What statistical tools should be used for the interval and ratio scales?

#1
Hello,
I have read a lot on the internet of examples of differences between the two scales, however I do not understand why statistical tools such as the relative standard deviation are used for the ratio scales and not for the interval scales. I found everything and its opposite on the internet. So I have a hypothesis and I would like to know if it is valid? Imagine that we are working on a ratio scale and imagine a variable X. Then define the variable Y such that Y = aX. My hypothesis is that the statistical tools that can be used for a ratio scale are those for which the result for X and Y will be equal. Now imagine that we are working on an interval scale and define Y as Y = aX + b. Then the statistical tools that can be used are those for which the result of X and Y will be equal. We cannot therefore use the relative standard deviation for interval scales because RSD (X) is not equal to RSD (Y). But on the other hand we can normalize the data of the 2 variables whatever the scale. (By normalization I mean defining a score zi = (xi - mean (x)) / standard deviation (x)). Here is my hypothesis. Can you validate it or refute it and explain it to me please?
Thank you
 
#2
My hypothesis is that the statistical tools that can be used for a ratio scale are those for which the result for X and Y will be equal.
This actually sounds a little like the statistical idea that the inference should not depend on the unit of measure. ie t-tests give the same p-value for kg as lb. 'equivariance principle? i think. So in short no because nearly all statistical tests would satisfy this.

The Y = aX + B thing and RSD thing has some character of the applicability of log transformations and/or log normal assumptions. Can't take the log of 0 right? So we have to agree on where 0 is. RSD is usually used in conjunction with log transformation because of the close relationship between CV and variance of logged data.

As for the internet providing contradictory advice, you get what you pay for in the advice department. Exception for this post of course.o_O
 
#3
This actually sounds a little like the statistical idea that the inference should not depend on the unit of measure. ie t-tests give the same p-value for kg as lb. 'equivariance principle? i think. So in short no because nearly all statistical tests would satisfy this.

The Y = aX + B thing and RSD thing has some character of the applicability of log transformations and/or log normal assumptions. Can't take the log of 0 right? So we have to agree on where 0 is. RSD is usually used in conjunction with log transformation because of the close relationship between CV and variance of logged data.

As for the internet providing contradictory advice, you get what you pay for in the advice department. Exception for this post of course.o_O
Hello,
Thanks for taking time to respond to me.
But then how do you differentiate between the tools that can be applied to interval scales and ratio scales?
Thank you
 
#4
Hmmm, Somehow I doubt that it produces a very strong grouping of statistical methods at all. The key consideration though will probablybe the range of admissible values. Intervals admit negatives by definition so right, so any stats methods which do not allow for the presence of negative values are a non-starter. By contrast ratio cant go below 0, so if you take mean - 2SEM and get a negative value you got a problem. Non-parametric tests are gunna be alot less subject to this sort of thing, since non-parametrics are dumb, in the sense that they are not very tailored to any specific problem and exist to give statisticians some sort of recourse when people won't stop going on about normality tests. well hope that helps, stay safe out there.