KANSAS CITY, Kan. (AP) — An expert witness called by Secretary of State Kris Kobach in a trial over Kansas’ voter registration law endured intense questioning over his estimation that 18,000 noncitizens have voted in the state.

Jesse Richman, an associate professor of political science at Old Dominion, testified Tuesday in the sixth day of a federal lawsuit challenging the law, which requires people to show documentation when registering to vote.

Richman has offered various estimates, ranging from 1,000 up to 18,000, based on surveys he conducted. Kobach has said the 18,000 estimate is the best available number to show the law is needed to address widespread voter fraud.

The Topeka Capital-Journal reports Richman acknowledged under cross-examination that his surveys weren’t peer reviewed. Instead, 200 political scientists signed a letter criticizing Richman’s work.