6

I do not know a whole lot about statistics in general and as a result I am not really sure how to go about answering this question.

I have a sample of observations that I have split into two groups based on a dichotomous variable. I want to test whether the kurtosis of the distribution of the variable of interest is statistically different for these two groups, similar to how you would test a difference of means of two groups in a sample.

I have also read some information regarding the L-kurtosis. Would any test for the difference of kurtosis also be applicable to the L-kurtosis statistic?

Richard
  • 61
  • 2
    Could you explain why the kurtosis is of interest? (Unless you are looking for an enormous difference in kurtosis, it's unlikely any physically realizable sample size will produce significant results.) – whuber Feb 25 '16 at 21:39
  • I'm looking at a social science theory that predicts that the distribution of certain variables should be leptokurtic. Some of the literature will test statistically whether the observed kurtosis is different than normal. The theory also predicts that these distributions should become more leptokurtic under certain conditions. As a result, some literature has compared the kurtosis or the l-kurtosis of two groups, but I have yet to see a test used to see if those differences are statistically significant. – Richard Feb 26 '16 at 00:06
  • 1
    The standard error of the kurtosis is proportional to the eighth moment of the data. This makes estimates of kurtosis extremely unstable. It sounds like interest might actually be focused in the behavior of one or both tails of the distribution. Using various techniques, those can be examined with far more precision and insight. – whuber Feb 26 '16 at 00:20
  • Can this be addressed with the use of L-moments instead of conventional moments? The use of L-kurtosis is moderately accepted in the literature. If not, can you point me in the direction of a technique that may be useful in comparing how "fat tailed" two distributions are? – Richard Feb 26 '16 at 01:03
  • 1
    The L-moments certainly are far more robust than the corresponding moments of the data. Without knowing more precisely how these are used in the literature, I can't say much more, but I suspect that even something simple like an appropriate probability plot would provide more insight than any single statistic could. – whuber Feb 26 '16 at 01:13

0 Answers0