let $*$ be a binary operation on a set $x$ and let $x_0,x_1,\ldots,x_n$ be $x$-valued indeterminate. define two parenthesizations of $x_0*x_1*\cdots*x_n$ to be equivalent if they give the same function from $x^{n+1}$ to $x$. under this equivalence relation, we study the number $c_{*,n}$ of equivalence classes and the largest size $\widetilde c_{*,n}$ of an equivalence class. we have $1\le c_{*,n}\le c_n$ and $1\le \widetilde c_{*,n}\le c_n$, where $c_n := \frac{1}{n+1}{2n\choose n}$ is the ubiquitous catalan number. moreover, $c_{*,n}=1 \leftrightarrow$ $*$ is associative $\leftrightarrow \widetilde c_{*,n}=c_n$. thus $c_{*,n}$ and $\widetilde c_{*,n}$ measure how far the operation $*$ is away from being associative. in this talk we will present various results on the nonassociativity measurements $c_{*,n}$ and $\widetilde c_{*,n}$, and show their connections to many known combinatorial results, assuming $*$ satisfies some multiparameter generalizations of associativity.