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The Buffalo News compared the performance of elementary schools in Erie and Niagara counties through a computerized regression analysis of 2003-04 fourth-grade mathematics and English language arts test scores as well as family income levels. The income levels are measured by free and reduced-price lunch rates, which federal and state governments consider the standard measure of poverty in schools. Last year, a child in a family of four with income of $23,920 qualified for free lunches. The income limit was $34,040 to qualify for a reduced-price lunch.

The analysis plotted raw test scores with family income levels and determined to what extent low income influenced the scores. The analysis then projected what scores a school would be expected to achieve given the family income of its students.

If the difference between projection and the actual scores was statistically significant, the school was considered to be exceeding -- or falling short of -- expectations.

Charles A. Upson Elementary School in Lockport, for example, has a free and reduced-price lunch rate of 44 percent. The News' analysis projected pupils there would be expected to get an average score of 665 on the math test and 655 on the language arts test.

But Upson's average scores were much higher -- 683 for math, 18 points higher than predicted, and 668 for language arts, 13 points higher than predicted. The differences between the actual and projected scores are statistically significant, according to the analysis. Upson, therefore, ranked among the highest performing schools. Schools, like Upson, that exceeded expectations on both tests were rated as the best in the two counties.