{"id":5071,"date":"2025-09-07T21:16:53","date_gmt":"2025-09-07T19:16:53","guid":{"rendered":"https:\/\/www.psyctc.org\/psyctc\/?post_type=docs&p=5071"},"modified":"2025-09-07T21:18:07","modified_gmt":"2025-09-07T19:18:07","password":"","slug":"s-value-index-self-information-surprisal","status":"publish","type":"docs","link":"https:\/\/www.psyctc.org\/psyctc\/glossary2\/s-value-index-self-information-surprisal\/","title":{"rendered":"S value\/index, self-information, surprisal"},"content":{"rendered":"\n

I think this may be the index with more names than any other, s-value, s-index (or without the hyphens), “self-information”, surprisal [index | value], information content and Shannon information are all names for this same index.<\/p>\n\n\n\n

The basic idea is nice and simple: it is that an improbable (suprising) new finding has more weight, conveys more information to us, than a less improbable one.<\/p>\n\n\n\n

Details<\/h4>\n\n\n\n

Largely following Claude Shannon, one of the pioneers of information theory, the s-index is <\/p>\n\n\n\n

$$s=-log_{2}{p}$$<\/p>\n\n\n\n

So converting from probabilities of new information, which is what a p value of frequentist statistical significance test is telling us, we have this table mapping from p to S.<\/p>\n\n\n\n

\n \n \n\n \n \n \n \n\n\n wdt_ID<\/th> wdt_created_by<\/th> wdt_created_at<\/th> P value<\/th> wdt_last_edited_by<\/th> wdt_last_edited_at<\/th> S value<\/th> <\/tr>\n<\/thead>\n \n\n \n \n\n\n
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1<\/td>\n chris<\/td>\n 07\/09\/2025 08:44 PM<\/td>\n 0.500<\/td>\n chris<\/td>\n 07\/09\/2025 08:44 PM<\/td>\n 1.00<\/td>\n <\/tr>\n
2<\/td>\n chris<\/td>\n 07\/09\/2025 08:44 PM<\/td>\n 0.050<\/td>\n chris<\/td>\n 07\/09\/2025 08:44 PM<\/td>\n 4.32<\/td>\n <\/tr>\n
3<\/td>\n chris<\/td>\n 07\/09\/2025 08:44 PM<\/td>\n 0.010<\/td>\n chris<\/td>\n 07\/09\/2025 08:44 PM<\/td>\n 6.64<\/td>\n <\/tr>\n
4<\/td>\n chris<\/td>\n 07\/09\/2025 08:44 PM<\/td>\n 0.005<\/td>\n chris<\/td>\n 07\/09\/2025 08:44 PM<\/td>\n 7.64<\/td>\n <\/tr>\n
5<\/td>\n chris<\/td>\n 07\/09\/2025 08:44 PM<\/td>\n 0.001<\/td>\n chris<\/td>\n 07\/09\/2025 08:44 PM<\/td>\n 9.97<\/td>\n <\/tr>\n <\/tbody> \n\n \n \n \n <\/table>\n\n<\/div>