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I am looking at submission data—the length of time it takes for someone to complete a flow which involves submitting an item of content. I am getting the following distributions. I have two quick questions:

  • What best describes the frequency distribution? I am thinking lognormal but am not sure.

  • Is the mean the best statistic to use, e.g., 'mean submission time is hh:mm'? Is there a better, e.g., median or % of submissions below hh:mm?

distribution of submission times

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    $\begingroup$ If you want to be able to see the ways in which a density function deviates from lognormal, you might plot log(f) vs log(x) (which should be quadratic if the original density were lognormal). On the other hand, if you have data, a normal QQ plot of log(X) would be a good approach. $\endgroup$ – Glen_b Sep 18 '15 at 1:02
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  1. In the real world, there is no distribution that's going to define this perfectly; parametric distributions are, at best, idealized descriptions of how the data is really distributed. That being said, it appears that something like a lognormal or wiebull distribution may be a reasonable description of the process you're observing. However, if dynamics change in the next data collection, this may no longer be the case. Summary: log normal or weibull is probably appropriate for this dataset.

  2. I would be a little hesitant to use the mean, as it is heavily influenced by extreme values, for which this dataset has more than a few. The median might be a more important measure. But much more importantly, you want the measure that really answers your question of interest!

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  • $\begingroup$ Agree on choosing a statistic that is aligned to what is needed - what I would like is to make improvements in the process and use the statistic as a basis of (a) comparison in time to track improvement (b) compare processes between different flows (which have same distro). Any ideas on pros cons (you mentioned median vs mean above)? $\endgroup$ – user7289 Sep 18 '15 at 6:50
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    $\begingroup$ Two reasonable approaches: take a log transformation of the data and then perform a t-test. If the data is approximately log-normal, this will have the most power. Alternatively, you could use the Wilcoxon Rank Sum test and have pretty good power, regardless of whether it's approximately log-normal or not. $\endgroup$ – Cliff AB Sep 18 '15 at 14:21

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