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For a given experiment, and a given sample size, there is a probability that a treatment effect of a given size will yield a statistically significant finding. That is, if the treatment effect is 1 unit, then that probability (the power) might be 50%, and the power for a treatment effect of 2 units might be 75%, etc. Unfortunately, before the experiment, we don't know the treatment effect size, and indeed after the experiment we can only estimate it.

So a statistically significant result means that, whatever the treatment effect size happens to be, Mother Nature gave you a "thumbs up" sign. That is more likely to happen with a large effect than with a small one.

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13y ago

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Anonymous

5y ago
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Q: What circumstances can a small treatment effect be statistically significant?
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