Ordinals are not just about order. That's certainly a primary use, but for some specific ordinal scales, specific operations are defined that give (quasi) meaningful results when performed upon the numbers. There's no general case, and additionally, I think that many of the specific defined operations fail any sort of rigor test at all. But never-the-less, they are defined and used in clinical contexts. That's an additional reason why the ordinal equivalent in ISO 21090 has a real number for value, not an integer. And for this reason, openEHR should probably have a real too. But I don't see a path from here to there, as it were
Grahame On Wed, Apr 21, 2010 at 7:49 PM, Thomas Beale <thomas.beale at oceaninformatics.com> wrote: > > Hi Mark, > > the openEHR model of 'ordinals' (right or not) is that each ordinal value is > an association of an integer with a symbol (which could be words, but also > anything else like '++'). The numbers are used to make the ordering > computable - in fact this is the definition of the 'ordinal' concept in > openEHR - that there is order without otherwise any proper scaled notion of > magnitude. > > This data type (DV_ORDINAL) is used in at least two ways (wrongly or > rightly): > > to model scales of symbols, such as 'none', '+', '++', '+++' and so on > (maybe pain, reaction, urinalysis analytes), where there are otherwise no > numerics built into the published scale - i.e. someone had to invent them > when creating archetypes or other openEHR artefacts > to model scales whose values are primarily expressed as numerics and whose > 'symbols' are just words > to model scales of numbers like Apgar and Barthel, where the primary > expression of 'value' is numeric, and the numbers are meant to be added up, > and the 'symbol' is in fact a term, i.e. explanatory phrase > > doing this has the desired effect in all cases of establishing computable > ordering between adjacent members (since computers don't understand that > '++' is somehow 'less than' '+++'). But it is clear that there are > downsides: > > in the first case above, it is us (i.e. archetype modellers) adding > arbitrary numbers to make the scale of values computable > in the second and third cases, there is no obvious reason why real numbers > should not be chosen, especially in the last case above, since the values > might be carefully chosen to make the subsequent additions have a certain > effect. > > At the very least it seems that we need is the ability to use real numbers > as well as just integers. Maybe there is more to it - I certainly don't have > a good enough feel for the use of these kinds of scales in medicine, nor > their implied semantics. With respect to literature, I have to admit we did > not find anything much on ordinal scales, although we tried to stick to > well-known notions of accuracy, precision, units etc in the design of the > main quantitative data types in openEHR (also proper mathematical notions > which lead to meaningful operations, e.g. + and - being defined on true > 'amounts' but not on dates). If you know of any literature on this topic of > scale design, I am sure it would be helpful here. > > - thomas > > On 21/04/2010 09:12, Mark Leaning wrote: > > I am hesitant to enter this discussion, but here goes. > > > > An assessment scale which assigns a numeric score as well as a symbol/term > is not an ordinal scale. The symbols do in fact comprise an ordinal scale > (?very low? < ?low? etc). However the numerics provide something else ? > usually to be added up with other scores. The designers of such scales are > bound to validate the composite numeric scores (cf SF36). > > > > What you then have is ordinal symbol + real number. If the scale designer > needs to use decimals, that is their choice. > > > > It might be worth looking at the measurement theory literature. > > > > Cheers > > Mark > > > > Mark S Leaning PhD > > _______________________________________________ > openEHR-clinical mailing list > openEHR-clinical at openehr.org > http://lists.chime.ucl.ac.uk/mailman/listinfo/openehr-clinical >
