Re: Comparing different scales

On 25 Nov 2005 13:14:01 -0800, "John Uebersax" <jsuebersax@xxxxxxxxx>
wrote:

> I like Rich's suggestion about transforming the reaction time variable.

That was Ray's suggestion. I'm not sure what shape was
going to result, which might matter.

>
> But, once that's done, I'm not yet convinced that there's a problem
> with subtracting z scores.

I couldn't understand what the OP's objection was.

I thought that Ray's suggestion of using outside
criteria was good, but unlikely to be available - I thought
that he was approaching what I see as a problem of
different *reliabilities* for the scores.

Or, to be more precise, there is a problem (perhaps)
of different *validity* coefficients, where validity is
in measuring the latent entity is always less than the
reliability.

For instance, if a subject has a measured z-score of
2.0 on each scale, the "true-score" estimates of his
tendencies are less -- multiply by the factor of the validity
to see the true-scores, which could be (say) 1.6 and 1.4.

>
> True, with z scores you lose track of whatever mean difference might
> exist between explicit and implicit self-esteem were both constructs
> measured on a common scale. That is, suppose, averaged over all
> people, implicit self-esteem is x "units" higher than explicit
> self-esteem. You'd lose that information with z-score subtraction.
>
> But if you're trying to correlate (ROSE - ISE) with other variables,
> such an overall mean difference doesn't matter, does it?
>
> A similar argument could be made for subtracting ranks on the two
> variables.

Yes, it is really hard to see how to get an anchoring that
is outside of the sample.

My own idea for what to do with these data was simpler:

If the one score is "integers from 1-7",
and the second is "times in msecs", then
recode the times into seven categories with
approximately the same counts, respectively,
in the ascending categories.

The resulting difference is somewhat transparent,
by reference to the original 7 categories.
And it doesn't pretend to the precision that
might be attributed to a z-score.



--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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