pooled sd

\[s^2_{pool} = \frac {(n_1-1)s^2_1 + (n_2-1)s^2_2} {(n_1 - 1) + (n_2 -1)}\]

Standart error of mean difference:

\[s_{m_1 - m_2} = \sqrt {(s^2_{pool}) (\frac {1} {n_1} + \frac {1}{n_2} )}\]

Independent t-test: \[t = \frac {(m_1 - m_2) - (\mu_1 - \mu_2)} {s_{m_1 - m_2}} = \frac {(m_1 - m_2) - 0} {s_{m_1 - m_2}} = \frac {m_1 - m_2} {s_{m_1 - m_2}}\]