The two-sample $t$ procedures assume that both our samples come from an SRS and will
give trustworthy conclusions only if this condition is met.
If the sum of the sample size is less than 15, the $t$ procedures yield trustworthy conclusions
only if you can reasonably assume that your data from both samples come from a normal distribution,
that is, if the distribution appears to be symmetric with one peak and no outliers.
If your data are obviously skewed or if there are any outliers,
it is not advisable to use the $t$ procedures. Non-parametric methods may be more advisable.
If the sum of the sample sizes is 15 or larger, the $t$ procedures can be trusted if there are no outliers
and the distribution is not obviously skewed.
If the sum of the sample sizes is 40 or larger, you may use $t$ procedures even if your distributions
appear to be skewed.
The two-sample $t$ procedures are more robust against non-normal data when the sample sizes of
both samples are equal. Therefore, when planning a two-sample study, try to choose equal sample sizes.