[kodos]

Suppose I reject a datum in a series using the Q test which has the form:



When I calculate Q for other questionable values, should I keep using the range and gaps for the old series (including the rejected value) or the ones from the new series without that value?

[JGK]

http://en.wikipedia.org/wiki/Dixon%27s_Q_test

Basically the scenario you are describing is:
1) test possible outlier against the full range, discard if identified as an outlier,
2) move on to the next possible outlier and test against the new range.

I'm not sure whether this can be mathematically or statistically justified. There are other methods of testing for outliers such as:
 
http://en.wikipedia.org/wiki/Grubbs'_test_for_outliers
http://www.statisticaloutsourcingservices.com/Outlier2.pdf
http://www.itl.nist.gov/div898/handbook/eda/section3/eda35h.htm

These may be more appropriate for your use.

Personally, coming from a regulatory GLP background, exclusion of data was only permissible if there was a sytemic reason available to justify it (e.g. exclusion of blood chemistry components due to haemolysed or clotted samples). This eliminated the arbitrary exclusion of  "inconvenient" data.

[kodos]

Thank you for your answer! So when I discard one value, the range of the series changes.

Yes, I also see the limitations of this test. And I'm also of the opinion that one should not discard one datum unless there's reason to do it, although I don't have much background to support that. I like to think of it as a helping tool rather than a procedure to be followed strictly.