# Reporting a variable and it's square root

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Hello y'all

In my thesis, I have this variable, which is expressed in a percentage (%). It's not an option to, e.g., display 20 % as 0.20, since that is absolutely not common for that variable.

Now, this variable does not satisfy the conditions for parametric testing. However, its square-root variant does. But if I report both this variable, in %, then do I have to change the "unit" (which in itself is demensionless) to something else than %?

Now I would report:

• Mean Var ± SD - %
• Mean VarROOT ± SD - %

But I'm not sure if this is quite right.

After all: e.g., in the case of 20 %, I took the root of 20, and not of 0.20.

So ... sqrt(20 %) = sqrt(20) * sqrt(0.01) = 4.47 * 0.1 = 0.447 ~ 44.7 %

And sqrt(0.20) = 0.447 ~ 44.7 %

But erm ... Is there a symbol for 1/10? Because now I see that I would incorrectly report 4.47 % (since I only rooted 20 without the %) instead of 44.7 %.

Thanks

F

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The variance is not dimensionless, nor is the standard deviation.

The variance has the units of the square of the variable being measured (the measurand) and the standard deviation has the same units as the measurand.

This arises directly from the definition of these quantities.

Similarly a % is a dimensionles quantity as it is a ratio of two quantities with the same dimensions.

I am not clear what your figures refer to to can you elaborate (just the maths please)?

Edited by studiot

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