I wonder about the existence of "standard" statistical procedures for rounded (log)normal data. Indeed, in my work I often encounter rounded data which potentially cause some problems: "awful" qqplots, zeros for lognormal data... Do there exist in the literature some theoretical studies of usual statistical procedures (such as goodness-of-fit, t-test, ...) for rounded data ?

EDIT: I have just discovered the MCMCtobit() function in the MCMCpack R package: Gaussian Linear Regression with a Censored Dependent Variable; the dependent variable may be censored from below, from above, or both. In my case the dependent variable is censored by its rounded value, hence the censoring is data-dependent. Is it correct to use MCMCtobit() in this context ?

EDIT2 : Now I have discovered the grouped R package. I think this is exactly what I was looking for. Thanks for the comments given below!

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    $\begingroup$ QQplots are not recommended for discrete distributions. There is a HUGE literature about dealing with rounded observations. Use also "grouped data" in your keywords. link $\endgroup$ – user10525 Apr 23 '12 at 8:57
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    $\begingroup$ This paper discusses the effect of rounding on testing for normality: tandfonline.com/doi/abs/10.1080/02664760903143925 $\endgroup$ – MånsT Apr 23 '12 at 9:00
  • $\begingroup$ Thanks to both of you. @Procrastinator: the animated Google search is very amazing :) $\endgroup$ – Stéphane Laurent Apr 23 '12 at 9:06
  • $\begingroup$ In fact, the goodness-of-fit is not my main interest. For example I am more interested in the t-test for two rounded samples. $\endgroup$ – Stéphane Laurent Apr 23 '12 at 13:44
  • $\begingroup$ Charles Manski has a research program on rounding, mostly focused on bounds. $\endgroup$ – Tristan Apr 24 '12 at 7:58

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