Security is top of mind for many consumers heading into the busy holiday shopping season, and consumers say they’re less likely to shop at retailers that have been hit by data breaches, according to research from CreditCards.com. 45% of consumers with credit or debit cards said they would definitely or probably avoid over the holidays a retailer that had experienced a data breach: 16% said they would definitely not shop at such retailers. Another 29% said they would probably not shop at a retailer that had been hit.

865 adult consumers in the United States with debit or credit cards were surveyed over the phone between Oct. 2 and 5 by Princeton Survey Research Associates International for CreditCards.com.

However, among the highest-income respondents (those living in households making more than $75,000 annually), only 31% said they would definitely or probably avoid retailers who experienced a data breach. That’s compared to 56% of consumers living in households earning less than $30,000 a year. Consumers with more education follow a similar pattern. 33% of college graduates said they would probably or definitely avoid retailers that had experienced a breach, compared to 55% of those with a high school education or less.

Although many consumers said they would switch to paying in cash because of fraud concerns, those with higher incomes and more education were likely to switch. 42% of consumers earning more than $75,000 said they were more likely to pay with cash compared to 51% of those earning less than $30,000. 37% of college graduates said they’re more likely to pay with cash, while 57% of those with some college and 50% of high school graduates said so.