  Let $p_{o}(n)$ (resp. $p_{e}(n)$) denote the number of partitions of $n$ with
more odd parts (resp. even parts) than even parts (resp. odd parts). Recently,
Kim, Kim, and Lovejoy proved that $p_{o}(n)>p_{e}(n)$ for all $n>2$ and
conjectured that $d_{o}(n)>d_{e}(n)$ for all $n>19$ where $d_{o}(n)$ (resp.
$d_{e}(n)$) denote the number of partitions into distinct parts having more odd
parts (resp. even parts) than even parts (resp. odd parts). In this paper we
provide combinatorial proofs for both the result and the conjecture of Kim, Kim
and Lovejoy. In addition, we show that if we restrict the smallest part of the
partition to be $2$, then the parity bias is reversed. That is, if $q_{o}(n)$
(resp. $q_{e}(n)$) denote the number of partitions of $n$ with more odd parts
(resp. even parts) than even parts (resp. odd parts) where the smallest part is
at least $2$, then we have $q_o(n)<q_e(n)$ for all $n>7$. We also look at some
more parity biases in partitions with restricted parts.
