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> It isn’t easy, of course. In 2013, Randall Lewis of Google and Justin Rao of Microsoft released the paper “On the Near Impossibility of Measuring the Returns on Advertising.” In it, they analyzed the results of 25 different field experiments involving digital ad campaigns, most of which reached more than 1 million unique viewers. The gist: Consumer behavior is so erratic that even in a giant, careful trial, it’s devilishly difficult to arrive at a useful conclusion about whether advertisements work. > > For example, when the researchers calculated the return on investment for each ad campaign, the median standard error was a massive 51 percent. In other words, even if the analysis suggested an ad buy delivered a 50 percent return, it was possible that the company actually lost money. You couldn’t say for sure. “As an advertiser, the data are stacked against you,” the researchers concluded. That bodes poorly for your typical marketing schmo trying to glean meaning from a Google analytics page—all he can do is try to stack enough data to overcome his statistical problems. > > Still, in an email, Lewis told me that he believes “online ads absolutely work.” Or, at least, they can work. For instance, Lewis and his Google colleague David Reiley have written papers showing that display ads on Yahoo led to more customers making purchases in stores. The problem, Lewis argues, is that most analytics firms aren’t scientific enough about measuring profitability. Because they don’t run real experiments, he thinks most end up conflating correlation and causation.
(It's a very nice paper, I think, one of the most insightful applications of power analysis I've seen.)