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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationMon, 20 Oct 2008 05:50:46 -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/t1224503529p1vkeqvq4dyndum.htm/, Retrieved Wed, 29 May 2024 06:41:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17205, Retrieved Wed, 29 May 2024 06:41:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords4 de cor
Estimated Impact162

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Pearson Correlation] [Correlatie tussen...] [2008-10-20 11:50:46] [d8c5724db236abb5950452133b88474d] [Current]
Feedback Forum
2008-10-27 23:38:11 [2b91075c702c6e89854c34747e80ec72] [reply] 
De correlatiecoëfficiënt van deze tijdreeks bedraagt 0.0550805362953196….
Het is inderdaad zo dat deze dichter bij 0 aanleunt dan bij 1, maar dat wil niet zeggen dat deze daarom negatief is. We kunnen dus stellen dat er in dit geval gewoon geen verband is want de correlatiefactor is praktisch gelijk aan 0.
Enige verduidelijking van de graad van de sterkte van een correlatiecoëfficiënt:
sterk verband: 0,5 - 1,0
gemiddeld verband: 0,3 - 0,5
zwak verband: 0,1 - 0,3
geen verband: <0

De verklaring van een negatieve correlatiecoëfficiënt is dat deze moet liggen tussen 0 en -1. De betekenis hiervan is dat als de waarden van de ene reeks stijgen, de waarden van de andere dalen. Als dus bvb.de waarden van de wisky stijgt, dan zal de waarden van de nationale consumptieprijs index dalen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3,42
3,42
3,43
3,47
3,51
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,58
3,6
3,61
3,61
3,61
3,63
3,68
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,78
3,79
3,79
3,8
3,8
3,8
3,8
3,81
3,95
3,99
4
4,06
4,16
4,19
4,2
4,2
4,2
4,2
4,2
4,23
4,38
4,43
4,44
4,44
4,44
4,44
4,44
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,46
4,46
4,46
4,48
4,58
4,67
4,68
4,68
Dataseries Y:
Download CSV
Histogram 
1,8
1,9
2,2
2,1
2,2
2,7
2,8
2,9
3,4
3
3,1
2,5
2,2
2,3
2,1
2,8
3,1
2,9
2,6
2,7
2,3
2,3
2,1
2,2
2,9
2,6
2,7
1,8
1,3
0,9
1,3
1,3
1,3
1,3
1,1
1,4
1,2
1,7
1,8
1,5
1
1,6
1,5
1,8
1,8
1,6
1,9
1,7
1,6
1,3
1,1
1,9
2,6
2,3
2,4
2,2
2
2,9
2,6
2,3
2,3
2,6
3,1
2,8
2,5
2,9
3,1
3,1
3,2
2,5
2,6
2,9

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=17205&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=17205&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17205&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
Mean3.983333333333332.19444444444444
Biased Variance0.1599888888888890.402469135802469
Biased Standard Deviation0.3999861108699760.634404552160898
Covariance0.0141737089201878
Correlation0.0550805362953196
Determination0.00303386547858002
T-Test0.461537482727014
p-value (2 sided)0.64584410102548
p-value (1 sided)0.32292205051274
Degrees of Freedom70
Number of Observations72

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3.98333333333333 & 2.19444444444444 \tabularnewline
Biased Variance & 0.159988888888889 & 0.402469135802469 \tabularnewline
Biased Standard Deviation & 0.399986110869976 & 0.634404552160898 \tabularnewline
Covariance & 0.0141737089201878 \tabularnewline
Correlation & 0.0550805362953196 \tabularnewline
Determination & 0.00303386547858002 \tabularnewline
T-Test & 0.461537482727014 \tabularnewline
p-value (2 sided) & 0.64584410102548 \tabularnewline
p-value (1 sided) & 0.32292205051274 \tabularnewline
Degrees of Freedom & 70 \tabularnewline
Number of Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17205&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]3.98333333333333[/C][C]2.19444444444444[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.159988888888889[/C][C]0.402469135802469[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.399986110869976[/C][C]0.634404552160898[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0141737089201878[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0550805362953196[/C][/ROW]
[ROW][C]Determination[/C][C]0.00303386547858002[/C][/ROW]
[ROW][C]T-Test[/C][C]0.461537482727014[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.64584410102548[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.32292205051274[/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=17205&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17205&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
Mean3.983333333333332.19444444444444
Biased Variance0.1599888888888890.402469135802469
Biased Standard Deviation0.3999861108699760.634404552160898
Covariance0.0141737089201878
Correlation0.0550805362953196
Determination0.00303386547858002
T-Test0.461537482727014
p-value (2 sided)0.64584410102548
p-value (1 sided)0.32292205051274
Degrees of Freedom70
Number of Observations72


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')