---
title: "S value/index, self-information, surprisal"
description: "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…"
url: "https://www.psyctc.org/psyctc/glossary2/s-value-index-self-information-surprisal/"
updated: "2026-06-01"
category: All OM book glossary entries
---

# S value/index, self-information, surprisal

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

- [Null hypothesis significance testing (NHST)](https://www.psyctc.org/psyctc/glossary2/null-hypothesis-significance-testing-nhst-paradigm/)
- [Odds ratios](https://www.psyctc.org/psyctc/glossary2/odds-odds-ratio/)
- Probability

#### 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](https://cecpfuns.psyctc.org/index.html).
- For the less geeky, I have also added to [my shiny apps](https://shiny.psyctc.org/index.html) one that takes a p value and gives you the S value: [https://shiny.psyctc.org/apps/get_Sval_from_Pval/](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.