Re: Grid Reflection

Chris Evans (
Sat, 13 Jan 1996 17:38:54 +0000

I launched the following at the list two days ago but ran foul of the
fact that my Email address had changed and, although the list reaches
me, it wouldn't recognise me as a legitimate poster to the list!
While I was sorting that out with the excellent help of the mailbase
administrators (it's one of those catch 22 situations: as it doesn't
recognise you as on the list you can't unsubscribe!) I realised that
my wonderful Mathcad file I mention in the posting below and had
mounted for the occasion wasn't readable over the net as the
MathBrowser uses an earlier engine than that in the version of
Mathcad I used to make the file. Much shuffling of floppies later
and some cursing and I think it's still worth posting this though I
though Rue Cromwell's answer was a model of brevity and sense and was
very intrigued by Devi's (though I don't agree with him about the
choice of matching score over correlation here, surely the ordinal
relationship between ratings of elements is the crucial thing here,
not the end of the pole toward which the ratings are clumped.
However, I think his argument applies perfectly to explain why matching
scores or some other distance measure should be used when considering
relationships between ELEMENTS rather than CONSTRUCTS.

Anyway after all the joys of sorting these IT things out (such as the
glories of IT huh?!) I do hope this isn't too late to be of some use
or at least some amusement to someone!

=========== original message from here on =============
F. Reid Creech said (edited to save bandwidth!)

> Two principle investigators are working with the same 18 x 18
> repertory grid. Columns of the grid represent role stereotypes
> (people) and rows of the grid represent constructs/contrasts.
> Subjects respond "+", "-", or <blank>, corresponding to elements
> which are part of the construct, part of the contrast, or neither
> (it does not apply), respectively.
> Our problem is that of reflecting certain rows of the grid;
> specifically, those rows which seem highly similar to other rows,
> excepting that they are reversed in direction.
> Our specific problem is that of applying a systematic procedure to
> determine which construct/contrasts should be reflected. Which is
> the best procedure?
> Three different approaches have been suggested: (1) One column of
> the grid contains the stereotype "Me as I wold like to be," and
> presumably represents the "Ideal Self." Some column elements
> contain "+", others "-", and others are blank. The procedure is to
> reflect any row where the Ideal Self entry is a "-". (2) Correlate
> two rows of the grid using Pearson Product-Moment correlation.
> Reflect one of the two rows if the correlation is statistically
> significant and negative (ignore bending assumptions underlying
> appropriateness of the significance test). (3) Count the number of
> cases in which a "+" occurs in one row and a "-" occurs in the
> other. Award half of a count for each case in which both rows
> contain matching blanks. Apply binomial probability distribution.
> If the number of matches is greater than 10, then p < .05, so
> reflect one of the rows.
My first reaction is that, provided you are mainly interested in some
form of anchoring to an ideal self concept, option (1) is
overwhelmingly the method of choice.

As to (2), you are right about bending assumptions. If you use a
Kendall tau c and treat the blanks as missing whether blank on
either or both constructs being compared you are not bending any
assumptions as (I think I remember rightly) the tau model doesn't
even assume a sampling model. However, you are throwing away some
information about the matching or non-matching of the blanks though I
don't see any way around that. You're also throwing away some more
information you have about the rating system that is not incorporated
into the rank correlation test (which you have tried to use in your
model (3), see below). However, the main problem I see is the
arbitrary nature of the p <.05 criterion. Why this criterion? Is there a
formal sense in which 1 in 20 is the risk you're willing to run of
reversing a construct where an observed negative correlation could
have arisen on random ratings?

Number 3 is interesting as it pulls back in the fact that you had
a dichotomous rating system supplemented with a "non-applicable"
option. You could apply a strict binomial model if you drop all
elements which have had a blank on one or more of the constructs and
then you have the probabilities and a strict model under which you've
derived them. (Though I don't agree with your equating 10 with the
.05 criterion for n=18. I make binomial(.5,10,18) = .167 and the
cumulative binomial for .5,10,18 = .407.

According to me the cumulative binomial scrapes under the .05
criterion when you have 13 matches (p=.048). Since you may find
yourself with fewer than 18 matchable elements here are the other
"significant" scores according to my calculations:
n criterion score
17 13
16 12
15 12
14 11
13 10
12 10
11 9
10 9
9 8
7 7
6 6
5 5
with four or fewer you can get all matched more often than 1 in 20 on
random matching since .5^4 = .063

I understand the motivation behind your giving a partial score for
matching blanks but it will certainly blow your binomial model out
and it makes it very difficult to model the probabilities for the
multinomial (which could handle the three option model). The problem
is that although the rather crass .5 model of random _AND_
_EQUIPROBABLE_ use of "+" and "-" by your raters is sensible for the
binomial, a .33.. model for use of "+" "-" and blank seems highly
implausible, so much so that probabilities derived from it would be
meaningless I'd say. That, of course, exposes the other problem with
the binomial model: that we have modelled in equal use of "+" and "-"
and, unless you went back to a rating system used in the very early
days of grids for precisely this reason, in which you required this
(you clearly didn't) then the p("+") = p("-") = .5 is clearly deeply
flawed. You can introduce fiddles in which you might use the
observed proportions of "+" and "-" responses in some way but this
gets you even further away from a simple comprehensible and tight

On balance, I'd recommend your model (1) after this thrashing around of
the "statistical" options. Bear in mind the way you will have
focussed the grid onto the ideal self. You might want to note this
and comment in your report on how the reversals would have been
different had you focussed on other elements.

One final thought: why are you concerned about reversing constructs?!

Hope this is helpful and meets your deadline. A Mathcad plus file
modelling the binomial and cumulative binomial distributions for a
related question of the analysing "mismatched cases" studies up at my
WWW site (general URL below) at:
and the browser you'd need to make sense of it is at:
but you'd be better getting from the American vendors:

It's public domain and excellent for animating simple (or very
complex if you can do it, I can't!) maths on the WWW

Best wishes,

Chris Evans, Senior Lecturer, ||| Psychotherapy Section
Cranmer Terrace ||| Dept.Ment.Health.Sci.
London SW17 0RE ||| St. George's Hosp.Med.Sch.
Britain ||| University of London
Tel/fax.: (+44|0) 181 725 2540 ||| Email:
World Wide Web: