Semantic and cognitive tools to aid statistical science: replace confidence and significance by compatibility and surprise

Table 1 P-values and binary S-values, with corresponding maximum-likelihood ratios (MLR) and deviance (likelihood-ratio) statistics for a simple test hypothesis H under background assumptions A

P-value p (compatibility of H with data given A)	S-value s = −log₂(p) (information against H given A in bits)	Maximum-likelihood ratio against H given A	Deviance statistic 2ln(MLR)
0.99	0.014	1.00	0.00016
0.90	0.15	1.01	0.016
0.50	1.00	1.26	0.45
0.25	2.00	1.94	1.32
0.10	3.32	3.87	2.71
0.05	4.32	6.83	3.84
0.025	5.32	12.3	5.02
0.01	6.64	27.6	6.63
0.005	7.64	51.4	7.88
0.0001	13.3	1935	15.1
5 sigma^a (~ 2.9 in 10 million)	21.7	5.2 × 10⁵	26.3
1 in 100 million (GWAS)	26.6	1.4 × 10⁷	32.8
6 sigma^a (~ 1 in a billion)	29.9	1.3 × 10⁸	37.4

^a5 and 6 sigma cutoffs are the upper standard-normal tail probabilities at 5 and 6 standard deviations above the mean [51]

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