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The usual methods of sample size determination which assume the homogeneity of within-group variances are not sufficiently robust against the violation of this assumption. A method using Satterthwaite's correction for unequal variances is given. It is shown that in the case of unequal variances the minimum total sample size is attained when the allocation ratio is equal to the proportion of the standard deviations.
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Júlia Singer (2001) studied this question.
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