However, audience size doesn't always correlate to the most actions. Wal-Mart, which boasts the largest fan base, saw its total actions—defined by Shareablee as post-level likes, shares, favorites, retweets and comments—drop about 90 percent over the Nov. 1 to 21 timeframe.
Although this decline caused the retailer to fall from the top slot for this metric to 19th, referral traffic to its site from Facebook alone increased 193 percent year-over year from Oct. 1 to Nov. 24.
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Shareablee, which is the social media measurement partner for comScore, determined its rankings by examining 87 big-box stores' presence across Facebook, Twitter and Instagram.
"A lot of retailers really picked up their game," said Tania Yuki, CEO of Shareablee.
Although it can be hard to determine how much of an impact social media has on a retailer's sales, Yuki said that more than half the retailers' in its top 20 list got as much as three times as many clicks as they did likes, comments and shares on Facebook. Facebook, she added, drives the most engagement by far.
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The big winners in terms of engagement tend to be those who are "not treating social media as though it's a magical cash machine," Yuki said. Instead, it's those who recognize social media is a place for friends and family to share things like recipes and spark conversations.
Although Wal-Mart's total actions fell over the past year—mostly, Shareablee said, because it posted fewer messages to Facebook than last November—it was one of only two big-box stores to rank as "genius" for its Digital IQ. That ranking was determined by think tank L2 in a study released Monday.
Wal-Mart spokesman Ravi Jariwala referred CNBC to a recent story by MediaPost, which found via its ListenFirst technology that Wal-Mart "has the biggest social media presence as measured by consumer engagement heading into Black Friday."
On its website, MediaPost said ListenFirst's methodology pulls data from Facebook, Google+, Instagram, Tumblr, Twitter, Wikipedia and YouTube. Its engagements encompass metrics that pertain to audience growth, page and profile views, interactions, hashtag volume and Wikipedia page views.
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Jariwala told CNBC the company's engagement metrics are up, and that "this is the biggest digital holiday plan that Wal-Mart has ever executed." He added that things such as page views across its digital channels are already up nearly four times what they were over the entire holiday period last year.
He called Shareablee's data "flawed," saying it didn't account for things such as the decline in a brand's organic reach—meaning the amount of consumers it can reach without paying for a sponsored post.
See a chart of the top 10 retailers in terms of their fan base, compared to their total actions, below.