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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 computationMon, 20 Oct 2008 14:13:02 -0600
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/Oct/20/t1224534292cwoqw14yw6vomwy.htm/, Retrieved Sat, 18 May 2024 14:53:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18080, Retrieved Sat, 18 May 2024 14:53:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [investigating Ass...] [2007-10-22 22:15:01] [8cd6641b921d30ebe00b648d1481bba0]
-    D    [Pearson Correlation] [] [2008-10-20 20:13:02] [7ed4ec9f8cdf7df79ef87b9dc09dff20] [Current]
- R  D      [Pearson Correlation] [Correlatie Totaal...] [2008-10-20 22:11:16] [84dda5145c389bd11bcc662bd33fe4ba]
F R  D      [Pearson Correlation] [Correlatie Totaal...] [2008-10-20 22:11:16] [84dda5145c389bd11bcc662bd33fe4ba]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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
17422
16704,5
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
22238,5
20682,2
17818,6
21872,1
22117
21865,9
Dataseries Y:
Download CSV
Histogram 
12300
12092,8
12380,8
12196,9
9455
13168
13427,9
11980,5
11884,8
11691,7
12233,8
14341,4
13130,7
12421,1
14285,8
12864,6
11160,2
14316,2
14388,7
14013,9
13419
12769,6
13315,5
15332,9
14243
13824,4
14962,9
13202,9
12199
15508,9
14199,8
15169,6
14058
13786,2
14147,9
16541,7
13587,5
15582,4
15802,8
14130,5
12923,2
15612,2
16033,7
16036,6
14037,8
15330,6
15038,3
17401,8
14992,5
16043,7
16929,6
15921,3
14417,2
15961
17851,9
16483,9
14215,5
17429,7
17839,5
17629,2

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=18080&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=18080&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18080&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
Mean17806.653333333314294.1416666667
Biased Variance4961000.601155553212271.93909722
Biased Standard Deviation2227.330375394621792.28121094242
Covariance4050469.08892655
Correlation0.997735193835747
Determination0.995475517018455
T-Test112.965234699188
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 17806.6533333333 & 14294.1416666667 \tabularnewline
Biased Variance & 4961000.60115555 & 3212271.93909722 \tabularnewline
Biased Standard Deviation & 2227.33037539462 & 1792.28121094242 \tabularnewline
Covariance & 4050469.08892655 \tabularnewline
Correlation & 0.997735193835747 \tabularnewline
Determination & 0.995475517018455 \tabularnewline
T-Test & 112.965234699188 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18080&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]17806.6533333333[/C][C]14294.1416666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4961000.60115555[/C][C]3212271.93909722[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2227.33037539462[/C][C]1792.28121094242[/C][/ROW]
[ROW][C]Covariance[/C][C]4050469.08892655[/C][/ROW]
[ROW][C]Correlation[/C][C]0.997735193835747[/C][/ROW]
[ROW][C]Determination[/C][C]0.995475517018455[/C][/ROW]
[ROW][C]T-Test[/C][C]112.965234699188[/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]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18080&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18080&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
Mean17806.653333333314294.1416666667
Biased Variance4961000.601155553212271.93909722
Biased Standard Deviation2227.330375394621792.28121094242
Covariance4050469.08892655
Correlation0.997735193835747
Determination0.995475517018455
T-Test112.965234699188
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom58
Number of Observations60


Figures (Output of Computation)

Input Parameters & R Code

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