One major reason that the two-sample t procedures are widely used is that they are quite robust. This means that

(a) t procedures do not require that we know the standard deviations of the populations.

(b) t procedures work even when the Random, Normal, and Independent conditions are violated.

(c) t procedures compare population means, a comparison that answers many practical questions.

(d) confidence levels and P-values from the t procedures are quite accurate even if the population distribution is not exactly Normal.

(e) confidence levels and P-values from the t procedures are quite accurate even if outliers and strong skewness are present

When the sample size is big, often above 40 observations, the t methods can be employed even for strongly skewed distributions. It's a parametric test of difference, which means it's based on the same data assumptions as other parametric tests.

"Robust" signifies that even if all prerequisites aren't met, the findings remain correct.

The Normal condition is the most significant requirement for the two-sample t methods.

If the population distribution is not quite Normal, excessively skewed, or contains outliers, the Normal criterion is not met.

Because two-sample t procedures are heavily influenced by strong skewness and outliers, robust two-sample t procedures mean that the findings of the two-sample t procedures remain correct even if the population distribution is not quite normal.