I'm not sure if there are any scholarly studies, but some stores use cards to make people shop more often and some don't use cards to make people shop more often.

Some people really like the feeling of saving money by being a part of a grocery store (card), as well as earning 'rewards' like gas points (even though 95% of people over-spend to earn gas points or buy stuff they don't need [sometimes giant, for example, has BUY 5 ITEMS for 20c off but it's never stuff people usually buy]),

while other stores market to people who like to know they're getting the most for their money and paying bottom dollar (where people will still spend more than they need because ITS SO CHEAP!).

Either way if you can stick to a budget/grocery list you'll do well, and if not, you'll spend extra.

disclaimer: I used to work for a Giant for about 2 years and now we shop at Aldi because it's cheaper than the Giant in our area.