z68\doc\web\2003\06\ohgap2.txt Date: Wed, 25 Jun 2003 13:00:10 -0700 (PDT) From: La Griffe du Lion Subject: Can regression to the mean explain trends in B/W reading gaps? Was: Race gap pretty much constant across districts in Ohio Ciao a tutti, CAN REGRESSION TO THE MEAN EXPLAIN TRENDS IN BLACK-WHITE READING GAPS? I pondered this question while on the hydrofoil between Ischia and Naples. Just now have I found time for a cursory look. Notwithstanding Arthur's love affair with black/white failure ratios (wrongly calculated in his post) there are several interesting observations that can be made from the data he found in the Columbus Dispatch. These data -- recent grade 4 reading pass rates from Franklin County, Ohio -- are published in their entirety by the Ohio Department of Education, disaggregated by race/ethnicity and downloadable as an excel file. 1. GAPS ARE BIGGER IN AFFLUENT SUBURBS. Contrary to the Columbus Dispatch the grade 4 reading gap, when assessed as a mean difference, is larger in affluent districts than in poor. We know generally that test scores increase monotonically with family income. Thus, a rank ordering on white (or black) pass rates should more-or-less parallel that made on affluence. Consequently, in the (temporary) absence of detailed demographic data, I used the white pass rate as a surrogate for affluence. The correlation between this rate and the gap is significant at 0.52. Regression to the mean could account for reading gaps increasing with affluence. Affluent blacks are farther out on the bell curve than similarly stationed whites. Consequently, black suburban kids may simply have regressed further toward the lower black mean ... to be investigated. 2. PERCENTAGE-POINT DIFFERENCES CAN MISLEAD. I have discussed this elsewhere (Pearbotham's Law, http://www.lagriffedulion.f2s.com/adverse.htm). Nonetheless, percent difference is the most commonly used gauge of racial and ethnic gaps -- both in the media and school boards. The present case illustrates the folly of such an approach. In Franklin County at least, white pass rates (and consequently, affluence) are negatively correlated with percentage-point gaps ( r = -0.14). (Defining the gap becomes increasingly relevant as Bush pushes for gap reduction.} 3. HU'S FAILURE-RATE RATIOS MUST GO. NB Arturo. In the limit of very high white pass rates the white failure rate becomes correspondingly very small and your ratio will blow up -- even without gap changes. We are already approaching this case, eg, the Reynoldsburg district in Franklin County where 93% of white fourth graders passed the most recent reading test. Further gains will drive you and your ratios up the wall. Migliori riguardi, --Griffe Arturo, here are the Franklin County grade 4 reading data. They include failure-rate ratios. Ciao, --Griffe PASS RATES GAP GAP HU DISTRICT BLACK WHITE (%) (SD) RATIO Reynoldsburg 76.6 93.0 16.4 0.75 3.34 Worthington 76.1 89.7 13.6 0.56 2.32 Dublin 64.0 86.8 22.8 0.76 2.73 Westerville 51.8 84.5 32.7 0.97 3.11 Hilliard 54.5 81.7 27.2 0.79 2.49 Gahanna-jefferson 55.8 80.9 25.1 0.73 2.31 Canal Winchester 57.9 77.6 19.7 0.56 1.88 Groveport Madison 52.6 74.8 22.2 0.60 1.88 Hamilton 46.2 66.7 20.5 0.53 1.62 South Western 40.6 66.5 25.9 0.66 1.77 Columbus 37.7 57.3 19.6 0.50 1.46 Whitehall 30.2 54.3 24.1 0.63 1.53