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.
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.
Details #
Largely following Claude Shannon, one of the pioneers of information theory, the s-index is
$$s=-log_{2}{p}$$
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.
| wdt_ID | wdt_created_by | wdt_created_at | P value | wdt_last_edited_by | wdt_last_edited_at | S value |
|---|---|---|---|---|---|---|
| 1 | chris | 07/09/2025 08:44 PM | 0.500 | chris | 07/09/2025 08:44 PM | 1.00 |
| 2 | chris | 07/09/2025 08:44 PM | 0.050 | chris | 07/09/2025 08:44 PM | 4.32 |
| 3 | chris | 07/09/2025 08:44 PM | 0.010 | chris | 07/09/2025 08:44 PM | 6.64 |
| 4 | chris | 07/09/2025 08:44 PM | 0.005 | chris | 07/09/2025 08:44 PM | 7.64 |
| 5 | chris | 07/09/2025 08:44 PM | 0.001 | chris | 07/09/2025 08:44 PM | 9.97 |
So the less likely the new event/finding was the more information it conveys to us. When working from a traditional NHST (Null Hypothesis Significance Test) p value all this is doing really is to replace a rather arbitrary, verging on silly, binary decision: “p<.05” versus “NS” with a continuous value. This has a bit in common with the logic of odds ratios and much in common with Bayesian ways of thinking about statistics though, to some extent, information theory is a sort of parallel realm to statistics.
If you want more explanation, there is a bit more in my shiny app that converts p values to S values, see below.
Try also #
Chapters #
Not covered in the OMbook.
Online resources #
- For those using R who might find it useful I have created a little function getSvalFromPval() in my R package: CECPfuns.
- For the less geeky, I have also added to my shiny apps one that takes a p value and gives you the S value: https://shiny.psyctc.org/apps/get_Sval_from_Pval/. That also has a bit more explanation of S values than I have given here (so far), have a look at that for more explanation of S values.
Dates #
First created 7.ix.25.
