Chudnovsky algorithm - Revision history

en>Abrahamic Faiths: fix

2015-01-09T03:30:28Z

fix

← Older revision		Revision as of 05:30, 9 January 2015
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	~~Named~~ for the ~~Dutch mathematician [[Bartel Leendert van der Waerden]],~~ the ~~'''Van der Waerden test'''~~ is ~~a [[statistical test]] that ''k'' population distribution functions are equal~~. ~~The Van Der Waerden test converts~~ the ~~ranks from a standard [[Kruskal~~-~~Wallis one-way analysis~~ of ~~variance]] to [[quantile]]s~~ of the ~~standard normal distribution (details given below). These are called normal scores~~ and the ~~test is computed~~ from ~~these normal scores~~.		If you are looking for a specific plugin, then you can just search for the name of the plugin. This one is one of the most beneficial features of Word - Press as this feature allows users to define the user roles. This CMS has great flexibility to adapt various extensions and add-ons. After confirming the account, login with your username and password at Ad - Mob. It is found that most of the visitors only look for the results that are displayed on the first page of the search engines and so if you get the service from professional service providers then they strive for the first page ranking of your site and improve the online visibility. <br><br>

	~~The ''k'' population version of the test~~ is ~~an extension of~~ the ~~test for two populations published by Van der Waerden (1952,1953)~~.		Thus, it is imperative that you must Hire Word - Press Developers who have the expertise and proficiency in delivering theme integration and customization services. While direct advertising is limited to few spots in your site and tied to fixed monthly payment by the advertisers, affiliate marketing can give you unlimited income as long as you can convert your traffic to sales. Several claim that Wordpress just isn't an preferred tool to utilise when developing a professional site. You can add new functionalities and edit the existing ones to suit your changing business needs. The biggest advantage of using a coupon or deal plugin is that it gives your readers the coupons and deals within minutes of them becoming available. <br><br>Digital photography is a innovative effort, if you removethe stress to catch every position and viewpoint of a place, you free yourself up to be more innovative and your outcomes will be much better. The nominee in each category with the most votes was crowned the 2010 Parents Picks Awards WINNER and has been established as the best product, tip or place in that category. Possibly the most downloaded Word - Press plugin, the Google XML Sitemaps plugin but not only automatically creates a site map linking to everyone your pages and posts, it also notifies Google, Bing, Yahoo, and Ask. Storing write-ups in advance would have to be neccessary with the auto blogs. If you liked this report and you would like to obtain a lot more information concerning [http://juegosdefutbol2013.org/profile/malewandow.html backup plugin] kindly check out our own page. Article Source: Stevens works in Internet and Network Marketing. <br><br>It is the convenient service through which professionals either improve the position or keep the ranking intact. Quttera - Quttera describes itself as a 'Saa - S [Software as a Service] web-malware monitoring and alerting solution for websites of any size and complexity. re creating a Word - Press design yourself, the good news is there are tons of Word - Press themes to choose from. If you are looking for Hire Wordpress Developer then just get in touch with him. It does take time to come up having a website that gives you the much needed results hence the web developer must be ready to help you along the route. <br><br>Instead, you can easily just include it with our bodies integration field in e - Panel. When you sign up with Wordpress, you gain access to several different templates and plug-in that allow you to customize your blog so that it fits in with your business website design seamlessly. The days of spending a lot of time and money to have a website built are long gone. You should stay away from plugins that are full of flaws and bugs. As for performing online business, websites and blogs are the only medium that are available to interact with customers and Word - Press perform this work with the help of cross-blog communication tools, comments and full user registration plug-ins.

	~~==Background==~~
	~~[[Analysis of Variance]] (ANOVA)~~ is ~~a [[data analysis]] technique for examining~~ the ~~significance of the factors ([[independent variables]]) in a multi-factor model. The one factor model~~ can ~~be thought of~~ as ~~a generalization of the [[two sample t-test]]~~. ~~That is, the two sample~~ t~~-test is~~ a ~~test of the hypothesis that two population means are equal~~. ~~The one factor ANOVA tests~~ the ~~hypothesis that ''k'' population means are equal~~. The ~~standard ANOVA assumes~~ that the ~~errors (i.e~~.~~, residuals) are [[normal distribution\|normally distributed]]. If this normality assumption is not valid, an alternative is to use a [[non-parametric test]].~~

