# Vii: Significant Relationships in the Life of a Psychometrician

Rules of Thumb, Shortcuts, Loose Ends, and Other Off-Topic Topics:

Unless you can prove your approximation is as good as my exact solution, I am not interested in your approximation. R. Daryl Bock[1]

Unless you can show me your exact solution is better than my approximation, I am not interested in your exact solution. Benjamin D. Wright[2]

Rule of Thumb Estimates for Rasch Standard Errors

The asymptotic standard error for Marginal Maximum Likelihood estimates of the Rasch difficulty d or ability b parameters is:

[1] I first applied to the University of Chicago because Prof. Bock was there.

[2] There was a reason I ended up working with Prof. Wright.

## 3 thoughts on “Vii: Significant Relationships in the Life of a Psychometrician”

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• In response to a rather shy question about “combining Rasch scores,” my first question is, Are they measuring the same aspect? If no, then you shouldn’t try to combine them. If yes, then, Do you have the original item responses and item difficulties? If yes again, then I would compute a new ability from the basic equation: raw score equals the sum of probabilities, using the pooled set of items. One could also start from the y-residuals, if available, using the relationships in the section “Everything you need to know” in this post.

If all else fails, two or more measures of the same aspect, taken close enough in time, could be combined by a weighted average, using reciprocals of the standard errors as weights.

If they weren’t taken close together in time, then you can compare them, analyze them, plot them, but I wouldn’t combine them. “Close together in time” means the object hasn’t had opportunity to change.

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• My second question should have been, “Are the two Rasch scores equated?” If so, then I stick to my last response. If not, they would need to be equated, which you could do if have several dozen, ideally more, people with measures on both scales. That would be the process described in the two posts on linking and equating.

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