welch.apple

λxs.λys.
{
  sum ⇐ [(+)/x];
  𝜇 ⇐ λxs.λn. sum xs%n;
  𝜎 ⇐ λxs.λn. {𝜇 ⟜ 𝜇 xs n; sum ([(x-𝜇)^2]'xs)%(n-1)};
  xsn ⟜ ℝ(:xs); ysn ⟜ ℝ(:ys);
  s₁ ⟜ 𝜎 xs xsn; s₂ ⟜ 𝜎 ys ysn;
  sn₁ ⟜ s₁%xsn; sn₂ ⟜ s₂%ysn;
  s ⟜ (sn₁+sn₂);
  t ← (𝜇 xs xsn-𝜇 ys ysn)%√s;
  -- Welch–Satterthwaite equation
  𝜈 ← s^2%((sn₁^2)%(xsn-1)+(sn₂^2)%(ysn-1));
  (t,𝜈)
}