	~~==Test definition==~~
	~~Let ''n~~<~~sub~~>j<~~/sub~~>~~'' (''j'' = 1~~, 2, .~~.., ''k'') represent~~ the ~~sample sizes for each of~~ the ~~''k'' groups (i.e.~~, ~~samples)~~ in the ~~data. Let ''N'' denote~~ the ~~sample size for all groups~~. ~~Let ''X<sub>ij</sub>'' represent the ''i''<sup>th</sup> value~~ in the ~~''j''<sup>th</sup> group~~. ~~The normal scores are computed as~~
	:~~<math>~~
	~~A_{ij} = \Phi^{-1}\left(\frac{R(X_{ij})}{N+1}\right)~~
	</~~math>~~
	~~where ''R''(''X<sub>ij<~~/~~sub>'') denotes the rank of observation ''X<sub>ij<~~/~~sub>'' and where ''Φ''<sup>-1<~~/~~sup> denotes the normal [[quantile function]~~]. ~~The average of the normal scores for each sample can then be computed as~~
	:<~~math~~>
	~~\bar{A}_j = \frac{1}{n_j}\sum_{i=1}^{n_j}A_{ij}\quad j=1,2,\ldots, k~~
	<~~/math~~>
	~~The variance of~~ the ~~normal scores can be computed~~ as
	~~:<math>~~
	~~s^2 = \frac{1}{N~~-~~1}\sum_{j=1}^k\sum_{i=1}^{n_j}A_{ij}^2~~
	~~</math>~~
	~~The Van Der Waerden test can then be defined~~ as ~~follows:~~
	~~:H<sub>0</sub>: All~~ of ~~the ''k'' population distribution functions are identical~~
	~~:H<sub>~~a~~</sub>: At least one of the populations tends to yield larger observations than at least one of the other populations~~

	~~The test statistic is~~
	~~:<math>~~
	~~T_1 = \frac{1}{s^2}\sum_{j=1}^kn_j\bar{A}_j^2~~
	~~</math>~~
	~~For [[significance level]] α~~, the ~~critical region~~ is
	~~:<math>~~
	~~T_1 > \chi_{\alpha,k-1}^2~~
	~~</math>~~
	~~where Χ<sub>α,k − 1</sub><sup>2</sup> is the α-[[quantile]]~~ of ~~the [[chi~~-~~squared distribution]]~~ with ~~''k'' − 1 degrees of freedom~~. ~~The null hypothesis is rejected if~~ the ~~test statistic is in~~ the ~~critical region. If~~ the ~~hypothesis of identical distributions is rejected, one can perform a [[multiple comparisons]] procedure to determine which pairs of populations tend to differ~~. ~~The populations ''j~~<~~sub>1</sub>'' and ''j<sub>2</sub~~>~~'' seem to be different if the following inequality is satisfied:~~
	:<~~math~~>
	~~\left\vert \bar{A}_{j_1} - \bar{A}_{j_2}\right\vert > s \~~,~~t_{1-\alpha/2}\sqrt{\frac{N-1-T_1}{N-k}}\sqrt{\frac{1}{n_{j_1}}+\frac{1}{n_{j_2}}}~~
	~~</math>~~
	with ~~''t''<sub>1 − α/2</sub> the (1 − α/2)~~-~~[[quantile]] of the [[Student's t-distribution\|t-distribution]]~~.

	~~==Comparison~~ with ~~the Kruskal~~-~~Wallis test==~~
	The ~~most common non-parametric test for the one-factor model is the [[Kruskal-Wallis one-way analysis~~ of ~~variance\|Kruskal-Wallis test]]~~. ~~The Kruskal-Wallis test is based on the ranks~~ of ~~the data~~. ~~The advantage of~~ the ~~Van Der Waerden test is~~ that ~~it provides the high efficiency of the standard ANOVA analysis when the normality assumptions~~ are ~~in fact satisfied, but it also provides~~ the ~~robustness~~ of ~~the Kruskal~~-~~Wallis test when the normality assumptions are not satisfied.~~

	~~==References==~~
	*{{cite book
	~~\|first= W. J.~~
	~~\|last=Conover~~
	~~\|year = 1999~~
	~~\|title = Practical Nonparameteric Statistics~~
	~~\|edition = Third Edition~~
	~~\|publisher = Wiley~~
	~~\|pages = 396–406}}~~

	*van der Waerden, ~~B.L. (1952). "Order tests for the two-sample problem~~ and ~~their power", ''Indagationes Mathematicae'', 14, 453–458.~~

	*van der Waerden, B.L. (1953). "Order tests for the two-~~sample problem. II, III", ''Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Serie A'', 564, 303–310, 311–316~~.

