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Table 2.

Estimators of the consistency between our fiducial 3 × 2 pt analysis and the Planck Collaboration VI (2020) TTTEEE+lowE results.

Metric Reference Value PTE PTE [σ]
τ Eq. (8) 3.1 3.1σ
dH Eq. (G.1) 0.95 3.1σ
pS Eq. (G.3) 0.9981 0.0019 3.1σ

R Eq. (9) 23 ± 6
lnR Eq. (G.5) 3.1 ± 0.3
lnS Eq. (G.4) −2.0 ± 0.1 0.08 ± 0.02 1.8 ± 0.1σ
QDMAP Eq. (G.10) 9.5 0.037 2.1σ
QUDM Eq. (G.11) 7.7 0.054 1.9σ

Notes. The considered tension metrics are: (1) the differences between the means in S8, divided by the standard deviations added in quadrature, τ; (2) the Hellinger distance, dH, between S8 posterior distributions (Appendix G.1); (3) the fraction of the S8 parameter shift distribution that has a higher probability than no shifts (Appendix G.2); (4) the Bayes ratio R between a model that assumes a single cosmology for both our 3 × 2 pt and the Planck data, and a model that uses separate cosmologies for the two data sets; (5) the logarithm lnR of the Bayes ratio; (6) the suspiciousness lnS (Handley & Lemos 2019; 7) and (8) the concordance-discordance estimators QDMAP and QUDM (Raveri & Hu 2019). The columns list the estimator metric considered, the relevant equation reference, the measured value, and the ‘probability-to-exceed’ the measured value (PTE), under the assumption that the two data sets are consistent.

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