Fig. 4

The probability ratio overcomes pre-sort abundance biases when carrying out between-group comparisons. a Simulations were carried out as in Fig. 3 with an additional 30 samples that were initiated with an exaggerated abundance of Species 10 (cases). This plot shows the species abundances in these case and control samples’ pre-sort, IgA⁺ and IgA⁻ fractions using the thresholds as in Fig. 3b. b Differences in the IgA⁺ and IgA⁻ fraction sizes as a percentage of total bacteria between cases and controls. P value shown from Mann-Whitney tests. c Heatmaps showing the scores estimated by the Kau and probability ratios across all samples. d Comparison of IgA binding scores for the ten species in cases and controls when using either the Kau score or the probability ratio. Significant differences are highlighted with * (FDR adjusted Mann-Whitney p < 0.05) and species are ordered by true IgA binding value. In all boxplots the boxes represent the median and interquartile range and the whiskers the largest and smallest values within one and half IQR of the upper and lower IQR limits. In (d), points outside this range are shown