# 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:

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

where:

$p = 2\Pr(t_v \ge |t|)$,
$v = \frac{(se^2_1+se^2_2)^2}{se^4_1/(n_1-b)+se^4_2/(n_2-b) }$,
$b =$Bessel's correction.