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Non-statisticians can be easily misled by the phrase "missing at random". Their natural interpretation tends to be closer to MCAR than to MAR.

I had to explain the concept to an ecologist today, and his reaction was something along the lines of "But why on Earth would you call it that?".

I must admit, I couldn't come up with a better answer than "that's just the name we've always used". Does anyone here have a better response?

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You gave a perfect explanation, and there isn't a better one (at least I did not find any during my dissertation work and subsequent research on missing data). There is little excuse for poor terminology, and this is one of the most striking examples (along with formative/reflective indicators in psychology, as well as mediation and moderation that are so easily confused).

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  • $\begingroup$ I suggest, for posterity's sake, that we rename MAR to MAAR ("Missing (Adjusted) At Random"), which would be the same length as MCAR and MNAR, and would also be pronounced the same as MAR when spoken as an acronym. $\endgroup$
    – Wayne
    Feb 19, 2012 at 17:50
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When, given the observed data, the missingness mechanism does not depend on the unobserved data.

Examples of MAR mechanisms

  1. A subject may be removed from a trial if his/her condition is not controlled sufficiently well (according to pre-defined criteria on the response).
  2. Two measurements of the same variable are made at the same time. If they differ by more than a given amount a third is taken. This third measurement is missing for those that do not differ by the given amount.

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    $\begingroup$ Good info, but I think the OP is asking why the term 'MAR' was chosen for this situation. Before I learned about missing data, if I heard the term 'missing at random,' I'd think of situations that would actually fall under the 'MCAR' setting. $\endgroup$
    – user5594
    Oct 18, 2011 at 13:34
  • $\begingroup$ There are big difference between MCAR and MAR. It would be more clear by mathematical equations. If you want to convince lay man then it is not really easy task. Note that it is only an assumption about your missing data. $\endgroup$
    – Biostat
    Oct 18, 2011 at 14:37

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