Pre-Registering the Detectable Effect: A Paired-MDE Budget for 4-bit Quantization Benchmarks, with a Pilot Audit

Abstract

This is a planning-method note with an unpaired pilot audit. We adapt the classical paired-binary sample-size calculation (Miettinen, 1968) to quantization benchmarks, giving a conservative minimum detectable effect (MDE) bound $δ^{*} \le (z_{1-α/2}+z_{1-β})\sqrt{ρ_d/m}$ in the paired item count $m$ and the FP16-NF4 disagreement rate $ρ_d$. The bound turns "how reliable is my quantization claim?" into a one-line budget a benchmark designer can commit to before running. We illustrate the bound on four models and four benchmarks ($k=5$ splits of $n=100$), and add a parallel MMLU prompt-template study to put the bound's quantization-noise scale alongside the prompt-noise scale. Assuming $ρ_d=0.10$ (an unmeasured planning value), all observed NF4-FP16 deltas fall below the implied MDE, and most cross-split SDs lie within $\pm 1.5$ pp of the binomial reference $\sqrt{p(1-p)/n}$, so much of the variance reported as "benchmark unreliability" on $n=100$ subsamples is binomial sampling noise. The single borderline cell (OPT-WinoGrande, $|Δ|=3.2$ pp) is below the implied MDE at $ρ_d=0.10$ but above it at $ρ_d=0.05$, illustrating the planning trade-off the bound makes explicit. On MMLU, prompt-template ranges of 2-10 pp meet or exceed the largest observed quantization delta (3.2 pp), so a quantization audit that does not first fix the prompt template absorbs template variance into its noise floor. We complement the bound with a five-line pre-registration template.