Re: Grid Reflection

Rue L. Cromwell (cromwell@KUHUB.CC.UKANS.EDU)
Thu, 11 Jan 1996 11:10:03 +0000

The simplist way to handle reflection, if you are doing a Pearson
correlation matrix (or any other degree of relationship matrix) is to
reverse the sign and reverse the construct and contrqst poles (labels) of
the construct to be reflected. This can be done either at the summary table
of principal components analysis (Depending upon the factor solution, you
may want to reflect everything to negative rather than everything to
positive, although this is rare).

An earlier level at which this can be done is in the correlation matrix
(i.e., reverse sign, reverse the construct and contrast pole labels). What
I have just described involves no mathematical manipulation. You may ignore
any testing of statistical significance at the point of reflection, since,
if a reflected construct is indeed not significant, it will indeed come out
that way anyway in the end product.

Reflection at an earlier stage on the grid itself was done by Kelly (and
later by me and by Fager) during the era before computer applications to
grids. I cannot think of any reason for doing it now.



>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. For example, consider the following two
>hypothetical construct/contasts:
> good/bad
> bad/good
>If the "+" responses of the second construct/contrast were changed to
>"-", and the "-" changed to "+", then the second construct/contrast would
>have been "reflected," and the two constructs would now read:
> good/bad
> good/bad
>Presumably, apart from various sources of error, the two
>construct/contrasts would be identical. The next operational step would
>be to cluster the rows of the grid, and the two "identical"
>construct/contrasts would fall into the same cluster.
>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.
>Prof. Robert Neimeyer has kindly referred us to an article by Nigel MacKay
>(*International J. of Pers. Construct Psych., 1992, pp 57-75).
>Unfortunately, our closest access to this journal seems to be Berkeley,
>California some 800 miles north of us and it would cost too much time
>(several weeks) to obtain a copy of the article -- other economic factors
>require that the work proceed apace and without delay.
>Other procedures for reflecting and recommendations will be most
>greatfully appreciated!
>F. Reid Creech, Ph.D.
>30504 Lilac Road
>Valley Center, CA 92082 USA
>Fax to above number with alerting phone call so faxmodem can be setup.

Rue L. Cromwell