Recently, Richard Stanley formulated a new partition function $t(n)$. This function counts the number of partitions $\pi$ for which the number of odd parts of $\pi$ is congruent to the number of odd parts in the conjugate partition $\pi'$ egthickspace $\pmod{4}$. G. E. Andrews has recently proven a nice generating function for $t(n)$ in terms of the generating function for $p(n)$, the usual partition function. He also showed that the egthickspace $\pmod{5}$ Ramanujan congruence for $p(n)$ also holds for $t(n)$. In light of these results, it is natural to ask the following questions: What is the size of $t(n)$? Are there other congruences satisfied by both $t(n)$ and $p(n)$? We will address both of these questions.