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My thesis is to examine the validity of the relationship between tourism represented by tourist exports (real growth) and economic growth using a dummy variable and force workers. I tested the normality of the variables and they are not normal, so I converted the variables using a logarithmic transformation in order to make them normal.

My question is: it is valid to log-transform a percentage variable?

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    $\begingroup$ Of course: you apply the logarithm function to the percentages. But nobody would come here to ask that, so you must have something else in mind. Could you please clarify what you are looking for? $\endgroup$ Commented Aug 24, 2013 at 14:28
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    $\begingroup$ Why are you transforming? You say it's because they're not normal, but why is that important? $\endgroup$ Commented Aug 24, 2013 at 16:13

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First, the data do not need to be normal, the residuals of the model do (at least for ordinary least squares regression).

Second, certainly it is possible to change a percentage to a log, as long as there are no 0%. But is that what you want? Say exports were 200 in 2010 and 205 in 2011. Then growth as a % is 205/200 * 100 = 2.5%. Log(205/200) = .0107, which is the difference between log(205) and log(200).

Third, it's a bit hard to tell what you are doing, exactly, but if you have longitudinal data, you will need to account for that.

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  • $\begingroup$ I do not understand your second point. Log(205) - log(200) is equal to 0.02469261, which basically is 2.5% and that's why you can compute growth rates either as (x-y)/y or log(x/y) $\endgroup$ Commented Oct 27, 2023 at 8:46

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