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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 05:29:46 -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/t1224502265b3bgp30v02v4skh.htm/, Retrieved Sun, 19 May 2024 14:39:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17199, Retrieved Sun, 19 May 2024 14:39:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords2 de cor
Estimated Impact120

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 11:29:46] [d8c5724db236abb5950452133b88474d] [Current]
Feedback Forum
2008-10-27 23:35:14 [2b91075c702c6e89854c34747e80ec72] [reply] 
De correlatiecoëfficiënt van deze tijdreeks bedraagt 0.245956990439531.
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 deze correlatiefactor zwak is i.p.v. negatief want hij is gelegen tussen 0,1 - 0,3.
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

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 
16.42
16.47
16.44
16.44
16.49
16.32
16.47
16.39
16.42
16.39
16.4
16.24
16.42
16.46
16.47
16.37
16.42
16.34
16.41
16.43
16.4
16.35
16.31
16.18
16.29
16.27
16.31
16.28
16.32
16.32
16.37
16.39
16.51
16.5
16.49
16.32
16.37
16.39
16.41
16.39
16.41
16.37
16.4
16.53
16.63
16.64
16.63
16.47
16.46
16.49
16.59
16.58
16.6
16.55
16.57
16.51
16.5
16.49
16.44
16.26
16.33
16.72
16.75
16.74
16.84
16.79
16.66
16.69
16.84
16.86
16.76
16.72
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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17199&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17199&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17199&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean16.4752.19444444444444
Biased Variance0.02382222222222220.402469135802469
Biased Standard Deviation0.1543444920372030.634404552160898
Covariance0.0244225352112676
Correlation0.245956990439531
Determination0.0604948411460718
T-Test2.12304209716531
p-value (2 sided)0.0372879503644179
p-value (1 sided)0.0186439751822089
Degrees of Freedom70
Number of Observations72

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 16.475 & 2.19444444444444 \tabularnewline
Biased Variance & 0.0238222222222222 & 0.402469135802469 \tabularnewline
Biased Standard Deviation & 0.154344492037203 & 0.634404552160898 \tabularnewline
Covariance & 0.0244225352112676 \tabularnewline
Correlation & 0.245956990439531 \tabularnewline
Determination & 0.0604948411460718 \tabularnewline
T-Test & 2.12304209716531 \tabularnewline
p-value (2 sided) & 0.0372879503644179 \tabularnewline
p-value (1 sided) & 0.0186439751822089 \tabularnewline
Degrees of Freedom & 70 \tabularnewline
Number of Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17199&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]16.475[/C][C]2.19444444444444[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0238222222222222[/C][C]0.402469135802469[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.154344492037203[/C][C]0.634404552160898[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0244225352112676[/C][/ROW]
[ROW][C]Correlation[/C][C]0.245956990439531[/C][/ROW]
[ROW][C]Determination[/C][C]0.0604948411460718[/C][/ROW]
[ROW][C]T-Test[/C][C]2.12304209716531[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0372879503644179[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0186439751822089[/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=17199&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17199&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
Mean16.4752.19444444444444
Biased Variance0.02382222222222220.402469135802469
Biased Standard Deviation0.1543444920372030.634404552160898
Covariance0.0244225352112676
Correlation0.245956990439531
Determination0.0604948411460718
T-Test2.12304209716531
p-value (2 sided)0.0372879503644179
p-value (1 sided)0.0186439751822089
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')