In reply to Mark Chatfield.

Thanks for writing. This article is from years ago, but I think the issue is that Kirkwood's statistic is not an estimate of the CV for a log-normal distribution. Kirkwood proposed his statistic in a short letter to the editor as a way to communicate the meaning of the log-normal scale to "non-statisticians" and to "those who have little facility with numbers" (Kirkwood, 1979, p. 908-909) who are familiar with arithmetic means and deviations. If Kirkwood's statistic helps you to communicate the dispersion in data, that's awesome.