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Consider a software A/B test with the hypothesis that "the addition of feature F is predicted to increase metric X".

At the end of the test, the data doesn't show any significant change in X, but it does show a significant increase in Y - something that wasn't expected or even considered at the beginning of the experiment.

At this point, is it scientifically valid to say that F increases Y, or should a new A/B test be designed and executed?

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It looks analagous to drug testing, where reporting of side effects during drug trials is obviously very important - i.e. the increase in Y seems analagous to a side effect. And some famous drugs have begun their lives as research into a side effect. Viagra is probably the most famous case, being a spinoff from a drug developed as angina medication. So in your write-up on your experiment you should definitely report the apparent effect on Y. However, if the effect on Y is commercially important, then you still need to go back and do an experiment around a hypothesis that references the increase in Y to validate the existence of the effect properly.

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  • $\begingroup$ "you still need to go back and do an experiment" - but why is this the case, if the data is clearly showing the effect on Y? $\endgroup$ – Jon Burgess Mar 28 '17 at 23:51
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    $\begingroup$ Essentially to show that the result is reproducible. Having said that, I'm guessing you're not a medical researcher, rather a marketing researcher so the cost of getting things wrong is far lower, and not really a scientific decision but a business decision. If we'e talking about altering a website design slightly and it's cheap with limited downside, it may not be necessary. The decision really rests on the risk of a negative outcome to the business vs the cost of doing another experiment. If the risk is negligible compared to the experiment cost, don't worry about it. $\endgroup$ – Robert de Graaf Mar 29 '17 at 0:01
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The problem is moving from estimating a single hypothesis into few ones. One could claim that X and Y are symmetric, if we were willing to examine X, why shouldn't we examine Y? The difference is that since Y wasn't part of the original plan, it is possible that there are many other variables there Y1, Y2, Yn...

Consider that we have extra n variables, all purely random. If we have a large enough n, one of them will have observations that seem to be correlated to F. In case that you consider a pair of variables, the number of options you have becomes O(n^2). The more complex hypothesis set you'll have, the more options you will have and more likely you will be to gat a false correlation.

It doesn't mean that you should ignore the result regarding Y. Many discoveries were accidentals. As Robert de Graaf suggested, you can do another experiment and check the Y-F relation. You can also check multiple hypothesis techniques in order to evaluate your current results in order to estimate whether the new relation is significant.

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