Re:measuring distances in grid space

Devi Jankowicz (
Fri, 28 May 1999 22:57:41 +0000

Tony Downing writes,


>But of course the whole enterprise is probabilistic, in that if you did the
>grid all over again you'd probably get different factors and factor

Depends what the grid was about, whether the person changed his or her
mind, and so on?

>But at this stage of deriving a distance, aren't we just wanting to know
>how far it is between those points, and the fuzziness of the entire
>enterprise has receded into the background ofour minds. (?)

You know how the clusters shown in a cluster analysis ought to "feel
right" to the person who provided the constructs and ratings? Looking at
the ratings and seeing how they have been clustered may have some
(In a grid on 'My Colleagues':
'Have you ever noticed that, whenever you talk of a colleague as being
"Dependable", you also tend to rate him/her as "Friendly"; and whenever
you rate a colleague as "Not very trustworthy", you also rate him/her as
"A bit stand-offish" ?'
'Oo-er. Really?'
'Well, look at the clusters: those two constructs are very highly matched
at 95%: the ratings only differ on one of the elements.'
'Gosh, yes. I see what you mean. Yes, actually, I do tend to think that
way now you mention it.'
'Well, that's only the case for these particular people; now, if we'd
included old Fred in the grid, then the match wouldn't have been so high,
you know...'
Or, of course,
'Nah, that's just a coincidence cos I used those ratings for those
people. Generally speaking I don't tend to make that particular
association about people.')

But, if there's any structure in a grid, people usually are able to
express feelings of 'ownership' to a greater or lesser degree.

Now, a little gobsmacked by Patrick's example of different grid distance
metrics as sent in this last e-mail and not really having the wit to
follow his correspondence with J. Maxwell in any sort of detail, I was
nevertheless reminded that I once offered a small number of students two
variants of a grid each had provided me with. One was cluster-analysed
using sums of distances, and the other using sums of (distances squared).
Having shown them how to read back a dendrogram, I asked them which felt
more "right" as a representation of their construct structure. To a man
(they were all male!) they preferred the sums of (distances squared)
variant, which surprised me, since the dendrograms tended to be flatter,
i.e., less obviously delineated clusters and in that sense, less readily
interpretable at a first glance.

It was really a case of mucking about, and I never did anything further
with this. Just a curio that you might find relevant to the current

Kind reegards,