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?
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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.
answered Jan 20, 2015 at 17:28
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3$\begingroup$ I don't think the interpretability is as bleak as you suppose. The exponentials (antilogs) of the mean, max, min, and median are the geometric mean, max, min, and median of the original data, respectively. The antilog of the SD is the geometric SD. The skewness and kurtosis of the logs are unitless values giving the same insight into the distribution of the logarithms as they give into the distribution of any set of numbers. More to the point is that when the logs have a "nicer" distribution than the original data, it suggests the logs may actually be better for interpreting many results. $\endgroup$– whuber ♦Commented Jan 20, 2015 at 17:59
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$\begingroup$ Good points. Since exponentials of the statistics of interest are interpretable, they (rather than the non-exponentiated values) could be reported; mean of logs of heights of a hundred trees is not interpretable while the exponential of it is. I agree on the remark on skewness and kurtosis; it does not seem to counter what I say but rather adds to it. And the last point about "nicer" distribution agrees with what I say in paragraphs 3 and 4. O course, I will be glad to correct any remaining factual mistakes (please point out specifically). $\endgroup$ Commented Jan 20, 2015 at 18:13
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$\begingroup$ Sorry; I don't think you made any factual mistakes, nor did I intend to intimate anything like that. I just had a different take on your claim that logarithms would be "much harder to interpret" than the original values. That's not even necessarily the case for trees: for purposes of estimating logging yields (which will depend on estimated volumes of harvestable material as computed from the product of height and squared diameter), I could imagine the logarithms might be more natural and easier to interpret and work with $\endgroup$– whuber ♦Commented Jan 20, 2015 at 18:20
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$\begingroup$ @whuber: I get it. No need for sorries :) I was just afraid that I said something really wrong that should be deleted not to confuse others. But with the discussion in the comments I guess it's fine to leave it in there. $\endgroup$ Commented Jan 20, 2015 at 18:37
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$\begingroup$ That's a good decision. In the meantime I have upvoted this post because--despite my misgivings about how might have hurt the feelings of some logarithms--it goes after the more fundamental issue of whether a transformation is the appropriate response to "larger values of variables." $\endgroup$– whuber ♦Commented Jan 20, 2015 at 18:42