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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationSun, 07 Dec 2008 12:10:32 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/07/t12286770649ff3r4ye92y68wd.htm/, Retrieved Sun, 19 May 2024 08:56:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30256, Retrieved Sun, 19 May 2024 08:56:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact235

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean versus Median] [Totale Invoer naa...] [2008-12-07 18:21:05] [299afd6311e4c20059ea2f05c8dd029d]
- RM D  [Variability] [Totale Invoer naa...] [2008-12-07 18:28:38] [299afd6311e4c20059ea2f05c8dd029d]
- RMP     [Stem-and-leaf Plot] [Totale Invoer naa...] [2008-12-07 18:32:41] [299afd6311e4c20059ea2f05c8dd029d]
- RMPD      [Quartiles] [Totale Invoer naa...] [2008-12-07 18:52:56] [299afd6311e4c20059ea2f05c8dd029d]
- RM D        [Harrell-Davis Quantiles] [Totale Invoer naa...] [2008-12-07 19:02:20] [299afd6311e4c20059ea2f05c8dd029d]
- RM D            [Pearson Correlation] [Totale Uitvoer vs...] [2008-12-07 19:10:32] [5e2b1e7aa808f9f0d23fd35605d4968f] [Current]
- RM D              [Kendall tau Rank Correlation] [Totale Uitvoer vs...] [2008-12-07 19:18:32] [299afd6311e4c20059ea2f05c8dd029d]
- RMPD              [Univariate Explorative Data Analysis] [Totale Uitvoer (2...] [2008-12-17 14:52:16] [299afd6311e4c20059ea2f05c8dd029d]
- RMPD              [Univariate Explorative Data Analysis] [Totale invoer naa...] [2008-12-17 14:56:01] [299afd6311e4c20059ea2f05c8dd029d]
-  MPD              [Pearson Correlation] [] [2010-12-20 11:15:41] [1908ef7bb1a3d37a854f5aaad1a1c348]
-  MPD              [Pearson Correlation] [] [2010-12-20 11:17:27] [1908ef7bb1a3d37a854f5aaad1a1c348]
-  MPD              [Pearson Correlation] [] [2010-12-20 11:18:50] [1908ef7bb1a3d37a854f5aaad1a1c348]
-  MPD              [Pearson Correlation] [Correlatie Oliepr...] [2010-12-21 12:13:11] [ae68acb0755efbaaf8db92ef09a2ce40]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14291.1
14205.3
15859.4
15258.9
15498.6
15106.5
15023.6
12083
15761.3
16943
15070.3
13659.6
14768.9
14725.1
15998.1
15370.6
14956.9
15469.7
15101.8
11703.7
16283.6
16726.5
14968.9
14861
14583.3
15305.8
17903.9
16379.4
15420.3
17870.5
15912.8
13866.5
17823.2
17872
17420.4
16704.4
15991.2
16583.6
19123.5
17838.7
17209.4
18586.5
16258.1
15141.6
19202.1
17746.5
19090.1
18040.3
17515.5
17751.8
21072.4
17170
19439.5
19795.4
17574.9
16165.4
19464.6
19932.1
19961.2
17343.4
18924.2
18574.1
21350.6
18594.6
19823.1
20844.4
19640.2
17735.4
19813.6
22160
20664.3
17877.4
Dataseries Y:
Download CSV
Histogram 
13429.9
13470.1
14785.8
14292
14308.8
14013
13240.9
12153.4
14289.7
15669.2
14169.5
14569.8
14469.1
14264.9
15320.9
14433.5
13691.5
14194.1
13519.2
11857.9
14616
15643.4
14077.2
14887.5
14159.9
14643
17192.5
15386.1
14287.1
17526.6
14497
14398.3
16629.6
16670.7
16614.8
16869.2
15663.9
16359.9
18447.7
16889
16505
18320.9
15052.1
15699.8
18135.3
16768.7
18883
19021
18101.9
17776.1
21489.9
17065.3
18690
18953.1
16398.9
16895.7
18553
19270
19422.1
17579.4
18637.3
18076.7
20438.6
18075.2
19563
19899.2
19227.5
17789.6
19220.8
21968.9
21131.5
19484.6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30256&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30256&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30256&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean17038.316495.7875
Biased Variance4765671.028611115392838.78026042
Biased Standard Deviation2183.041691908592322.24864738047
Covariance4918918.41971831
Correlation0.956807836321042
Determination0.915481235645354
T-Test27.5357667386437
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom70
Number of Observations72

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 17038.3 & 16495.7875 \tabularnewline
Biased Variance & 4765671.02861111 & 5392838.78026042 \tabularnewline
Biased Standard Deviation & 2183.04169190859 & 2322.24864738047 \tabularnewline
Covariance & 4918918.41971831 \tabularnewline
Correlation & 0.956807836321042 \tabularnewline
Determination & 0.915481235645354 \tabularnewline
T-Test & 27.5357667386437 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 70 \tabularnewline
Number of Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30256&T=1

[TABLE]
[ROW][C]Pearson Product Moment Correlation - Ungrouped Data[/C][/ROW]
[ROW][C]Statistic[/C][C]Variable X[/C][C]Variable Y[/C][/ROW]
[ROW][C]Mean[/C][C]17038.3[/C][C]16495.7875[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4765671.02861111[/C][C]5392838.78026042[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2183.04169190859[/C][C]2322.24864738047[/C][/ROW]
[ROW][C]Covariance[/C][C]4918918.41971831[/C][/ROW]
[ROW][C]Correlation[/C][C]0.956807836321042[/C][/ROW]
[ROW][C]Determination[/C][C]0.915481235645354[/C][/ROW]
[ROW][C]T-Test[/C][C]27.5357667386437[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]70[/C][/ROW]
[ROW][C]Number of Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30256&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30256&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean17038.316495.7875
Biased Variance4765671.028611115392838.78026042
Biased Standard Deviation2183.041691908592322.24864738047
Covariance4918918.41971831
Correlation0.956807836321042
Determination0.915481235645354
T-Test27.5357667386437
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom70
Number of Observations72


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$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')