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I am wondering if my logic is OK here or not.

98% of a group without a device has an event occur 2% of group with device has an event occur Since we know that correlation isn't causation I can't say that the device made a difference one way or the other but I am wondering if I can reasonably conclude:

Of the 2% where the device was present and the event occurred... It likely would have occurred in 98% of that group anyway since we have observed that it happens 98% of the time when the device isn't present.

I don't have any data beyond that unfortunately so I am trying to figure out how much it mattered if I assume it mattered - based on the data I have.

If that doesn't extrapolate mathematically, what am I missing?

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What you are describing is commonly called conditional probability. In other words, the probability of an event occurring, given that another event has occurred. Bayes' theorem is a way of conducting statistical inference based on conditional probability. It might be useful to frame your problem as statistical inference (in contrast to extrapolation).

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  • $\begingroup$ Perfect, thanks! Even better that the conditional probability leads me to base rate fallacies which seems like it might give me other things to consider. So, impossible or not . . . actually better than perfect in answering the question that I asked. $\endgroup$
    – Rodger
    Mar 2, 2023 at 17:40

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