Distribution of inferred S₈ values from 100 realisations of the data vector sampled from the covariance matrix. Left: the distribution of the maximum of the marginal distribution for S₈. Results are shown for COSEBIs (orange), band powers (pink) and 2PCFs (cyan). For comparison we show a Gaussian distribution centred at the input value of S₈ and a standard deviation equal to the mean of the individual standard deviations for each realisation and set of two-point statistics (grey dashed curve). Right: the difference between the S₈ posterior modes of pairs of two-point statistics (as indicated in the legend) given the same noise realisation. The same reference Gaussian distribution is shown in grey (dashed curve) but centred on zero.