en>TakuyaMurata: /* The cotangent sheaf */

2015-01-01T00:53:35Z

The cotangent sheaf

en>Wikidsp: morphisms matter.

2014-01-04T16:33:25Z

morphisms matter.

← Older revision		Revision as of 18:33, 4 January 2014
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	~~Man or woman who wrote the short post is called Roberto Ledbetter~~ and ~~his wife isn't really like it at each of. In his~~ [~~http~~:~~//Www~~.~~Bing~~.~~com/search?q=professional+life&form=MSNNWS&mkt=en~~-~~us&pq=professional+life professional life~~] ~~he is also a people manager. He's always loved living for Guam and he [http://search.Usa.gov/search?query=delivers delivers~~] everything that he needs there. The precious hobby for him plus his kids is you will need but he's been taking on new things not too lengthy ago. He's been working on a website for some era now. Check it out here: http://prometeu.net<br><br>		{{redirect\|Standardize\|industrial and technical standards\|Standardization}}
			{{about\|\|Fisher z-transformation in statistics\|Fisher transformation\|Z-values in ecology\|Z-value\|z-transformation to complex number domain\|Z-transform\|Z-factor in high-throughput screening\|Z-factor\|Z-score financial analysis tool\|Altman Z-score}}
			[[Image:Normal distribution and scales.gif\|thumb\|350px\|right\|Compares the various grading methods in a normal distribution. Includes: Standard deviations, cumulative percentages, percentile equivalents, Z-scores, T-scores, standard nine, percent in [[stanine]]]]

	~~Here~~ is ~~my weblog~~; [http://~~prometeu~~.~~net hack clash~~ of ~~clans~~]		In [[statistics]], the '''standard score''' is the (signed) number of [[standard deviation]]s an observation or [[data\|datum]] is ''above'' the [[mean]]. Thus, a positive standard score represents a datum above the mean, while a negative standard score represents a datum below the mean. It is a [[dimensionless number\|dimensionless quantity]] obtained by subtracting the [[population mean]] from an individual [[raw score]] and then dividing the difference by the [[statistical population\|population]] [[standard deviation]]. This conversion process is called '''standardizing''' or '''normalizing''' (however, "normalizing" can refer to many types of ratios; see [[normalization (statistics)]] for more).

			Standard scores are also called '''z-values, ''z''-scores, normal scores,''' and '''standardized variables;''' the use of "Z" is because the [[normal distribution]] is also known as the "Z distribution". They are most frequently used to compare a sample to a [[standard normal deviate]] (standard normal distribution, with ''μ'' = 0 and ''σ'' = 1), though they can be defined without assumptions of normality.

			The z-score is ''only'' defined if one knows the population parameters; if one only has a sample set, then the analogous computation with sample mean and sample standard deviation yields the [[Student's t-statistic]].

			The standard score is not the same as the [[z-factor]] used in the analysis of [[high-throughput screening]] data though the two are often conflated.

			== Calculation from raw score ==

			The standard score of a raw score ''x'' <ref>Kreyszig 1979, p880 eq(5)</ref> is

			:<math>z = {x- \mu \over \sigma}</math>

			where:

			: ''μ'' is the [[mean]] of the population;
			: ''σ'' is the [[standard deviation]] of the population.

			The absolute value of ''z'' represents the distance between the raw score and the population mean in units of the standard deviation. ''z'' is negative when the raw score is below the mean, positive when above.

			A key point is that calculating ''z'' requires the population mean and the population standard deviation, not the sample mean or sample deviation. It requires knowing the population parameters, not the statistics of a sample drawn from the population of interest. But knowing the true standard deviation of a population is often unrealistic except in cases such as [[standardized testing]], where the entire population is measured. In cases where it is impossible to measure every member of a population, the standard deviation may be estimated using a random sample.

			It measures the sigma distance of actual data from the average.

			The Z value provides an assessment of how off-target a process is operating.

