Elucidatory example of the statistical test outlined in Sect. 4. In the top panel, the blue histogram on the right-hand side shows the distribution of the likelihood-ratio test statistic λ evaluated from the mock catalogues that do not include all relativistic RSDs (i.e. under the null hypothesis, ℋ₀, which we try to rule out using the observed data). The red histogram on the left-hand side, instead, displays the distribution of λ in the mock light cones that account for all effects (i.e. under the alternative hypothesis, ℋ₁). The solid and dashed curves represent Gaussian models for the histograms, as is described in the main text. The S/N is a measure of the separation between the two histograms in units of their RMS scatter. The shaded region highlights the realisations in which ℋ₀ is ruled out at the 95% confidence level. The bottom panel only differs from the top one in the fact that the covariance matrix C_𝒪 has been used to compute all likelihood functions. We use this approximation in the remainder of this paper.