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Beer and Diapers: The Impossible Correlation

At TDWI's recent Executive Summit, Mark Madsen asked: is there a statistically significant correlation between sales of beer and sales of diapers or has the correlation been misused.

At TDWI's Executive Summit in San Diego, Mark Madsen posed the provocative question: is there a statistically significant correlation between sales of beer and sales of diapers?

Madsen, a research analyst with information management consultancy Third Nature, wasn't strictly interested in answering this question -- although he did. His presentation, aptly titled "Beer, Diapers, and Correlation: A Tale of Ambiguity," traced the origin and evolution of the claim that sales of beer and diapers are closely correlated. He wanted to look at the ways this claimed correlation has been used -- and misused -- since its discovery.

Origin of the Story

Madsen managed to trace the beer-and-diapers story to its origin in 1992. Karen Heath, then an industry consultant with Teradata -- now a senior manager for health analytics with Accenture -- was attached to an unspecified Midwest retailer.

Heath's beer-and-diapers discovery is a good example of something going (digitally) viral back before that was common. Turns out, Heath and her team were looking at sales of items such as diapers, in particular, because baby supplies are high-margin goods. They were looking for correlates, Madsen says -- they didn't just blindly stumble into a hitherto hidden (and irresistible) relationship.

"She wrote SQL queries that discovered this [ostensible correlation], and she said, 'Hey, look, this is interesting!' -- and she sent it off to someone in an email," Madsen told Upside. From there, he says, someone inside Teradata -- neither Heath nor any of the other members of her team remember who -- took the beer-and-diapers story and ran with it.

"It's not entirely an urban myth. They did do this, but all of the explanations [as to] the value or the idea that you could use analytics to discover stuff like this, that didn't have a rigorous statistical basis."

Not Data Mining -- Just SQL

What's most interesting about the original beer-and-diapers connection -- questionable correlation or no -- is that it isn't an example of data mining or of other types of advanced analysis.

Heath and her team used SQL queries running against data in the retailer's Teradata data warehouse to find the correlation. The idea was to identify items that tended to be purchased together and place them together on store shelves. Heath's working hypothesis was that doing so could boost sales by an additional percentage. After all, she reasoned, every retailer knows that if you put two products next to each other on a shelf, they're more likely to be sold together.

Attempts to Repeat the Finding

Through the rest of the 1990s, in a number of different retail settings, Madsen validated and then invalidated the claimed correlation. "Somewhere around 1993 or 1994, I was working in a drug store chain and I read this and I thought it seemed legit. [However,] a year later, working in a grocery store chain, I had access to all of this data, and I tried it, but I found no correlation," he said.

Later on, Madsen was working with another drug store chain in which he was able to validate the beer-and-diapers correlation. Then in 1997, he found a case in which the correlation seemed especially strong.

"There was a 0.95 correlation. I asked them about it. They said, 'We read this article in Chain Store Age magazine that said beer and diapers are correlated, so we put beer next to diapers in all of our stores," he said. "What they did was they created the data that actually validates the data. In effect, they created the signal they used to validate the signal."

In another drug store retailer that same year, he found no correlation. Then, while working with a grocery retailer in the year 2000, he found an example of very weak correlation.

A Self-Fulfilling Story?

At this point, however, it was becoming increasingly difficult to validate the correlation: the story itself was too well known -- in 1998, IBM even aired a television ad that used the beer-and-diapers example. Even if an ostensible correlation were detected, retailers would have to control for cross-promotion at the store level. A store manager, reading or hearing about the beer-and-diapers correlation, could have positioned them on adjacent shelves.

"Cross-promoting means you have no baseline. It means you can't say whether it [a meaningful connection] mattered or not. You can't seek correlations in data you created because any correlation is due to your actions," he explained.

Madsen also cited a couple of pop-culture near misses -- beer and diapers referenced together in a 1988 episode of MacGyver and a sequence from the 1987 movie Raising Arizona in which beer and diapers figure prominently.

Takeaway -- Is Your Insight Actionable?

Madsen's presentation wasn't solely concerned with the history of the beer-and-diapers connection, however. In a sense, this correlation is a great example of how and why advanced analytics is different from business intelligence (BI) and data warehousing.

"If you're saying, 'I want to know if beer and diapers is true,' that's the wrong way to look at it. The right way is to say, 'I want to know whether or not it's true from the perspective I'm operating in,'" Madsen told Upside.

"You can't always just take someone else's model and apply it in your environment. Unlike BI and the data warehouse, where the data is the data and you're basically just adding it up, now you're building models -- and models have randomness and biases. You have to validate a model and scale it out."

The deeper lesson, he stressed, is that analytics insights aren't always actionable. "This is one of the problems with deploying analytics because you have to have some level of trust in the model," he said. "You have to believe that it's going to be better than some decision you can make yourself."

As for a definitive answer to the question "Are sales of beer and diapers correlated?" -- it depends, Madsen said.

About the Author

Stephen Swoyer is a technology writer with 20 years of experience. His writing has focused on business intelligence, data warehousing, and analytics for almost 15 years. Swoyer has an abiding interest in tech, but he’s particularly intrigued by the thorny people and process problems technology vendors never, ever want to talk about. You can contact him at [email protected].

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