[Fis] June 2020 Posts

[Loet Leydesdorff]

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
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