If we cannot make the strong assumption that the variances of two samples are equal,then we must use the pooled standard deviation in calculating the standard error of a difference between the means.

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When we cannot assume equal variances between two samples, we should not use the pooled standard deviation; instead, we use methods that adjust for unequal variances, such as the Welch's t-test, which does not assume equal population variances.

If We Cannot Make the Strong Assumption That the Variances