Dixon Test

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calculated (by adaptive quadrature) unpublished Dixon tables that I believe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

"Mike Middleton" wrote:

> 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
>
> "Kevin Clark" wrote in message
>
> >I am looking for a way to automate the Dixon Test for determining outliers
> >in
> > a data set in an Excel spreadsheet.

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

"Mike Middleton" wrote:

> 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
>
> "Kevin Clark" wrote in message
>
> >I am looking for a way to automate the Dixon Test for determining outliers
> >in
> > a data set in an Excel spreadsheet.