Independent Samples t-Test - Comparing Two Coefficients

Where ${\hat {\beta }}_{1}$ and ${\hat {\beta }}_{1}$ are two coefficients and $n_{1}$, $n_{2}$ are their effective sample sizes and $se_{1}$ and $se_{2}$ are their standard errors, the test statistic is:

$t={\frac {{\hat {\beta }}_{1}-{\hat {\beta }}_{2}}{\sqrt {se_{1}^{2}+se_{2}^{2}}}}$,

where:

$p=2\Pr(t_{v}\geq |t|)$,

$v={\frac {(se_{1}^{2}+se_{2}^{2})^{2}}{se_{1}^{4}/(n_{1}-b)+se_{2}^{4}/(n_{2}-b)}}$,

$b=$Bessel's correction.