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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 11:45:07 -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/t1224524753cgdova1jsxkzz5u.htm/, Retrieved Sun, 19 May 2024 14:06:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17779, Retrieved Sun, 19 May 2024 14:06:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122

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 17:45:07] [270782e2502ae87124d0ebdcd1862d6a] [Current]
Feedback Forum
2008-10-24 10:37:39 [Nathalie Koulouris] [reply] 
De student heeft enkel het verband tussen twee tijdreeksen onderzocht namelijk werkloosheid en de handelsbalans. De conclusie die hij hierbij getrokken heeft is niet correct. De correlatie tussen de twee tijdreeksen bedraagt 0,58. Dit wijst op een sterk verband. De student zou best ook negatieve waarden proberen weg te werken.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,6
-0,2
1,7
1,1
0,9
0
0,4
0,7
0,7
1
1,1
0,3
1,4
-0,5
1,2
1,2
0,8
-0,2
0,3
0,2
0,7
0,9
0,7
0,3
1,2
-0,6
1,1
1
0,2
-1
-0,6
0
-0,4
0,1
0,7
0,8
1,2
-0,7
0,9
0,7
0,5
-0,2
0,3
0,5
0,9
0,5
0,3
0,9
0,4
-0,1
0,6
0,2
-0,5
-1,7
-2
-1
-1,7
-1,6
-1,7
-0,9
Dataseries Y:
Download CSV
Histogram 
8,3
8,3
8,4
8,4
8,4
8,3
8
8
8,2
8,6
8,7
8,7
8,5
8,4
8,4
8,4
8,5
8,5
8,5
8,5
8,5
8,4
8,4
8,4
8,5
8,6
8,6
8,6
8,6
8,5
8,4
8,4
8,3
8,2
8,1
8,2
8,1
8
7,9
7,8
7,7
7,7
7,9
7,8
7,6
7,4
7,3
7,1
7,1
7
7
7
6,9
6,8
6,7
6,6
6,6
6,6
6,6
6,6

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'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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17779&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17779&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17779&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean0.2433333333333337.94166666666667
Biased Variance0.7594555555555550.448097222222222
Biased Standard Deviation0.8714674724598480.66940064402585
Covariance0.34545197740113
Correlation0.582305827889088
Determination0.339080077193596
T-Test5.45494921524176
p-value (2 sided)1.05773215408611e-06
p-value (1 sided)5.28866077043055e-07
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.243333333333333 & 7.94166666666667 \tabularnewline
Biased Variance & 0.759455555555555 & 0.448097222222222 \tabularnewline
Biased Standard Deviation & 0.871467472459848 & 0.66940064402585 \tabularnewline
Covariance & 0.34545197740113 \tabularnewline
Correlation & 0.582305827889088 \tabularnewline
Determination & 0.339080077193596 \tabularnewline
T-Test & 5.45494921524176 \tabularnewline
p-value (2 sided) & 1.05773215408611e-06 \tabularnewline
p-value (1 sided) & 5.28866077043055e-07 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17779&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]0.243333333333333[/C][C]7.94166666666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.759455555555555[/C][C]0.448097222222222[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.871467472459848[/C][C]0.66940064402585[/C][/ROW]
[ROW][C]Covariance[/C][C]0.34545197740113[/C][/ROW]
[ROW][C]Correlation[/C][C]0.582305827889088[/C][/ROW]
[ROW][C]Determination[/C][C]0.339080077193596[/C][/ROW]
[ROW][C]T-Test[/C][C]5.45494921524176[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.05773215408611e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]5.28866077043055e-07[/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=17779&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17779&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
Mean0.2433333333333337.94166666666667
Biased Variance0.7594555555555550.448097222222222
Biased Standard Deviation0.8714674724598480.66940064402585
Covariance0.34545197740113
Correlation0.582305827889088
Determination0.339080077193596
T-Test5.45494921524176
p-value (2 sided)1.05773215408611e-06
p-value (1 sided)5.28866077043055e-07
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')