Dividing Variable by its mean

[Nives Saa]

Dear all,

I have question regarding to my independent variable and interpretation of it.

I have divided my independent variable by its mean to get the better results and the results are really better.

But now I have a problem with the interpretation of that variable.

Does anyone knows how to interpret that variable?

Thans everyone in advance.

[Carlo Lazzaro]

Nives:
you ought to have something expressed in n times the mean. That said, your approach is quite unusual, as far as I know. It's more frequent to center the variable around its mean. However, your research field might well have different habits.
As an aside, without knowing/reading what you typed and what Stata gave you back, I find difficult to reply more positively.

[Nick Cox]

I agree with @Carlo Lazzaro.

It's hard to see how dividing a variable by its mean gives "better results" in any sense but one: you are more likely to avoid coefficients that are extremely large or small depending on units of measurement and actual magnitudes.

[Richard Williams]

Before you subtracted the mean, zero meant zero. Whether that was an interesting or even possible value depends on the variable, e.g. nobody gets a score of zero on a scale that ranges between 400 and 1200.

After subtracting the mean, zero means average. A score of 10 means 10 pts above average.

This handout discusses ways centering independent variables can sometimes be an aid to interpretation.

https://www3.nd.edu/~rwilliam/stats2/l53.pdf

[Nick Cox]

Variable/mean to my mind means that zero goes to zero and the mean goes to one. 10 means the value is 10 times the mean. It's a linear rescaling that removes units of measurement, but the marginal distribution is unchanged in shape, modulo sign.

However, if values can be negative and the mean is too, then the sign of skewness is reversed.

A good reason for not using this scaling, however, is that it is undefined if the mean is zero and likely to create outliers if the mean is close to zero.

[Richard Williams]

Whoops. I was thinking of subtracting the mean, not dividing by it. Dividing by the mean seems quite odd to me. I really don't know why you would do this.