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Business Insider/Hayley Peterson
A customer shops for food at Walmart in Richmond, Virginia.
The retailer's groceries are about 4% cheaper than Kroger's, according to a recent price check by Barclays.
Analysts compared prices on a basket of 78 identical items at Walmart and Kroger stores in Nashville to determine which retailer was cheaper.
Walmart offered lower prices than Kroger on 74% of the items checked.
Barclays found the biggest price differences between the two retailers on non-perishable and frozen items, where Walmart had a 5.6% price advantage over Kroger.
Kroger was cheaper than Walmart in the "fresh" category, however, which includes proteins, dairy, and vegetables.
Kroger was 3.3% cheaper in that category, but mostly due to steep discounts on a small number of items including eggs, apples, green grapes, baby carrots, bell peppers, and chicken breasts. Excluding those items, Kroger's "fresh" products were 15% more expensive than Walmart's, according to Barclays.
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Barclays Research
But Kroger appears to be losing the battle.
The chain's same-store sales, or sales at stores open at least a year, fell 0.7% in the most recent quarter, marking the end to a staggering 13-year streak of quarterly same-store sales increases.
The company blamed food price deflation for the decline, but its clear that Kroger is also feeling pressure from competitors.
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Barclays Research
Barclays analysts said Kroger may have a hard time catching up to Walmart on price.
"While we feel Kroger has clearly proven over the years that it is a superior operator, the magnitude of Walmart's investments may prove difficult to overcome," analysts wrote.