(Bloomberg) – A majority of big companies say gender and racial diversity are key factors in picking a new director. Fewer than half are willing to show whether they are succeeding.

About 45 percent of companies disclose the gender of directors and about 40 percent reveal the race or ethnicity, according to a detailed analysis of the regulatory filings of 500 of the largest U.S.-listed public companies by Equilar. That's less than the 60-plus percent that say each of those factors is important in picking board members, according to the study being released Wednesday.

"There is no standard" for how companies disclose such information, said Matthew Goforth, Equilar senior governance adviser and one of the study's authors. "But if that were to happen, that would put more pressure on boards to diversify if they were perceived as being less diverse."