[Rasch] Logarithmic Scale

Anthony James luckyantonio2003 at yahoo.com
Fri Jan 18 23:09:38 EST 2008

Hi everyone,
  This has been bothering me for some time now. I’d be grateful for some clarifications.
  I read one of Mike’s papers in RMT, “Log-odds in Sherwood forest”.
  A logarithmic scale sounds deficient. Constant ratios on the ratio scale represent equal steps on the logarithmic scale. For example 10 is 5 times 2 and they are 8 points apart. 100 is 5 times 20 and they are 80 points apart but on the logarithmic scale both pairs are 1.69 logits apart!!!
  This doesn’t make sense to me. This means that in order to add to the ability of a person whose measure is 2 to have a measures of 10 we need to add 1.69 logit ability. And in order to add to the ability of a person whose ability is 20 to have an ability of 100 we need to add 1.69 logit too.
  What’s wrong with a ratio scale?
  If length measured in centimeters is on a ratio scale then it’s both additive and multiplicative.

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