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DSHW-WS5-PearsonCorrelation

*The author of this computation has been verified*

R Software Module: /rwasp_correlation.wasp (opens new window with default values)

Title produced by software: Pearson Correlation

Date of computation: Wed, 04 Nov 2009 13:35:29 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/04/t1257366997v4kipzn7li6ensf.htm/, Retrieved Wed, 04 Nov 2009 21:36:37 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Nov/04/t1257366997v4kipzn7li6ensf.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

SDHW, DSHW

Dataseries X:

» Textbox « » Textfile « » CSV «

103,974 102,114 87,696 76,096 77,024 81,43 83,248 81,43 75,276 72,738 71,732 87,548 90,306 89,436 82,28 77,952 79,73 82,476 82,476 79,808 77,18 75,364 72,64 81,016 81,648 80,028 75,04 71,732 71,732 73,44 73,44 72,522 74,24 68,376 60,336 63,6 59,714 54,46 55,86 55,86 58,176 58,254 54,528 48,824 44,032 40,138 45,37 63,756 69,362 62,85 55,062 50,028 54,372 64,526 67,84 66,24 59,906 53,144 54,612 66,258 71,214

Dataseries Y:

» Textbox « » Textfile « » CSV «

59,892 60,822 53,418 48,708 50,132 53,04 53,664 53,04 48,708 48,114 43,766 51,084 51,678 52,548 52,19 51,576 53,89 56,898 57,768 57,104 56,44 52,622 45,92 43,788 40,824 41,634 42,72 42,976 43,766 45,12 44,32 42,186 43,52 40,348 34,848 38,55 36,792 33,88 33,18 32,48 35,568 38,252 37,204 32,912 29,056 25,864 29,51 43,428 45,346 40,05 31,326 27,984 32,016 42,658 49,12 50,72 47,278 42,632 43,956 52,164 54,282

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	70.0244262295082	44.6767213114754
Biased Variance	181.394796605214	74.4815176436442
Biased Standard Deviation	13.4682885551659	8.6302675302475
Covariance	101.018873154098
Correlation	0.854844779808507
Determination	0.730759597565855
T-Test	12.6544465066255
p-value (2 sided)	0
p-value (1 sided)	0
Degrees of Freedom	59
Number of Observations	61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/04/t1257366997v4kipzn7li6ensf/1d2xn1257366925.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/04/t1257366997v4kipzn7li6ensf/1d2xn1257366925.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

bitmap(file='test1.png')

histx <- hist(x, plot=FALSE)

histy <- hist(y, plot=FALSE)

maxcounts <- max(c(histx$counts, histx$counts))

xrange <- c(min(x),max(x))

yrange <- c(min(y),max(y))

nf <- layout(matrix(c(2,0,1,3),2,2,byrow=TRUE), c(3,1), c(1,3), TRUE)

par(mar=c(4,4,1,1))

plot(x, y, xlim=xrange, ylim=yrange, xlab=xlab, ylab=ylab)

par(mar=c(0,4,1,1))

barplot(histx$counts, axes=FALSE, ylim=c(0, maxcounts), space=0)

par(mar=c(4,0,1,1))

barplot(histy$counts, axes=FALSE, xlim=c(0, maxcounts), space=0, horiz=TRUE)

dev.off()

lx = length(x)

makebiased = (lx-1)/lx

varx = var(x)*makebiased

vary = var(y)*makebiased

corxy <- cor.test(x,y,method='pearson')

cxy <- as.matrix(corxy$estimate)[1,1]

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Statistic',1,TRUE)

a<-table.element(a,'Variable X',1,TRUE)

a<-table.element(a,'Variable Y',1,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm','Mean',''),header=TRUE)

a<-table.element(a,mean(x))

a<-table.element(a,mean(y))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/biased.htm','Biased Variance',''),header=TRUE)

a<-table.element(a,varx)

a<-table.element(a,vary)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/biased1.htm','Biased Standard Deviation',''),header=TRUE)

a<-table.element(a,sqrt(varx))

a<-table.element(a,sqrt(vary))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/covariance.htm','Covariance',''),header=TRUE)

a<-table.element(a,cov(x,y),2)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/pearson_correlation.htm','Correlation',''),header=TRUE)

a<-table.element(a,cxy,2)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/coeff_of_determination.htm','Determination',''),header=TRUE)

a<-table.element(a,cxy*cxy,2)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/ttest_statistic.htm','T-Test',''),header=TRUE)

a<-table.element(a,as.matrix(corxy$statistic)[1,1],2)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'p-value (2 sided)',header=TRUE)

a<-table.element(a,(p2 <- as.matrix(corxy$p.value)[1,1]),2)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'p-value (1 sided)',header=TRUE)

a<-table.element(a,p2/2,2)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Degrees of Freedom',header=TRUE)

a<-table.element(a,lx-2,2)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Number of Observations',header=TRUE)

a<-table.element(a,lx,2)

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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