An assumption for indepedent-sample t-Tests is that the variances for the dependent variable should be equal within each group of the independent variable, when the standard deviation for each group is approximately double.

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The assumption for independent-sample t-tests is that the variances should be equal (homogeneity of variance), not that one standard deviation is approximately double the other.

An Assumption for Indepedent-Sample T-Tests Is That the Variances for the Dependent