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Depending on the size of the effect, 11 participants can be very valid in an experiment. For example, assume you have 11 participants having a hormone measured after an experiment. If normal readings are 300 with a SD of 30, and at the end of the experiment their mean is 520 with a SD of 40, then you've just shown a strong, significant effect.

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Yeah, except it usually would be (in the best case scenario) more like "520 with a SD of 40" for 10 people and "1 outlier", which you wouldn't really be able to properly conceptualize let alone explain, since your "outlier" is freaking 10% of the group.

That is, ignoring the fact that experiments without a control group can be hardly considered valid at all.

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