Dixon's Q test

Consider the data set:

:$0.189,\backslash \; 0.167,\backslash \; 0.187,\backslash \; 0.183,\backslash \; 0.186,\backslash \; 0.182,\backslash \; 0.181,\backslash \; 0.184,\backslash \; 0.181,\backslash \; 0.177\; \backslash ,$

Now rearrange in increasing order:

:$0.167,\backslash \; 0.177,\backslash \; 0.181,\backslash \; 0.181,\backslash \; 0.182,\backslash \; 0.183,\backslash \; 0.184,\backslash \; 0.186,\backslash \; 0.187,\backslash \; 0.189\; \backslash ,$

We hypothesize that 0.167 is an outlier. Calculate Q:

:$Q=\backslash frac\{\backslash text\{gap\}\}\{\backslash text\{range\}\}\; =\; \backslash frac$

With 10 observations and at 90% confidence, Q = 0.455 > 0.412 = Q_table, so we conclude 0.167 is indeed an outlier. However, at 95% confidence, Q = 0.455 < 0.466 = Q_table 0.167 is not considered an outlier.

McBaneHalpern, Arthur M. "Experimental physical chemistry : a laboratory textbook." 3rd ed. / Arthur M. Halpern, George C. McBane. New York : W. H. Freeman, c2006 [http://lccn.loc.gov/2006286239 Library of Congress]{{dead link|date=December 2016 |bot=InternetArchiveBot |fix-attempted=yes }} notes: Dixon provided related tests intended to search for more than one outlier, but they are much less frequently used than the r₁₀ or Q version that is intended to eliminate a single outlier.

This table summarizes the limit values of the two-tailed Dixon's Q test.

• Grubbs's test for outliers

{{Reflist}}

• Robert B. Dean and Wilfrid J. Dixon (1951) "Simplified Statistics for Small Numbers of Observations". Anal. Chem., 1951, 23 (4), 636–638. [http://pubs.acs.org/doi/abs/10.1021/ac60052a025 Abstract] [http://depa.fquim.unam.mx/amyd/archivero/ac1951_23_636_13353.pdf Full text PDF] {{Webarchive|url=https://web.archive.org/web/20150501042023/http://depa.fquim.unam.mx/amyd/archivero/ac1951_23_636_13353.pdf |date=2015-05-01 }}
• Rorabacher, D. B. (1991) "Statistical Treatment for Rejection of Deviant Values: Critical Values of Dixon Q Parameter and Related Subrange Ratios at the 95 percent Confidence Level". Anal. Chem., 63 (2), 139–146. [http://pubs.acs.org/doi/pdf/10.1021/ac00002a010 PDF] (including larger tables of limit values)
• McBane, George C. (2006) "Programs to Compute Distribution Functions and Critical Values for Extreme Value Ratios for Outlier Detection". J. Statistical Software 16(3):1–9, 2006 [http://www.jstatsoft.org/v16/i03 Article (PDF) and Software (Fortan-90, Zipfile)]
• Shivanshu Shrivastava, A. Rajesh, P. K. Bora (2014) "Sliding window Dixon's tests for malicious users' suppression in a cooperative spectrum sensing system" IET Communications, 2014, 8 (7)
• W. J. Dixon. The Annals of Mathematical Statistics. Vol. 21, No. 4 (Dec., 1950), pp. 488–506 {{doi| 10.1214/aoms/1177729747}}

• [https://cran.r-project.org/web/packages/outliers/index.html Main page of GNU R's package 'outlier'] includes 'dixon.test' function.
• [https://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6809387&newsearch=true&queryText=dixon%27s%20test Dixon's test in Communications] – use of Dixon's test in cognitive radio communications (by Shivanshu Shrivastava)

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Category:Statistical tests

Category:Robust statistics

Category:Statistical outliers