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I work for a commission-based company that gives accounts to employees for about a month and the employees try and resolve the account, if they are successful they get a commission, otherwise the account goes to another employee to try and resolve.

We are running some reports to measure some performance characteristics for the company. We have years of data that we can analyze.

My question is:

What summary(median or mean) can best describe the central tendency of length of time to resolve an account per employee?

Almost every employee's median is greater than their mean, some are further apart than others.

One thing that we are trying to find out is if we give an employee an account, how long should it take for him or her to resolve it.

It seems to me that median is a better summary.

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  • $\begingroup$ @Jose: would it mean that if I write an answer to this question, will you then use it to sack employees who take longer than they "should", according to my answer? $\endgroup$
    – Matt
    Commented Apr 13, 2011 at 13:53
  • $\begingroup$ @Jose: Also, are all accounts the same? Or are some more difficult to "resolve" than others? $\endgroup$
    – Matt
    Commented Apr 13, 2011 at 13:55
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    $\begingroup$ I think you should look at some histograms by employee to get a feel for the distribution. Since you report that the median is greater than the mean, it almost sounds like you might be including the "unresolved" cases for each employee in your estimate. There is also some (informative) censoring in your data. $\endgroup$
    – cardinal
    Commented Apr 13, 2011 at 15:06
  • $\begingroup$ The employee-specific data do not seem to address the question, due to passing unresolved accounts along at the end of a month: you have information about how long each employee has an account but this does not tell you directly how long it takes to resolve each account. Therefore, no kind of average of the employee-specific data will be an appropriate solution. $\endgroup$
    – whuber ♦
    Commented Apr 13, 2011 at 15:16

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You should use the median, not the mean. However, you'll need to use methods appropriate for time-to-event (survival) data that deal appropriately with censoring: if the account was handled to another employee without being resolved you know only that the time this employee would have taken to resolve it is greater than or equal to the observed time for which they handled the account, so the observed time is right-censored.

The appropriate method would be to construct the Kaplan–Meier estimator of the survival function. If you want a single number for each employee, you could use this method to obtain the median 'survival' time, which gives you the median time taken to resolve an account. You can also get confidence intervals for the median if you so wish. It's possible that the median may not be estimable for some employees though if they fail to resolve more than half the accounts before they are re-assigned, in which case you could consider switching to some other percentile that is estimable for all (or at least the great majority of) employees.

The Kaplan-Meier estimator isn't difficult -- it's perfectly possible, if somewhat tedious, to construct by hand, and straightforward to program. Confidence intervals are a bit more tricky, but are available in any decent statistical software package.

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  • $\begingroup$ +1 This seems appropriate in conjunction with using the data correctly. Specifically, each account should be tracked, not accounts per employee (which is a biased approach). The times to resolve accounts will still be censored: there will always be some open accounts (or accounts closed solely because they were deemed unresolvable). Use censored methods to estimate the mean resolution time, multiply by the number of accounts to get total time required, and divide that by the number of employees to obtain mean "length of time to resolve an account per employee." $\endgroup$
    – whuber ♦
    Commented Apr 13, 2011 at 15:44
  • $\begingroup$ Note that the K-M estimator is not appropriate for the account times per employee, because the most intractable accounts are shared among several employees. This induces substantial dependence among the data, contrary to a fundamental assumption of independent data in the K-M approach. $\endgroup$
    – whuber ♦
    Commented Apr 13, 2011 at 15:46
  • $\begingroup$ To add to @whuber's comments, in addition, the K-M estimator will (likely) be biased if used for account times per employee due to the informative nature of the censoring. $\endgroup$
    – cardinal
    Commented Apr 13, 2011 at 17:14

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