[Fis] June 2020 Posts

[Michel Petitjean]

Dear Loet,
I doubt that the square root of (observed - expected) makes sense: is the
quantity inside parentheses always non-negative?
May be you meant a chi-2 test on a 2x2 contingency table
http://www.stat.yale.edu/Courses/1997-98/101/chisq.htm
Best regards,
Michel.

Michel Petitjean
Université de Paris, BFA, CNRS UMR 8251, INSERM ERL U1133, F-75013 Paris,
France
Phone: +331 5727 8434; Fax: +331 5727 8372
E-mail: petitjean.chiral at gmail.com (preferred),
        michel.petitjean at univ-paris-diderot.fr
http://petitjeanmichel.free.fr/itoweb.petitjean.html

Le dim. 5 juil. 2020 à 17:01, Loet Leydesdorff <loet at leydesdorff.net> a
écrit :

> Dear Marcus and colleagues:
>
>
> – I enjoyed your re-examination of Bateson’s `difference that makes a
> difference’. I seem to recall him also saying `differences themselves must
> be differentiated’. For my own purposes/thinking, I reframe this as
> `differentiated(/ing) differences’ which then ties to `levels’, and `levels
> of abstraction’ noted by Korzybski (although I have never see him
> articulating those levels?). Still, a `difference that makes a difference‘
> I believe points to specific `meta levels’, but where `differentiated
> differences’ points to a meta-meta (general/universal/priamry) informatic
> level. This meta versus meta-meta perspective is yet another way of viewing
> (I believe) primary and secondary roles.
>
> On second thought, it seems to me that a simple and most appropriate
> measure for the difference that one difference makes for another could be
> chi-square statistics.
>
> For example, one can ask whether a specific treatment makes a difference
> differently for man and women. The two variables can be cross-tabled as in
> Table 1.
>
> Observed Treatment  No treatment
> male 156 63 219
> female 86 74 160
> 242 137 379
> This table with observed values may make a difference with reference to
> the expected values. The latter are determined using the margin totals:
>
> Expected Treatment  No treatment
> male 140 79 219
> female 102 58 160
> 242 137 379
> for example for the first cell: 219 * 242/ 379 = 140.
>
> Each corresponding cell contributes to the chi-square with the so-called
> standardized residual to the chi-square:
>
> The residual of the chi-square is the square root of this:
>
>
>  This is a *z-*statistic. For the four cells of the matrix, we can derive:
> Treatment No Treatment
> male -1.37 1.82
> female 1.60 -2.13
>
> The difference between expected and observed is only significant (p <.05)
> for women without treatment:* z *= - 2.13. The threshold is 1.96 for the
> 5% level. The z-values can directly be used for the measurement of
> Bateson's information : "a difference that makes a difference. The
> difference of receiving treatment makes a difference for all four
> categories, but this difference is in tis case only significant for women
> without treatment.
>
> Thus, Bateson-type information can be measured. There is also a link to
> Shannon-type information via the log-likelyhood chi-square (which is a
> Shannon-type measure.)
>
> Problems solved? One can measure the value of the difference that makes a
> difference.
>
> Best,
> Loet
>
> _______________________________________________
> Fis mailing list
> Fis at listas.unizar.es
> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
> ----------
> INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
>
> Ud. recibe este correo por pertenecer a una lista de correo gestionada por
> la Universidad de Zaragoza.
> Puede encontrar toda la información sobre como tratamos sus datos en el
> siguiente enlace:
> https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas
> Recuerde que si está suscrito a una lista voluntaria Ud. puede darse de
> baja desde la propia aplicación en el momento en que lo desee.
> http://listas.unizar.es
> ----------
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://listas.unizar.es/pipermail/fis/attachments/20200705/3bcba8d6/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: 1.png
Type: image/png
Size: 7273 bytes
Desc: not available
URL: <http://listas.unizar.es/pipermail/fis/attachments/20200705/3bcba8d6/attachment-0002.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: 2.png
Type: image/png
Size: 6918 bytes
Desc: not available
URL: <http://listas.unizar.es/pipermail/fis/attachments/20200705/3bcba8d6/attachment-0003.png>