We describe the distribution of frequencies ordered by sample values in a random sample of size $n$ from the two parameter GEM$(α,θ)$ random discrete distribution on the positive integers. These frequencies are a $($size$-α)$-biased random permutation of the sample frequencies in either ranked order, or in the order of appearance of values in the sampling process. This generalizes a well known identity in distribution due to Donnelly and Tavaré (1986) for $α= 0$ to the case $0 \le α< 1$. This description extends to sampling from Gibbs$(α)$ frequencies obtained by suitable conditioning of the GEM$(α,θ)$ model, and yields a value-ordered version of the Chinese Restaurant construction of GEM$(α,θ)$ and Gibbs$(α)$ frequencies in the more usual size-biased order of their appearance. The proofs are based on a general construction of a finite sample $(X_1,\dots,X_n)$ from any random frequencies in size-biased order from the associated exchangeable random partition $Π_\infty$ of $\mathbb{N}$ which they generate.