Consider two forms of sampling from a population: (i) drawing $s$ samples of $n$ elements with replacement and (ii) drawing a single sample of $ns$ elements. In this paper, under the setting where the descending order population frequency follows the Poisson--Dirichlet distribution with parameter $θ$, we report that the magnitude relation of the Fisher information, which sample partitions converted from samples (i) and (ii) possess, can change depending on the parameters, $n$, $s$, and $θ$. Roughly speaking, if $θ$ is small relative to $n$ and $s$, the Fisher information of (i) is larger than that of (ii); on the contrary, if $θ$ is large relative to $n$ and $s$, the Fisher information of (ii) is larger than that of (i). The result represents one aspect of random distributions.