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RE: st: Dependent continuous variable with bounded range

From   "Verkuilen, Jay" <>
To   <>
Subject   RE: st: Dependent continuous variable with bounded range
Date   Thu, 17 Apr 2008 00:13:05 -0400

Anders Alexandersson wrote:

>>Other standardized ranges than 0-1 sometimes make more sense. For
example, Celsius uses the range 0-100 rather than 0-1; for what it's
worth, the Swede in me strongly believes that Celsius makes more sense
than, say, Fahrenheit. Does the range 0-10 make more sense than the
range 0-1 for "reputation"?<<

Fahrenheit and Celsius have exactly the same information, i.e., both are interval scales. The measurement theorist in me says that these are affine transformations of a scale that's being treated as interval, i.e., interpretation has not been changed one bit. One may be more used to Celsius or Fahrenheit subjectively, but the information in both scales is exactly the same, unlike degrees Kelvin, or the Imperial equivalent degrees Rankine, at the ratio level of measurement. It is trivial to transform back to the original scale.

>>Is "reputation" a one-dimensional concept that is best measured at the
continuous level as the mean-score of the 3 original variables? Maybe,
but I would not take it for granted. If this would be my analysis, I
would try really hard to get hold of the original raw data to see
empirically what is going on or be cautious about strong conclusions.<<

This is a more important question. If the raw data are not available, however, it is not difficult to compute a reliability coefficient from the covariance matrix of the raw scores (or, not as accurately, the correlation matrix), if that is available. With three items, it won't be all that high, though. From what I recall earlier in the thread, though, the original data are not available, so it doesn't matter.  



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