[Fis] June 2020 Posts

[Loet Leydesdorff]

Dear Michel,

Any residual with an absolute value which is equal to or greater than 
the tabled critical two-tailed .05 value z 05 = 1.96 is significant at 
the .05 level. Any residual which is equal to or greater than the tabled 
critical two-tailed .01 z 01 = 2.58 is significant at the .01 level. Any 
cell in a contingency table that has a significant residual makes a 
significant contribution to the obtained chi-square value. For any cell 
whit a significant residual, one can conclude that the observed 
frequency of the cell differs significantly from its expected frequency. 
The sign of the standardized residual indicates whether the observed 
frequency of the cell is above (+) or below (-) the expected frequency. 
The sum of the squared residuals for all r x c cells will equal the 
obtained value of chi-square.




Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric 
Statistical Procedures (5th Edition). Boca Raton, FL: Chapman & 
Hall/CRC. p. 672.



>I doubt that the square root of (observed - expected) makes sense: is 
>the quantity inside parentheses always non-negative?
The sign is meaningful: above or below expectation?
>
>May be you meant a chi-2 test on a 2x2 contingency table
>http://www.stat.yale.edu/Courses/1997-98/101/chisq.htm
>
You are right: the formulas were not correctly typed. However, the 
computation and interpretation was correct.
The mail should have been without these typos:

>>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 en 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
>>----------
------------ pr�xima parte ------------
Se ha borrado un adjunto en formato HTML...
URL: <http://listas.unizar.es/pipermail/fis/attachments/20200705/2933766a/attachment-0001.html>
------------ pr�xima parte ------------
A non-text attachment was scrubbed...
Name: 1.png
Type: image/png
Size: 7690 bytes
Desc: no disponible
URL: <http://listas.unizar.es/pipermail/fis/attachments/20200705/2933766a/attachment-0002.png>
------------ pr�xima parte ------------
A non-text attachment was scrubbed...
Name: 1.png
Type: image/png
Size: 7470 bytes
Desc: no disponible
URL: <http://listas.unizar.es/pipermail/fis/attachments/20200705/2933766a/attachment-0003.png>