  For a partition $\lambda \vdash n$, we let $\operatorname{pd}(\lambda)$, the
parity difference of $\lambda$, to be the number of odd parts of $\lambda$
minus the number of even parts of $\lambda$. We show that as $n\to \infty$, the
normalised parity difference $n^{-\frac 14}\operatorname{pd}(\lambda)$ for
partitions of $n$ into distinct parts is normally distributed with mean $0$ and
variance $\frac{\sqrt{3}}{\pi}$. We also establish analogous results for
generalised parity differences modulo $N$.
