Facebook split-testing issues
Facebook trials: "divergent delivery" --> limited inference
Researchers are interested in running trials using Facebook ads. However, inference can be difficult. Facebook doesn't give you full control of who sees what version of an advertisement.
With A/B split testing etc: They have their own algorithm, which presumably uses something like Thomson sampling to optimize for an outcome (clicks, or a targeted action on the linked site with a 'pixel'). Statistical inference is challenging with adaptive designs and reinforcement learning mechanisms. As the procedure is not transparent, it is even more difficult to make statistical inferences about how one treatment performed relative to another.
Segmentation and composition of population: Facebook's 'PageRank' algorithm determines who sees an ad. I don't think you can turn this off.
We haven't found a way to be able to set it to "show all versions of an ad to comparable populations"
(And even if you could, it would be difficult for you to specifically describe "which population" your results pertain to.)
Divergent delivery and "the A/B test deception"
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