Dixon Test

[Kevin Clark]

I am looking for a way to automate the Dixon Test for determining outliers in
a data set in an Excel spreadsheet.

 

[Mike Middleton]

Kevin -

Referring to

http://www.statistics4u.info/fundstat_eng/cc_outlier_tests_dixon.html#

it's a simple matter to compute the test statistic Q using Excel's ABS, MIN,
MAX, and LARGE or SMALL worksheet functions.

But I don't have access to a source that describes how to compute the
sampling distribution of Q for determining a p-value or conducting a
hypothesis test.

- Mike
http://www.mikemiddleton.com

 

[Jerry W. Lewis]

Thanks for a reference that I hadn't seen before. The algorithm for
selecting among Dixon-type statistics based on sample size is endorsed by
ASTM (E-178).

http://www.jstatsoft.org/counter.php?id=158&url=v16/i03/v16i03.pdf&ct=1
gives a method for calculating p-values by Gaussian-type quadrature. The
abscissas and weights used there give about 3-place accuracy in the range of
Dixon's tables.

Note that the tables in your reference have not been previously published,
and extend Dixon's tables to smaller p-values and larger n than Dixon
published. The larger n may not be useful in practice since the range
becomes a very inefficient estimator of variance for large n. However the
accuracy of these tables is not bad. The author says they are based on Monte
Carlo simulation with 10^6 reps per value. Around the turn of the century I
calculated (by adaptive quadrature) unpublished Dixon tables that I believe
to be accurate to 6 decimal places over an even broader range of p-values for
n<=100. Comparing your reference to my tables, your reference seems to have
an error of no more than 0.003 in its tabled values, which is better than
Dixon's original tables.

Jerry

 

[Jerry W. Lewis]

Note also, that these p-values are for 1-sided outlier tests, whereas outlier
testing is inherently 2-sided, unless there is some objective basis for
believing that outliers can only occur in one direction. Thus for most
cases, these p-values should be doubled, as in Rorabacher's tables
(Analytical Chemistry 63[2]:139-146, 1991) and USP <111>.

Jerry