	~~{{NIST-PD}}~~

	~~[[Category:Statistical tests]]~~
	~~[[Category:Non-parametric statistics]]~~

en>David Eppstein: improve sourcing

2013-10-22T03:40:11Z

improve sourcing

← Older revision		Revision as of 05:40, 22 October 2013
Line 1:		Line 1:
	~~The main advantage of using~~ the ~~blog~~ is that ~~anyone can use~~ the ~~Word~~ - ~~Press blog and customize the elements in the theme regardless~~ to limited knowledge about internet and website development. You can either install Word - Press yourself or use free services offered on the web today. One really cool features about this amazing and free wp plugin is that the ~~code it generates is completely portable~~. s and ~~intelligently including a substantial amount of key words in~~ the ~~title tags, image links, etc. Understanding how Word - Press works can be a challenge, but it~~ is ~~not too difficult when you learn more about it~~. ~~<br><br>~~		Named for the Dutch mathematician [[Bartel Leendert van der Waerden]], the '''Van der Waerden test''' is a [[statistical test]] that ''k'' population distribution functions are equal. The Van Der Waerden test converts the ranks from a standard [[Kruskal-Wallis one-way analysis of variance]] to [[quantile]]s of the standard normal distribution (details given below). These are called normal scores and the test is computed from these normal scores.

	~~purcase and download~~ - ~~WPZOOM Tribune wordpress Theme, find and use~~ the ~~WPZOOM Discount Code~~. ~~WPTouch~~ is ~~among~~ the ~~more well known Word~~ - ~~Press smartphone plugins which~~ is ~~currently in use by thousands~~ of ~~users~~. ~~With~~ the ~~free Word - Press blog, you have~~ the ~~liberty to come up with your own personalized domain name~~. ~~E-commerce websites~~ are ~~meant~~ to ~~be buzzed with fresh contents~~, ~~graphical enhancements~~, ~~and functionalities~~. ~~For more info on [https:~~//~~deathcontrol~~.de/~~index~~/~~users~~/~~view~~/id/~~49661 wordpress dropbox backup] review~~ the ~~web~~-~~page. You~~ can ~~also get~~ a ~~free keyword tool that is~~ to ~~determine how strong other competing sites are and number~~ of the ~~searches on~~ the ~~most popular search sites.~~ <br><br>~~Usually~~, ~~Wordpress owners selling~~ the ~~ad space on monthly basis and this means a residual income source. After sending these details, your Word~~ - ~~Press blog will be setup within a few days. This platform can be customizedaccording to the requirements of the business~~. The ~~first thing you need to do~~ is ~~to choose~~ the ~~right web hosting plan~~. ~~After that~~ the ~~developer adds the unordered list for navigations~~. <br><br>~~There has been a huge increase in the number of developers releasing free premium Word - Press themes over the years. I have compiled a few tips on how you can start a food blog~~ and ~~hopefully~~ the following ~~information and tips can help you to get started on your food blogging creative journey. However, you may not be able to find a theme that~~ is ~~in sync with your business. Fast Content Update~~ - ~~It'~~s ~~easy to edit or add posts~~ with ~~free Wordpress websites. OSDI, a Wordpress Development Company based on ahmedabad, India.~~ <br><br>~~More it extends numerous opportunities where your firm is at comfort and rest assured~~ of ~~no risks & errors~~. ~~Mahatma Gandhi is known as one of~~ the most ~~prominent personalities and symbols of peace,~~ non-~~violence and freedom. By~~ the ~~time you get~~ the ~~Gallery Word~~ - ~~Press Themes, the first thing that you should know~~ is on ~~how to install it~~. ~~If this~~ is ~~not possible you still have~~ the ~~choice~~ of the ~~default theme that is Word~~ - ~~Press 3~~. ~~Get started today so that people searching~~ for ~~your type~~ of ~~business will be directed to you~~.		The ''k'' population version of the test is an extension of the test for two populations published by Van der Waerden (1952,1953).

			==Background==
			[[Analysis of Variance]] (ANOVA) is a [[data analysis]] technique for examining the significance of the factors ([[independent variables]]) in a multi-factor model. The one factor model can be thought of as a generalization of the [[two sample t-test]]. That is, the two sample t-test is a test of the hypothesis that two population means are equal. The one factor ANOVA tests the hypothesis that ''k'' population means are equal. The standard ANOVA assumes that the errors (i.e., residuals) are [[normal distribution\|normally distributed]]. If this normality assumption is not valid, an alternative is to use a [[non-parametric test]].

			==Test definition==
			Let ''n<sub>j</sub>'' (''j'' = 1, 2, ..., ''k'') represent the sample sizes for each of the ''k'' groups (i.e., samples) in the data. Let ''N'' denote the sample size for all groups. Let ''X<sub>ij</sub>'' represent the ''i''<sup>th</sup> value in the ''j''<sup>th</sup> group. The normal scores are computed as
			:<math>
			A_{ij} = \Phi^{-1}\left(\frac{R(X_{ij})}{N+1}\right)
			</math>
			where ''R''(''X<sub>ij</sub>'') denotes the rank of observation ''X<sub>ij</sub>'' and where ''Φ''<sup>-1</sup> denotes the normal [[quantile function]]. The average of the normal scores for each sample can then be computed as
			:<math>
			\bar{A}_j = \frac{1}{n_j}\sum_{i=1}^{n_j}A_{ij}\quad j=1,2,\ldots, k
			</math>
			The variance of the normal scores can be computed as
			:<math>
			s^2 = \frac{1}{N-1}\sum_{j=1}^k\sum_{i=1}^{n_j}A_{ij}^2
			</math>
			The Van Der Waerden test can then be defined as follows:
			:H<sub>0</sub>: All of the ''k'' population distribution functions are identical
			:H<sub>a</sub>: At least one of the populations tends to yield larger observations than at least one of the other populations

