en>BG19bot: /* Applications in building physics */WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9479)

2013-09-13T17:27:36Z

Applications in building physics: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9479)

← Older revision		Revision as of 19:27, 13 September 2013
Line 1:		Line 1:
	I'~~m a 50 years old~~ and ~~work at the high school (Modern Languages and Classics).<br>In my spare time~~ I ~~learn Norwegian~~. ~~I have been there~~ and ~~look forward~~ to ~~returning sometime in~~ the ~~future.~~ I ~~love~~ to ~~read, preferably on my beloved Kindle~~. I ~~like~~ to ~~watch CSI and The Vampire Diaries as well as docus about anything scientific~~. I ~~like Meteorology~~.<br><br>		{{DISPLAYTITLE:Moran's ''I''}}
			{{multiple issues\|primarysources = March 2013\|refimprove = March 2013}}
			[[File:Checkerboard pattern.svg\|thumb\|right\|The white and black squares are perfectly dispersed so Moran's ''I'' would be −1. If the white squares were stacked to one half of the board and the black squares to the other, Moran's ''I'' would be close to +1. A random arrangement of square colors would give Moran's ''I'' a value that is close to 0.]]
			In [[statistics]], '''Moran's ''I''''' is a measure of [[spatial autocorrelation]] developed by [[Patrick Alfred Pierce Moran]].<ref>{{cite jstor\|2332142}}</ref><ref>{{cite journal \|last1=Li \|first1=Hongfei \|first2=Catherine A. \|last2=Calder \|first3=Noel \|last3=Cressie \|title=Beyond Moran's ''I'': Testing for Spatial Dependence Based on the Spatial Autoregressive Model \|journal=Geographical Analysis \|year=2007 \|volume=39 \|issue=4 \|pages=357–375 \|doi=10.1111/j.1538-4632.2007.00708.x}}</ref> Spatial autocorrelation is characterized by a correlation in a signal among nearby locations in space. Spatial autocorrelation is more complex than one-dimensional [[autocorrelation]] because spatial correlation is multi-dimensional (i.e. 2 or 3 dimensions of space) and multi-directional.

	~~Take~~ a ~~look at my web page~~ :: ~~[http~~://~~www.gameoz.net~~/~~profile~~/~~325887~~/~~ra2002~~.~~html wordpress dropbox backup~~]		Moran's ''I'' is defined as

			:<math> I = \frac{N} {\sum_{i} \sum_{j} w_{ij}} \frac {\sum_{i} \sum_{j} w_{ij}(X_i-\bar X) (X_j-\bar X)} {\sum_{i} (X_i-\bar X)^2} </math>

			where <math>N</math> is the number of spatial units indexed by <math>i</math> and <math>j</math>; <math>X</math> is the variable of interest; <math>\bar X</math> is the mean of <math>X</math>; and <math>w_{ij}</math> is an element of a matrix of spatial weights.

			The expected value of Moran's ''I'' under the null hypothesis of no spatial autocorrelation is
			:<math> E(I) = \frac{-1} {N-1} </math>

			Its variance equals
			:<math> \operatorname{Var}(I) = \frac{NS_4-S_3S_5} {(N-1)(N-2)(N-3)(\sum_{i} \sum_{j} w_{ij})^2} </math>
			where
			:<math> S_1 = \frac {1} {2} \sum_{i} \sum_{j} (w_{ij}+w_{ji})^2 </math>

			:<math> S_2 = \frac {\sum_{i} ( \sum_{j} w_{ij} + \sum_{j} w_{ji})^2} {1} </math>

			:<math> S_3 = \frac {N^{-1} \sum_{i} (x_i - \bar x)^4} {(N^{-1} \sum_{i} (x_i - \bar x)^2)^2} </math>

			:<math> S_4 = \frac {(N^2-3N+3)S_1 - NS_2 + 3 (\sum_{i} \sum_{j} w_{ij})^2} {1} </math>

			:<math> S_5 = S_1 - 2NS_1 + \frac {6(\sum_{i} \sum_{j} w_{ij})^2} {1} </math>

			Negative (positive) values indicate negative (positive) spatial autocorrelation. Values range from −1 (indicating perfect dispersion) to +1 (perfect correlation). A zero value indicates a random spatial pattern. For statistical hypothesis testing, Moran's ''I'' values can be transformed to Z-scores in which values greater than 1.96 or smaller than −1.96 indicate spatial autocorrelation that is significant at the 5% level.

			Moran's ''I'' is inversely related to [[Geary's C\|Geary's ''C'']], but it is not identical. Moran's ''I'' is a measure of global spatial autocorrelation, while Geary's ''C'' is more sensitive to local spatial autocorrelation.

			==Sources==
			{{reflist}}

			== See also ==
			* [[Indicators of spatial association]]

			[[Category:Spatial data analysis]]
			[[Category:Covariance and correlation]]

en>PJ Geest at 08:42, 13 May 2012

2012-05-13T08:42:10Z

New page

I'm a 50 years old and work at the high school (Modern Languages and Classics).<br>In my spare time I learn Norwegian. I have been there and look forward to returning sometime in the future. I love to read, preferably on my beloved Kindle. I like to watch CSI and The Vampire Diaries as well as docus about anything scientific. I like Meteorology.<br><br>

Take a look at my web page :: [http://www.gameoz.net/profile/325887/ra2002.html wordpress dropbox backup]

Heat flux sensor - Revision history

en>BG19bot: /* Applications in building physics */WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9479)

en>PJ Geest at 08:42, 13 May 2012