak correlation (the top graph) and failing to account for the substantial intra-group differences (the bottom graph) of students defined as low-SES or economically disadvantaged.
It's all based on a lie.