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We like to think we’re a progressive society that is accepting of all sexual orientations, but the latest survey shows anti-gay sentiment is higher than we think, and current methods for assessing attitudes about sexuality are not as accurate as they should be.

In a study published in the National Bureau of Economic Research, scientists found that current methods may not accurately capture both the size of the lesbian, gay, bisexual and transgender (LGBT) population as well as attitudes toward them.

Overall, it’s hard to measure sexual orientation and opinions about sexual orientation because of persistent biases toward more socially acceptable responses. Researchers have found this trend even in computer-generated surveys where responses are anonymous.

(MORE: New Insight into the (Epi)Genetic Roots of Homosexuality)

So a team from Ohio State University and Boston University compared these survey techniques to another strategy that provided even more privacy and anonymity to participants, by guaranteeing that even the researchers could not connect the volunteers to their answers. Among the 2,516 U.S. volunteers who were randomly assigned to answer questions about their sexuality using one or the other survey method, those taking the more veiled survey were 65% more likely to report a non-heterosexual identity themselves and 59% more likely to report having a same-sex sexual experience than those using the standard survey technique.

The veiled method also revealed more people with anti-gay sentiment than among those taking the other type of survey. The participants were 67% more likely to disapprove of an openly gay manager at work and 71% more likely to admit that it was acceptable to discriminate against people who are lesbians, gay or bisexual.

“Comparing the two methods shows sexuality-related questions receive biased responses even under current best practices, and, for many questions, the bias is substantial,” the authors write.

Did the enhanced anonymity lead to more truthful responses? The researchers aren’t sure, but previous studies revealed that when responses are blinded, people do tend to express attitudes and opinions that are more raw and closer to their true beliefs. The scientists also can’t explain why those who were questioned under the more veiled technique were more likely to admit to both non-heterosexual orientation or experiences as well as more bias against them. While they suspect the two trends are independent of each other, it’s possible that the results also reveal something deeper about sexuality and social acceptance — or lack thereof — of LGBT identities.