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Table 1.

Percentage of 1000 simulations meeting the specific significance level in a given test.

Selected flares Signalness Nsrc Mean A.I.
Flaring sources
Mean flux density
(Y/N) p ≤ 3σ p ≤ 2σ p ≤ 3σ p ≤ 2σ p ≤ 3σ p ≤ 2σ
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Any N 1158 6.3 33.1 0.3 16.3 0 0.2
≥ Median N 1158 46.8 88.1 9.2 57.1 0 0.8
Maximum N 1158 100 100 70.9 100 0 0.9
Median Y 1158 15 50.7 1.7 31.1 0 1.6
Maximum Y 1158 41.5 82.3 10.8 67.9 0 1.4
Median, no flux cut Y 5000 0.1 40.2 0.1 13.5 0 0
Maximum, no flux cut Y 5000 0.5 97.8 0.9 60.7 0 0
Median, ≥0.5 Jy Y 5000 4.6 56 7.1 37.1 100 100
Maximum, ≥0.5 Jy Y 5000 60.4 98.9 43.0 82.9 100 100
Median, ≥1.0 Jy Y 5000 4.0 84.1 40.1 78.7 100 100
Maximum, ≥1.0 Jy Y 5000 42.8 100 94.9 100 100 100

Notes. Column (1) indicates which flares were selected to be associated with neutrinos and in the case of 5000 simulations also which flux density cutoff was used to pick the associated sources. Column (2) indicates whether the signalness of the neutrinos was accounted for in the simulations. Column (3) gives the number of sources in the simulation where 1158 mimics the real CGRaBS sample of H21 and 5000 the new OVRO monitoring sample. Columns (4) and (5) give the fraction of simulations (in %) that have smaller post-trial p-value than 3σ (Col. 4) or 2σ (Col. 5) when looking at the mean activity index of the associated samples. Columns (6) and (7) give the same information for the test with the number of flaring sources, and Cols. (8) and (9) for the mean flux density of the associated sample (see text for details). The significance for the CGRaBS sample in H21 (without accounting for the trial factor due to multiple studied samples) was 2.3σ (p-value = 0.01) for the mean A.I., 2.8σ (p-value = 0.005) for the number of flaring sources, and 2.0σ (p-value = 0.027) for the mean flux density.

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