@Sosi. The TTest function performs the Welsh t-test when you ask it to verify the equal variance assumption and then it only seems to do it when that test is rejected. data1 = RandomVariate[NormalDistribution[0, 1], 100];
data2 = RandomVariate[NormalDistribution[0, 2], 100];
t = TTest[{data1, data2}, 0, "HypothesisTestData",
VerifyTestAssumptions -> "EqualVariance"]
t["DegreesOfFreedom"]. So a "conditional" Welch t-test, yes. "Always perform a Welch t-test", not with TTest.