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In contrast to the many threads on this site that recommend Dixon's and Grubb's tests, the author of one answer, at this thread, contends that "Really, these have been discredited long ago" and advocates 2 other methods. I don't feel qualified to sort out these arguments, but I would like to ask whether there is any consensus among statisticians as to the merits of either position.

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It sounds like this is soliciting opinion. What are your thoughts on whether this should be CW? –  cardinal May 10 '12 at 22:47
    
@cardinal: Not cw, but probably asking for references is better than asking for consensus.. –  naught101 May 11 '12 at 0:45
    
It's fine with me if this is mada a CW....Is their any precedent on this site of someone asking for a vote? That's what I'm really looking for, as a way of seeing whether there's any consensus. Asking for references is of course valuable in that it might allow some to go and read up and settle the issue for themselves, but that's not my aim here. What I want to know is which conclusions have most commonly been reached by those who have already settled the issue for themselves. –  rolando2 May 11 '12 at 1:53
    
look at the index of any recent textbook on the subsject. That's a good place to look for what is the consensus in any field. amazon.com/Robust-Statistics-Theory-Methods-Probability/dp/… –  user603 May 11 '12 at 8:19
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2 Answers

The issue becomes less contentious if you state the facts[1]. After all, all multivariate robust estimation procedures have at their core an outlier detection algorithm and all will in some form or another output a list of suspect observations. Stated otherwise, given a robust fit, identifying outliers is in principle not an issue.

The main difference between robust estimation approaches and the testing approaches (Dixon, Grubbs) is that the latter can sustain at most a single outlier. In contrast, most state of the art robust estimation procedures have been designed to handle nearly 50% contamination (they can in principle be tuned to handle anywhere between 0 and nearly 50 percent outliers trading off robustness for computational costs).

[1] Rousseeuw P. J. and Van Zomeren B. C., Unmasking Multivariate Outliers and Leverage Points.

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I say no! I have done research on Dixon's test back in the 1980s. I took a look at that post and commented there. I think there is confusion because robust estimation and outlier detection though similar have different objectives and some people I think seem to feel that since the outlier methods are not mentioned in the robustness literature that there is something wrong with them. I hope other will agree with me in answering this question.

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