			== Applications ==

			The z-score is often used in the [[z-test]] in [[standardized testing]] – the analog of the [[Student's t-test]] for a population whose parameters are known, rather than estimated. As it is very unusual to know the entire population, the t-test is much more widely used.

			{{anchor\|prediction intervals}}
			Also, standard score can be used in the calculation of [[prediction interval]]s. A prediction interval [''L'',''U''], consisting of a lower endpoint designated ''L'' and an upper endpoint designated ''U'', is an interval such that a future observation ''X'' will lie in the interval with high probability <math>\gamma</math>, i.e.

			:<math>P(L<X<U) =\gamma,</math>

			For example <math>\gamma= 0.95 (95\%)</math>.

			For the standard score ''Z'' of ''X'' it gives:<ref>Kreyszig 1979, p880 eq(6)</ref>
			:<math>P\left( \frac{L-\mu}{\sigma} < Z < \frac{U-\mu}{\sigma} \right) = \gamma.</math>
			By determining the quantile z such that
			:<math>P\left( -z < Z < z \right) = \gamma</math>
			it follows:
			:<math>L=\mu-z\sigma,\ U=\mu+z\sigma</math>

			==Standardizing in mathematical statistics==
			{{further2\|[[Normalization (statistics)]]}}
			In [[mathematical statistics]], a [[random variable]] ''X'' is '''standardized''' by subtracting its [[expected value]] <math>\operatorname{E}[X]</math> and dividing the difference by its [[standard deviation]] <math>\sigma(X) = \sqrt{\operatorname{Var}(X)}:</math>

			:<math>Z = {X - \operatorname{E}[X] \over \sigma(X)}</math>

			If the random variable under consideration is the [[sample mean]] of a random sample <math> \ X_1,\dots, X_n</math> of ''X'':

			:<math>\bar{X}={1 \over n} \sum_{i=1}^n X_i</math>

			then the standardized version is

			:<math>Z = \frac{\bar{X}-\operatorname{E}[X]}{\sigma(X)/\sqrt{n}}.</math>

			See [[normalization (statistics)]] for other forms of normalization.

			==See also==
			* [[Standard normal deviate]]
			* [[Z-test]]

			==References==
			*Kreyszig, E (fourth edition 1979). ''Applied Mathematics'', Wiley Press.
			{{reflist}}

			==Further reading==
			* {{Cite book\|last=Carroll\|first=Susan Rovezzi\|last2=Carroll\|first2=David J.
			\|title=Statistics Made Simple for School Leaders \|url=http://books.google.com/?id=gccHkMDikb0C
			\|accessdate=7 June 2009 \|edition=illustrated \|year=2002\|publisher=Rowman & Littlefield \|isbn=978-0-8108-4322-6\|postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}
			*Richard J. Larsen and Morris L. Marx (2000) ''An Introduction to Mathematical Statistics and Its Applications, Third Edition,'' ISBN 0-13-922303-7. p. 282.

			== External links ==
			* [http://staff.argyll.epsb.ca/jreed/math30p/statistics/standardCurve.htm Interactive Flash on the z-scores and the probabilities of the normal curve] by Jim Reed

			{{Statistics}}

			[[Category:Statistical terminology]]
			[[Category:Statistical ratios]]

134.76.83.150: /* The tautological one-form */

2011-05-25T18:28:11Z

The tautological one-form

New page

Man or woman who wrote the short post is called Roberto Ledbetter and his wife isn't really like it at each of. In his [http://Www.Bing.com/search?q=professional+life&form=MSNNWS&mkt=en-us&pq=professional+life professional life] he is also a people manager. He's always loved living for Guam and he [http://search.Usa.gov/search?query=delivers delivers] everything that he needs there. The precious hobby for him plus his kids is you will need but he's been taking on new things not too lengthy ago. He's been working on a website for some era now. Check it out here: http://prometeu.net<br><br>

Here is my weblog; [http://prometeu.net hack clash of clans]

Cotangent bundle - Revision history

en>TakuyaMurata: /* The cotangent sheaf */

en>Wikidsp: morphisms matter.

134.76.83.150: /* The tautological one-form */