The two samples are independent of each other.
For the usual two-sample t test, the two different samples are assumed to come from populations with the same variance, allowing for a pooled estimate of the variance. However, if the two sample variances are clearly different, a variant test, the Welch-Satterthwaite t test, is used to test whether the means are different.
Ways to detect before performing the t test whether your data violate any assumptions.
Ways to examine t test results to detect assumption violations.
Possible alternatives if your data or t test results indicate assumption violations.
To properly analyze and interpret results of the two-sample unpaired t test, you should be familiar with the following terms and concepts:
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