Linear trans on normal distribution Let's say a variable fits a ratio measurement level and is also normally distributed (for example, height). Why is it possible to do a linear transformation on such a variable if the only transformation which is allowed on ratio measurements is multiplication or division?

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*A variable won't be both ratio and exactly normal (at least not for strictly non-negative variables like height).


*Leaving aside the issue of normality:
Lets say I have a ratio variable like $X_i$ = "number of hours worked on day $i$", and the corresponding daily pay is "\$10 + \$30 per hour" (perhaps the ten dollars is some meal allowance or travel allowance or something, it's not important). Then the daily pay amount is a linear transformation of the hours worked and Stevens' "rule" about transformation of a ratio variable in that situation is plainly no help to us - a linear transformation is not only possible in that situation, it's inherent in the definition of the pay amount variable.
You might find my answer here on issues with Stevens' typology of scale of some interest.
