Re: Comparing different scales

Uri wrote:
> Thanks for helping out Thom.
>
> I am not interested in predicting one using the other. I want to have,
> for each one of
> my subjects, a score that signifies how large a discrepancy there is
> between his/her
> explicit self esteem (ROSE score) and his implicit self esteem (ISE
> score).
>
> Let's call the thing DSE. If a subject has high ROSE and low ISE I
> would like him to
> have a high (positive) DSE. If he/she has low ROSE and high ISE I would
> like him to
> have a low DSE (a negative value). If they're equal, DSE = 0 :)
>
>
> Thanks,
> Uri.

If the 70 pairs of scores are all the information you have then you
do indeed have a problem, one to which I see no unassailably correct
solution.

First, you may want to do some sort of nonlinear transformation to
one (or both) of the variables. For instance, you may want to replace
the time measure by the logistic cdf of a linear function of time:
y = 1/(1 + exp(a-b*t)), so that both measures are bounded.

If you are willing to assume that the two variables have the same mean
and standard deviation in the population from which your sample was
drawn then standardize each variable separately (or, equivalently,
give one variable the mean and s.d. of the other) and take differences.

Otherwise you're going to have to specify a priori the ratio of the
standard deviations, and the difference between the means relative to
the standard deviations. However, you should recognize that you're
never going to be able to use the data to support the conclusion that
any particular person's true DSE is positive (or negative).

A better solution would be to use both ESE & ISE as predictors in
multiple regressions with several different DVs that are expected on
theoretical grounds to be related to ESE & ISE only through DSE. If
the same relative weights are found for all DVs then those weights
establish the relative units for the two variables, and all that
remains is to find zero. So find another variable on which zero-DSE
people are expected to behave in an a-priori-specifiable way that
distinguishes them from the nonzero-DSE people.

.

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