= Welch's t-test
{c}
{title2=$t=(\overline X-\overline Y)/\sqrt{s_X^2/n_X+s_Y^2/n_Y}$}
For two <independent> samples from approximately <normal distributions>, <Welch's t-test> compares their means without assuming equal unknown <variances>. The displayed <test statistic> uses sample <variances> $s_X^2,s_Y^2$. Under the equal-mean <null hypothesis>, its reference <Student t-distribution> has approximate <statistical degrees of freedom>
$$
\nu=\frac{(s_X^2/n_X+s_Y^2/n_Y)^2}{(s_X^2/n_X)^2/(n_X-1)+(s_Y^2/n_Y)^2/(n_Y-1)}.
$$
A <p-value> from this approximation addresses the specified statistical error model; it cannot distinguish a material effect from an unmeasured experimenter bias when sample and experimenter are confounded.
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