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The test isn't significant, can we just run it longer?

Asked at Two Sigma

Your planned 14-day A/B test of a new execution algo ends at p=0.09p = 0.09, just short of significance. The PM says, "we're so close, let's just keep it running until it hits p<0.05p < 0.05."

What is wrong with extending the test this way, and what are the sound alternatives?

Show a hint

Stopping early the first time p<0.05p < 0.05 inflates the false-positive rate. Does continuing until p<0.05p < 0.05 do anything different?

Your answer

This one is open-ended. Work it through, then check your reasoning against the full solution.

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