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The Atlanta Journal-Constitution’s investigation found concentrations of extreme swings in test scores in several urban school systems, resembling a statistical pattern that indicated organized cheating in Atlanta. The degree of changes in these districts defies statistical probability.

Atlanta

Enrollment: 50,009

Eligible for free or reduced-price meals: 75 percent

AJC analysis: Questionable scores peaked in 2008, when 54 percent of schools and 22 percent of classes were flagged.

History of irregularities: State investigators in 2011 confirmed cheating at nearly two-thirds of elementary and middle schools. Almost 200 educators were implicated.

High stakes for teachers: Bonuses were based on meeting district-set targets, primarily test scores.

Baltimore

Enrollment: 84,212

Eligible for free or reduced-price meals: 83 percent

AJC analysis: Since 2005, unusual test-score deviations occurred in at least one grade in at least 29 percent of schools.

History of irregularities: From 2008 to 2010, investigators found evidence that educators at three elementary schools changed students’ answers on state achievement test. Sixteen schools have been implicated.

High stakes for teachers: Student progress heavily influences teacher evaluations.

Detroit

Enrollment: 75,263

Eligible for free or reduced-price meals: 85 percent

AJC analysis: Fifty-one percent of schools had at least one flagged grade in 2009, compared to 13 percent statewide.

History of irregularities: Analysis by USA Today found irregularities in 2009 test data.

Houston

Enrollment: 204,245

Eligible for free or reduced-price meals: 79 percent

AJC analysis: Since 2005, 22 percent to 28 percent of schools were flagged, two to three times greater than in Texas as a whole.

History of irregularities: The Dallas Morning News identified possible cheating from 2004 to 2007.

High stakes for teachers: In 2010, 88 percent of the district’s teachers received bonuses through a pay-for-performance system.

Dallas

Enrollment: 157,575

Eligible for free or reduced-price meals: 76 percent

AJC analysis: In 2006, 2008, 2009 and 2011, 242 classes exhibited suspcious scores; 130 would be expected. Odds: 1 in 100 billion.

History: In 2011, an investigation found that students at one elementary school were being taught only reading and math — the only subjects on the state tests. The students’ social studies and science grades were fabricated.

High stakes: Since 2007, some teacher bonuses have been based on student performance.

East St. Louis, Ill.

Enrollment: 7,275

Eligible for free or reduced-price meals: 100 percent

AJC analysis: In 2007, 2008, 2010 and 2011, suspicious scores surfaced in 46 classes, compared to an expected 12. Odds: 1 in 100 billion.

History: In 2003, news reports said the district excluded special-needs students from testing and violated test-security policies.

Gary, Ind.

Enrollment: 10,221

Eligible for free or reduced-price meals: 94 percent

AJC analysis: In 2006 and 2007, 40 classes had questionable scores, while eight would have been expected. Odds: 1 in 1 trillion.

History: No public reports of cheating.

Los Angeles

Enrollment: 664,233

Eligible for free or reduced-price meals: 79 percent

AJC analysis: In 2004, 2006, 2007 and 2011, 740 classes showed unusual changes, compared to an expected 572. Odds: 1 in 1 trillion.

History: In 2010, Los Angeles shut down six charter schools accused of cheating on state tests. Last year, the district accused teachers of giving questions to students in advance of testing, improperly coaching students and changing answers.

Mobile County, Ala.

Enrollment: 63,000

Eligible for free or reduced-price meals: 68 percent

AJC analysis: From 2008 to 2010, suspicious scores occurred in 91 classes; 42 would be expected. Odds: 1 in 10 billion.

History: No public reports of cheating.

High stakes: The district began offering performance-based bonuses to teachers in low-performing schools in 2004.

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Many urban districts that serve poor children did not show large percentages of classes flagged for high scores changes. Here’s a sampling:

Chicago

Enrollment: 407,157

Free or reduced-price meals: 78%

Flagged classes: 3.2-5%

Fresno, Calif.

Enrollment: 75,468

Free or reduced-price meals: 81%

Flagged classes: 1.5-6.6%

Amarillo, Texas

Enrollment: 31,890

Free or reduced-price meals: 64%

Flagged classes: 1.7-4.8%

Notes: "Classes" refers to grade-wide test administrations. Also, numbers for enrollment and free or reduced-price meals are for 2011 or the most recent year for which data was available.

Sources: School districts, National Center for Education Statistics, National Center for Performance Initiatives, staff reports