Engineered to detect subtle anomalies, ensemble null tests examine the full multivariate structure of repeated observations rather than reducing them to a single number. They compare the distribution of data points to that of a reference ensemble built from simulations or other observations, exposing patterns that otherwise escape standard checks. In simulations of the cosmic microwave background (CMB), these tests identified systematic effects that standard χ² diagnostics failed to flag.

The core idea behind the test is called PQM‑ASS. It partitions the measurement space into Voronoi cells around reference points and counts how many data and reference vectors fall into each cell. By comparing these proportions, the test retains joint correlations and directional information typically lost when observations are simply averaged or compressed into a scalar. The method is non‑parametric and does not rely on a Gaussian model or a complete covariance matrix.

When applied to mock CMB spectra, the PQM‑ASS test achieved higher detection rates than established multivariate methods—Hotelling’s T², Kolmogorov–Smirnov χ², Fisher χ², and a per‑spectrum χ²—across six different injected systematic errors. Using ensembles of 100 spectra, PQM‑ASS flagged contamination 50 % more often at a nominal 5 % false‑positive rate than the next best test. Even with smaller ensembles of 20 spectra, its performance stayed robust.

Traditional single‑number χ² summaries discard directional and joint structure. They can be mis‑calibrated when covariance estimates are inaccurate or when observations are coadded, which smooths out observation‑to‑observation variation that may contain the very signal indicating contamination. Averaging repeated measurements before testing can therefore suppress detectable contamination entirely.