
$${t}_{\mathrm{obs}}=\frac{\stackrel{}{x}\stackrel{}{y}}{s\sqrt{\left(1/{n}_{x}\right)+\left(1/{n}_{y}\right)}}$$ 
$${s}^{2}=\frac{\left({n}_{x}1\right){s}_{x}^{2}+\left({n}_{y}1\right){s}_{y}^{2}}{{n}_{x}+{n}_{y}2}$$ 
$$\left(\stackrel{}{x}\stackrel{}{y}\right)\pm {t}_{1\alpha /2}s\sqrt{\left(1/{n}_{x}\right)+\left(1/{n}_{y}\right)}\text{.}$$ 
$${t}_{\mathrm{obs}}^{\prime}=\frac{\stackrel{}{x}\stackrel{}{y}}{\mathrm{se}\left(\stackrel{}{x}\stackrel{}{y}\right)}$$ 
$$f=\frac{\mathrm{se}{\left(\stackrel{}{x}\stackrel{}{y}\right)}^{4}}{\frac{{\left({s}_{x}^{2}/{n}_{x}\right)}^{2}}{\left({n}_{x}1\right)}+\frac{{\left({s}_{y}^{2}/{n}_{y}\right)}^{2}}{\left({n}_{y}1\right)}}\text{.}$$ 
$$\left(\stackrel{}{x}\stackrel{}{y}\right)\pm {t}_{1\alpha /2}\mathrm{se}\left(x\stackrel{}{y}\right)\text{.}$$ 
On entry,  ${\mathbf{TAIL}}\ne \text{'T'}$, $\text{'U'}$ or $\text{'L'}$, 
or  ${\mathbf{EQUAL}}\ne \text{'E'}$ or $\text{'U'}$, 
or  ${\mathbf{NX}}<2$, 
or  ${\mathbf{NY}}<2$, 
or  ${\mathbf{XSTD}}\le 0.0$, 
or  ${\mathbf{YSTD}}\le 0.0$, 
or  ${\mathbf{CLEVEL}}\le 0.0$, 
or  ${\mathbf{CLEVEL}}\ge 1.0$. 