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 $s{e}_1$ and $s{e}_2$ are their standard errors, the test statistic is:

$t=\frac{{\hat{\beta }}_1-{\hat{\beta }}_2}{\sqrt{s{e}_1^2+s{e}_2^2}}$,

where:

$p=2\mathrm{Pr}(t_v\ge |t|)$,

$v=\frac{(s{e}_1^2+s{e}_2^2{)}^2}{s{e}_1^4/(n_1-b)+s{e}_2^4/(n_2-b)}$,

$b=$Bessel's correction.