			The test statistic is
			:<math>
			T_1 = \frac{1}{s^2}\sum_{j=1}^kn_j\bar{A}_j^2
			</math>
			For [[significance level]] α, the critical region is
			:<math>
			T_1 > \chi_{\alpha,k-1}^2
			</math>
			where Χ<sub>α,k − 1</sub><sup>2</sup> is the α-[[quantile]] of the [[chi-squared distribution]] with ''k'' − 1 degrees of freedom. The null hypothesis is rejected if the test statistic is in the critical region. If the hypothesis of identical distributions is rejected, one can perform a [[multiple comparisons]] procedure to determine which pairs of populations tend to differ. The populations ''j<sub>1</sub>'' and ''j<sub>2</sub>'' seem to be different if the following inequality is satisfied:
			:<math>
			\left\vert \bar{A}_{j_1} - \bar{A}_{j_2}\right\vert > s \,t_{1-\alpha/2}\sqrt{\frac{N-1-T_1}{N-k}}\sqrt{\frac{1}{n_{j_1}}+\frac{1}{n_{j_2}}}
			</math>
			with ''t''<sub>1 − α/2</sub> the (1 − α/2)-[[quantile]] of the [[Student's t-distribution\|t-distribution]].

			==Comparison with the Kruskal-Wallis test==
			The most common non-parametric test for the one-factor model is the [[Kruskal-Wallis one-way analysis of variance\|Kruskal-Wallis test]]. The Kruskal-Wallis test is based on the ranks of the data. The advantage of the Van Der Waerden test is that it provides the high efficiency of the standard ANOVA analysis when the normality assumptions are in fact satisfied, but it also provides the robustness of the Kruskal-Wallis test when the normality assumptions are not satisfied.

			==References==
			*{{cite book
			\|first= W. J.
			\|last=Conover
			\|year = 1999
			\|title = Practical Nonparameteric Statistics
			\|edition = Third Edition
			\|publisher = Wiley
			\|pages = 396–406}}

			*van der Waerden, B.L. (1952). "Order tests for the two-sample problem and their power", ''Indagationes Mathematicae'', 14, 453–458.

			*van der Waerden, B.L. (1953). "Order tests for the two-sample problem. II, III", ''Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Serie A'', 564, 303–310, 311–316.

			{{NIST-PD}}

			[[Category:Statistical tests]]
			[[Category:Non-parametric statistics]]

en>David Eppstein: primary sources

2012-08-29T05:24:50Z

primary sources

New page

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purcase and download - WPZOOM Tribune wordpress Theme, find and use the WPZOOM Discount Code. WPTouch is among the more well known Word - Press smartphone plugins which is currently in use by thousands of users. With the free Word - Press blog, you have the liberty to come up with your own personalized domain name. E-commerce websites are meant to be buzzed with fresh contents, graphical enhancements, and functionalities. For more info on [https://deathcontrol.de/index/users/view/id/49661 wordpress dropbox backup] review the web-page. You can also get a free keyword tool that is to determine how strong other competing sites are and number of the searches on the most popular search sites. Usually, Wordpress owners selling the ad space on monthly basis and this means a residual income source. After sending these details, your Word - Press blog will be setup within a few days. This platform can be customizedaccording to the requirements of the business. The first thing you need to do is to choose the right web hosting plan. After that the developer adds the unordered list for navigations. There has been a huge increase in the number of developers releasing free premium Word - Press themes over the years. I have compiled a few tips on how you can start a food blog and hopefully the following information and tips can help you to get started on your food blogging creative journey. However, you may not be able to find a theme that is in sync with your business. Fast Content Update - It's easy to edit or add posts with free Wordpress websites. OSDI, a Wordpress Development Company based on ahmedabad, India. More it extends numerous opportunities where your firm is at comfort and rest assured of no risks & errors. Mahatma Gandhi is known as one of the most prominent personalities and symbols of peace, non-violence and freedom. By the time you get the Gallery Word - Press Themes, the first thing that you should know is on how to install it. If this is not possible you still have the choice of the default theme that is Word - Press 3. Get started today so that people searching for your type of business will be directed to you.