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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 10:32:32 -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/t1224520382ws7pcoc54dx28kj.htm/, Retrieved Tue, 28 May 2024 16:26:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17611, Retrieved Tue, 28 May 2024 16:26:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [uitvoer van belgi...] [2008-10-13 19:28:16] [1e1d8320a8a1170c475bf6e4ce119de6]
- RMPD  [Pearson Correlation] [Pearson Correlati...] [2008-10-18 11:07:04] [1e1d8320a8a1170c475bf6e4ce119de6]
-    D      [Pearson Correlation] [frankrijkvsLuxemburg] [2008-10-20 16:32:32] [5d823194959040fa9b19b8c8302177e6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3258.1
3140.1
3627.4
3279.4
3204
3515.6
3146.6
2271.7
3627.9
3553.4
3018.3
3355.4
3242
3311.1
4125.2
3423
3120.3
3863
3240.8
2837.4
3945
3684.1
3659.6
3769.6
3592.7
3754
4507.8
3853.2
3817.2
3958.4
3428.9
3125.7
3977
3983.3
4299.6
4306.9
4259.5
3986
4755.6
3925.6
4206.5
4323.4
3816.1
3410.7
4227.4
4296.9
4351.7
3800
4277
4100.2
4672.5
4189.9
4231.9
4654.9
4298.5
3635.9
4505.1
4910.1
4908.7
4101.4
Dataseries Y:
Download CSV
Histogram 
335.8
368.9
404.3
382.5
333
344.1
320.3
277.8
357.7
407.8
336.8
349.9
352.2
390
455.9
400.6
376.7
417.4
376.8
351
432.8
430.2
436.6
423.3
382
391.8
463.9
431
406.2
420.4
416
364.1
471.7
449.6
470.6
724.6
472.8
441.5
555.5
468.8
460.9
447.2
432
398.6
459.7
443.5
464.7
444
449.2
432.4
519.5
420
455.5
474.6
424.2
355.2
415.3
496.9
499.7
487

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17611&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17611&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17611&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean3827.82422.883333333333
Biased Variance289185.1802666674346.61505555556
Biased Standard Deviation537.75940741810165.9288635997585
Covariance28011.113559322
Correlation0.776904306686576
Determination0.603580301748149
T-Test9.39731776214154
p-value (2 sided)2.94875235340442e-13
p-value (1 sided)1.47437617670221e-13
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3827.82 & 422.883333333333 \tabularnewline
Biased Variance & 289185.180266667 & 4346.61505555556 \tabularnewline
Biased Standard Deviation & 537.759407418101 & 65.9288635997585 \tabularnewline
Covariance & 28011.113559322 \tabularnewline
Correlation & 0.776904306686576 \tabularnewline
Determination & 0.603580301748149 \tabularnewline
T-Test & 9.39731776214154 \tabularnewline
p-value (2 sided) & 2.94875235340442e-13 \tabularnewline
p-value (1 sided) & 1.47437617670221e-13 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17611&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]3827.82[/C][C]422.883333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]289185.180266667[/C][C]4346.61505555556[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]537.759407418101[/C][C]65.9288635997585[/C][/ROW]
[ROW][C]Covariance[/C][C]28011.113559322[/C][/ROW]
[ROW][C]Correlation[/C][C]0.776904306686576[/C][/ROW]
[ROW][C]Determination[/C][C]0.603580301748149[/C][/ROW]
[ROW][C]T-Test[/C][C]9.39731776214154[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.94875235340442e-13[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.47437617670221e-13[/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=17611&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17611&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
Mean3827.82422.883333333333
Biased Variance289185.1802666674346.61505555556
Biased Standard Deviation537.75940741810165.9288635997585
Covariance28011.113559322
Correlation0.776904306686576
Determination0.603580301748149
T-Test9.39731776214154
p-value (2 sided)2.94875235340442e-13
p-value (1 sided)1.47437617670221e-13
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')