Table 2.

Values of the log-likelihood statistic |$\Pi _S$|⁠, defined in equation (10) based on the null distribution of the power entropy, |$S(l)$|⁠, are listed in second column for various data sets listed in first column. The statistic values mentioned against different data releases were evaluated using the distribution obtained from a corresponding simulation ensemble of 1000 mocks. The p-values of |$\Pi _S$| thus obtained are given in the third column. The likelihood-based p-values are smaller than those of Table 1, which are evaluated with a cut-off of |$p \le 0.05$|⁠. This is evidence that using a hard cut-off on assessing multiple p-values tends to create a bias against detecting a signal.

Data set|$\Pi _S$|p-value
WILC 1 yr75.5100.033
WILC 3 yr72.7790.067
WILC 5 yr74.9400.042
WILC 7 yr78.6640.018
WILC 9 yr75.6030.028
PR1 ILC78.8240.013
PR2 smica74.7360.035
PR3 smica77.4830.019
Data set|$\Pi _S$|p-value
WILC 1 yr75.5100.033
WILC 3 yr72.7790.067
WILC 5 yr74.9400.042
WILC 7 yr78.6640.018
WILC 9 yr75.6030.028
PR1 ILC78.8240.013
PR2 smica74.7360.035
PR3 smica77.4830.019
Table 2.

Values of the log-likelihood statistic |$\Pi _S$|⁠, defined in equation (10) based on the null distribution of the power entropy, |$S(l)$|⁠, are listed in second column for various data sets listed in first column. The statistic values mentioned against different data releases were evaluated using the distribution obtained from a corresponding simulation ensemble of 1000 mocks. The p-values of |$\Pi _S$| thus obtained are given in the third column. The likelihood-based p-values are smaller than those of Table 1, which are evaluated with a cut-off of |$p \le 0.05$|⁠. This is evidence that using a hard cut-off on assessing multiple p-values tends to create a bias against detecting a signal.

Data set|$\Pi _S$|p-value
WILC 1 yr75.5100.033
WILC 3 yr72.7790.067
WILC 5 yr74.9400.042
WILC 7 yr78.6640.018
WILC 9 yr75.6030.028
PR1 ILC78.8240.013
PR2 smica74.7360.035
PR3 smica77.4830.019
Data set|$\Pi _S$|p-value
WILC 1 yr75.5100.033
WILC 3 yr72.7790.067
WILC 5 yr74.9400.042
WILC 7 yr78.6640.018
WILC 9 yr75.6030.028
PR1 ILC78.8240.013
PR2 smica74.7360.035
PR3 smica77.4830.019
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