in a controlled experiment, why should there be several individuals in the control group and in each of the experimental groups
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Because if you only use one individual, what happens to that one individual does not provide enough data to warrant a generalization concerning other individuals. For example, if you use two mice and give one Vitamin C, but not the other, and the one receiving Vitamin C dies, you cannot state that Vitamin C kills mice. But if you have 50 mice taking Vitamin C, and 50 not taking it, and you see a pattern of response in 40 of the 50 Vitamin C mice, that you don't see in the control group, now you have demonstrated something useful. And if one of the mice in either group dies, that is insignificant. Mice die sometimes, for a wide range of reasons.