[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. Iâ€™d be grateful for some clarifications.
I read one of Mikeâ€™s papers in RMT, â€œLog-odds in Sherwood forestâ€.
http://www.rasch.org/rmt/rmt53d.htm
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 doesnâ€™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.
Whatâ€™s wrong with a ratio scale?
If length measured in centimeters is on a ratio scale then itâ€™s both additive and multiplicative.
Cheers
Anthony
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