The data for my variable is in the form of Z-scores only. I'd like to log transform the scores, but I don't know the mean or standard deviation in order to covert to raw scores. Can I assign an arbitrary mean and standard deviation, use that to convert to raw scores, then log transform the raw scores? Or is there some other way to log transform Z-scores? Thanks.
A few quick points about logs
The following R code is a reminder that the log of a negative number is not a number and that the log of zero is negative infinity. Thus, if you are going to take a log of a z-score, you first need to make all values obtained greater than zero.
A simple strategy of logs on z-scores
A simple strategy for log transforming a variable is to first add a constant to the variable such that the minimum value is one. i.e.,
The following code shows a simple example of some standardised positively skewed data. The minimum of
But exactly what transformation should you perform?
You cannot assign arbitrary Mean and SD to covert z-score data into Raw data (x). However, you can check a shape of the distribution of z-scores by calculating skewness or kurtosis. Log-transform only useful if you're data is positively skewed. Moreover, it would be good if you explain that what is your objective? as @Karl asked. It might be helpful to visit this URL.