  In this article, we study hook lengths of ordinary partitions and $t$-regular
partitions. We establish hook length biases for the ordinary partitions and
motivated by them we find a few interesting hook length biases in $2$-regular
partitions. For a positive integer $k$, let $p_{(k)}(n)$ denote the number of
hooks of length $k$ in all the partitions of $n$. We prove that $p_{(k)}(n)\geq
p_{(k+1)}(n)$ for all $n\geq0$ and $n\ne k+1$; and $p_{(k)}(k+1)-
p_{(k+1)}(k+1)=-1$ for $k\geq 2$. For integers $t\geq2$ and $k\geq1$, let
$b_{t,k}(n)$ denote the number of hooks of length $k$ in all the $t$-regular
partitions of $n$. We find generating functions of $b_{t,k}(n)$ for certain
values of $t$ and $k$. Exploring hook length biases for $b_{t,k}(n)$, we
observe that in certain cases biases are opposite to the biases for ordinary
partitions. We prove that $b_{2,2}(n)\geq b_{2,1}(n)$ for all $n>4$, whereas
$b_{2,2}(n)\geq b_{2,3}(n)$ for all $n\geq 0$. We also propose some conjectures
on biases among $b_{t,k}(n)$.
