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: From 2005 through 2009, questionable scores appeared in 233 classes, compared to the 65 that would be expected, based on other Georgia scores. Odds: less than 1 in 1 trillion.

History: State investigators in 2011 confirmed cheating at nearly two-thirds of elementary and middle schools. About 180 educators were implicated in the scandal.

High stakes: Teacher bonuses were based on meeting district-set targets, primarily test scores. Principals were allowed “no excuses” not to boost scores.

BALTIMORE

Enrollment: 84,212

Eligible for free or reduced-price meals: 83 percent

AJC analysis: From 2006 through 2009, suspicious changes in 228 classes; 116 would be expected. After district began aggressively investigating cheating, fewer classes flagged, and those were mostly for decreases. Odds: 1 in 100 billion.

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

High stakes: Student progress heavily influences teacher evaluations.

DALLAS

Enrollment: 157,575

Eligible for free or reduced-price meals: 76 percent

AJC analysis: In 2006, 2008, 2009 and 2011, 242 classes exhibited suspicious 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 taught 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.

DETROIT

Enrollment: 75,263

Eligible for free or reduced-price meals: 85 percent

AJC analysis: Suspicious scores in 181 classes in 2008 and 2009, compared to an expected 57. Odds: less than 1 in 1 trillion.

History: The state identified questionable erasures on some Detroit tests in 2009.

High stakes: N/A

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.

High stakes: N/A

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.

High stakes: N/A

HOUSTON

Enrollment: 204,245

Eligible for free or reduced-price meals: 79 percent

AJC analysis: Since 2006, 307 classes exhibited improbable changes, compared to an expected 177. Odds: less than 1 in 1 trillion.

History: After the Dallas Morning News identified possible cheating in 2004 and 2007, the district fired numerous principals and teachers.

High stakes: In 2011, 75 percent of the district’s teachers received bonuses through a pay-for-performance system.

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.

High stakes: N/A

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.

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

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