Pattern theory - Revision history

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2015-01-07T12:33:43Z

Tagging using AWB (10703)

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	The '~~''runs test''' (also called '''Wald–Wolfowitz test''' after [[Abraham Wald]] and [[Jacob Wolfowitz]])~~ is ~~a [[non-parametric statistic\|non-parametric]] statistical test that checks a randomness hypothesis for a two-valued data sequence~~. ~~More precisely, it can be used to [[Statistical hypothesis testing\|test the hypothesis]] that the elements of the sequence are mutually [[Statistical independence\|independent]].~~		The author's title is Christy. Credit authorising is how she makes a living. Ohio is where his house is and his family enjoys it. My spouse doesn't like it the way I do but what I truly like performing is caving but I don't have the time recently.<br><br>Visit my page :: [http://brazil.amor-amore.com/irboothe real psychic readings]

	~~A "run" of a sequence~~ is a ~~maximal non-empty segment of the sequence consisting of adjacent equal elements~~. ~~For example, the 22-element-long sequence "++++−−−+++−−++++++−−−−" consists of 6 runs, 3 of which consist of "+" and the others of "−". The run test~~ is ~~based on the null hypothesis that the two elements +~~ and ~~- are independently drawn from the same distribution~~.

	~~Under the null hypothesis, the number of runs in a sequence of~~ '~~'N'' elements<ref>''N'' is~~ the ~~number of elements, not the number of runs.</ref>~~ is ~~a [[random variable]] whose [[conditional distribution]] given the observation of~~ '~~'N''<sub>+</sub> positive values<ref>''N''<sub>+</sub> is~~ the ~~number of elements with positive values, not the number of positive runs</ref> and ''N''~~<~~sub~~>−<~~/sub~~> ~~negative values ({{nowrap\|1= ''N'' = ''N''<sub>+</sub> + ''N''<sub>−</sub>}}) is approximately normal, with~~: ~~<ref>http~~:~~//www.itl.nist.gov/div898/handbook/eda/section3/eda35d.htm</ref> <ref>~~http://~~support~~.~~sas~~.com/~~kb/33/092.html</ref>~~

	* [[mean]] <math>\mu=\frac{2\ N_+\ N_-}{N} + 1\,</math>

	* [[variance]] <math>\sigma^2=\frac{2\ N_+\ N_-\ (2\ N_+\ N_--N)}{N^2\ (N-1)}=\frac{(\mu-1)(\mu-2)}{N-1}\,.</math>

	These parameters do not assume that the positive and negative elements have equal probabilities of occurring, but only assume that the elements are [[independent and identically distributed]]. If the number of runs is significantly higher or lower than expected, the hypothesis of statistical independence of the elements may be rejected.

	~~Runs tests can be used to test:~~
	#the randomness of a distribution, by taking the data in the given order and marking with + the data greater than the [[median]], and with – the data less than the median; (Numbers equalling the median are omitted.)
	#whether a function fits well to a [[data set]], by marking the data exceeding the function value with + and the other data with −. For this use, the runs test, which takes into account the signs but not the distances, is complementary to the [[chi square test]], which takes into account the distances but not the signs.

	~~The [[Kolmogorov–Smirnov test]] is more powerful, if it can be applied.{{citation needed\|date=April 2013}}~~

	~~==References==~~
	~~<references/>~~

	~~{{DEFAULTSORT:Wald-Wolfowitz Runs Test}}~~
	~~[[Category:Statistical tests]]~~
	~~[[Category:Non-parametric statistics]~~]

en>Addbot: Bot: Migrating interwiki links, now provided by Wikidata on d:q7148392

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Bot: Migrating interwiki links, now provided by Wikidata on d:q7148392

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	~~Greetings! I am Myrtle Shroyer~~. ~~What I love doing~~ is ~~to gather badges but I've been taking~~ on ~~new things lately~~. ~~Bookkeeping~~ is ~~what I do~~. ~~California~~ is ~~our beginning location.~~<br><br>~~Also visit my web site~~ :: ~~home std test - [~~http://~~facehack~~.ir/~~index~~.~~php?do~~=/~~blog/20/what~~-~~you~~-~~have~~-to-do-~~facing~~-~~candida~~/ ~~simply click~~ the ~~up coming website page~~] -		The '''runs test''' (also called '''Wald–Wolfowitz test''' after [[Abraham Wald]] and [[Jacob Wolfowitz]]) is a [[non-parametric statistic\|non-parametric]] statistical test that checks a randomness hypothesis for a two-valued data sequence. More precisely, it can be used to [[Statistical hypothesis testing\|test the hypothesis]] that the elements of the sequence are mutually [[Statistical independence\|independent]].

			A "run" of a sequence is a maximal non-empty segment of the sequence consisting of adjacent equal elements. For example, the 22-element-long sequence "++++−−−+++−−++++++−−−−" consists of 6 runs, 3 of which consist of "+" and the others of "−". The run test is based on the null hypothesis that the two elements + and - are independently drawn from the same distribution.

			Under the null hypothesis, the number of runs in a sequence of ''N'' elements<ref>''N'' is the number of elements, not the number of runs.</ref> is a [[random variable]] whose [[conditional distribution]] given the observation of ''N''<sub>+</sub> positive values<ref>''N''<sub>+</sub> is the number of elements with positive values, not the number of positive runs</ref> and ''N''<sub>−</sub> negative values ({{nowrap\|1= ''N'' = ''N''<sub>+</sub> + ''N''<sub>−</sub>}}) is approximately normal, with: <ref>http://www.itl.nist.gov/div898/handbook/eda/section3/eda35d.htm</ref> <ref>http://support.sas.com/kb/33/092.html</ref>

			* [[mean]] <math>\mu=\frac{2\ N_+\ N_-}{N} + 1\,</math>

			* [[variance]] <math>\sigma^2=\frac{2\ N_+\ N_-\ (2\ N_+\ N_--N)}{N^2\ (N-1)}=\frac{(\mu-1)(\mu-2)}{N-1}\,.</math>

			These parameters do not assume that the positive and negative elements have equal probabilities of occurring, but only assume that the elements are [[independent and identically distributed]]. If the number of runs is significantly higher or lower than expected, the hypothesis of statistical independence of the elements may be rejected.

			Runs tests can be used to test:
			#the randomness of a distribution, by taking the data in the given order and marking with + the data greater than the [[median]], and with – the data less than the median; (Numbers equalling the median are omitted.)
			#whether a function fits well to a [[data set]], by marking the data exceeding the function value with + and the other data with −. For this use, the runs test, which takes into account the signs but not the distances, is complementary to the [[chi square test]], which takes into account the distances but not the signs.

			The [[Kolmogorov–Smirnov test]] is more powerful, if it can be applied.{{citation needed\|date=April 2013}}

			==References==
			<references/>

			{{DEFAULTSORT:Wald-Wolfowitz Runs Test}}
			[[Category:Statistical tests]]
			[[Category:Non-parametric statistics]]

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