The idea is that if customers do not see their image, they could be at a fraudulent Web site, dummied up to look like their bank's, and should not enter their passwords. The Harvard and M.I.T. researchers tested that hypothesis. In October, they brought 67 Bank of America customers in the Boston area into a controlled environment and asked them to conduct routine online banking activities, like looking up account balances. But the researchers had secretly withdrawn the images. Of 60 participants who got that far into the study and whose results could be verified, 58 entered passwords anyway. Only two chose not to log on, citing security concerns.