Taking a log of Ratio Variable

[Abdullah Ijaz]

Hi,

I am conducting a panel data analysis. My dependent variable is a ratio which defines the business entry rate per 1000 population. When I graph box the variable I get the following result :

This shows that the data is highly skewed. If I take a log, it gets normal. However, I just want to know as I take natural log the data results into some negative values ( most probably beacuse of low values i.e. 0.00).



I have tried to read some previous posts and searched on google about the given subject. There are different opinions on this. Is it a fine practice to conduct a research study?

Your feedback shall be appreciated.

[Maarten Buis]

That is just a property of the logarithm. Remember that when we write \( \log_{a} b \) , we are asking "to what power do we need to raise \(a\) to get \(b\)". The numerical example I always have in mind when dealing with logarithms is \(\log_{2} 8 = 3\) because \(2^3=2\times 2\times 2=8\). Based on that we can see that the logarithm of 1 = 0, regardless of the base, as any number raised to the power 0 equals 1. The logarithm of numbers between 0 and 1 will be negative, and the logarithm of numbers larger than 1 will be positive, again regardless of the base.

[Nick Cox]

Maarten Buis is right, and to his account I add a note that the logarithm of zero is undefined.

[Abdullah Ijaz]

Thanks a lot both of you. Your valuable comments are highly appreciated.