Because of larger values of variables, I did a log- transformation in my dataset. Now I want to give a descriptive table regarding my variables like mean, max, min, median, skewness, kurtosis. Can I give standard measures like arithmetic mean or should I give geometric mean? In terms of skewness or kurtosis, do I need a transformation?
Best Answer
The different descriptive statistics will naturally fit different distributions of data and will have different interpretations, so you should think which is the most appropriate one. For example, geometric mean would make sense for log-normally distributed variables while arithmetic mean would make sense for normally distributed variables (that's just one possible example).
Your variables in logs will have different subject-matter interpretations than the same variables in the original scale. For example, a log of height or weight does not say much to me. An arithmetic mean of logs of heights of, say, a hundred trees will be much harder to interpret than an arithmetic mean on the original heights.
On the other hand, if you are determined to model your variables in logs, you may care about their skewness or kurtosis for the sake of building a good model. In such a context you could report the skewness and kurtosis of the logs of variables.
Also, a model in log-transformed data will typically have a different interpretation than a model in the original data. You should think whether the model in logarithms makes sense. It very well may, but it is not automatically warranted.
Finally, if you just need to change the scale of the variables, you might alternatively scale the variables by their inverse standard deviation or use different measurement units (kilometers instead of meters, kilograms instead of grams etc.).
More specific advice would require more details on your problem.