Hold on to your hats, because much of what you thought you knew about online advertising might be wrong.

New data from analytics firm RapidBlue and reported by VentureBeat suggest that online ads may have a bigger effect on offline sales.

The company said that it found a significant correlation: when brick-and-mortar stores ran Google AdWords campaigns, they saw double-digit increases in the number of shoppers and in the time people spent in retail stores. In some cases, apparently, the offline results of the campaigns exceeded the online results.

What makes this so important is the fact that it goes against the way many businesses have approached online marketing. For the most part, companies have conceptually split their strategies into two parts: offline and online. And they assumed little to no crossover.

If you advertised in traditional print or broadcast, you were either trying to promote your brand or run sales-oriented campaigns. Even if you included attempts to get people to go to a website or to take a given action on social media, the primary thrust was to make something happen offline. Similarly, online promotions were usually for online shoppers. The idea was to get people to click a link, go to a site, maybe place an order online.

Over the last few years, I've spoken with marketing people and companies that have stretched the bounds a bit. For example, they've found ways to make online promotions fuel store traffic. Or maybe they've created successful brand-oriented video campaigns on YouTube to affect consumer perceptions and attitudes.

But for the most part, such crossover efforts have been marginal. However, if RapidBlue is right (and doesn't just have a service or software selling ax to grind), things are a lot more complicated. Just because you don't see the reaction you expected online doesn't mean you aren't getting one. Instead of watching clickthroughs, page views, or similar metrics, you might have to create a more complex model to calculate the ROI of marketing.

Somehow, you'd have to connect online activity with in-store action, when possible. That might mean better sourcing questions from sales associates or customer service personnel. You might have to run special promotions and online coupons, not for every campaign, but to see patterns of how online ads might influence buying behavior in stores.

If the findings are accurate and applicable to your business, that might mean you'll have to rethink almost everything: marketing, promotion, sales processes and channels, and brand communication.