Editing Bayes factor (section)

== Interpretation ==
A value of ''K'' > 1 means that ''M''<sub>1</sub> is more strongly supported by the data under consideration than ''M''<sub>2</sub>. Note that classical [[hypothesis testing]] gives one hypothesis (or model) preferred status (the 'null hypothesis'), and only considers evidence ''against'' it. The fact that a Bayes factor can produce evidence ''for'' and not just against a null hypothesis is one of the key advantages of this analysis method.<ref>{{cite journal |last1=Williams |first1=Matt |last2=Bååth |first2=Rasmus |last3=Philipp |first3=Michael |title=Using Bayes Factors to Test Hypotheses in Developmental Research |journal=Research in Human Development | date=2017 |volume=14 |issue=4 |pages=321–337 |doi=10.1080/15427609.2017.1370964|url=https://osf.io/88c5k/ }}</ref> 

[[Harold Jeffreys]] gave a scale ('''Jeffreys' scale''') for interpretation of <math>K</math>:<ref>{{cite book | url = https://books.google.com/books?id=vh9Act9rtzQC&pg=PA432 |first = Harold |last = Jeffreys |title = The Theory of Probability |edition=3rd |location= Oxford, England |orig-year=1961 |page = 432 |year = 1998 |isbn = 9780191589676 }}</ref>

{{alternating rows table|class=wikitable style="text-align: center; margin-left: auto; margin-right: auto; border: none;"}}
! ''K'' !! dHart !! bits !! Strength of evidence
|-
| '''< 10<sup>0</sup>''' || < 0 || < 0 || Negative (supports ''M''<sub>2</sub>)
|-
| '''10<sup>0</sup> to 10<sup>1/2</sup>''' || 0 to 5 || 0 to 1.6 || Barely worth mentioning
|-
| '''10<sup>1/2</sup> to 10<sup>1</sup>''' || 5 to 10 || 1.6 to 3.3 || Substantial
|-
| '''10<sup>1</sup> to 10<sup>3/2</sup>''' || 10 to 15 || 3.3 to 5.0 || Strong
|-
| '''10<sup>3/2</sup> to 10<sup>2</sup>''' || 15 to 20 || 5.0 to 6.6 || Very strong
|-
| '''> 10<sup>2</sup>''' || > 20 || > 6.6 || Decisive
|-
|}

The second column gives the corresponding weights of evidence in [[hartley (unit)|decihartley]]s (also known as [[deciban]]s); [[bit]]s are added in the third column for clarity. The table continues in the other direction, so that, for example, <math>K \leq 10^{-2}</math> is decisive evidence for <math>M_2</math>.

An alternative table, widely cited, is provided by Kass and Raftery  (1995):<ref name=kassraftery1995/>

{{alternating rows table|class=wikitable style="text-align: center; margin-left: auto; margin-right: auto; border: none;"}}
! log<sub>10</sub> ''K'' !! ''K'' !! Strength of evidence
|-
| '''0 to 1/2''' || 1 to 3.2 || Not worth more than a bare mention
|-
| '''1/2 to 1''' || 3.2 to 10 || Substantial
|-
| '''1 to 2''' || 10 to 100 || Strong
|-
| '''> 2''' || > 100 || Decisive
|-
|}
According to [[I. J. Good]], the [[just-noticeable difference]] of humans in their everyday life, when it comes to a change [[Bayesian probability|degree of belief]] in a hypothesis, is about a factor of 1.3x, or 1 deciban, or 1/3 of a bit, or from 1:1 to 5:4 in odds ratio.<ref>{{cite journal |last=Good |first=I.J. |author-link=I. J. Good |year=1979 |title=Studies in the History of Probability and Statistics. XXXVII A. M. Turing's statistical work in World War II |journal=[[Biometrika]] |volume=66 |issue=2 |pages=393–396 |doi=10.1093/biomet/66.2.393 |mr=548210}}</ref>