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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 computationSun, 02 Oct 2011 15:13:11 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/02/t1317582810lvsblz6tdgdmv9o.htm/, Retrieved Fri, 01 Nov 2024 00:09:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=125143, Retrieved Fri, 01 Nov 2024 00:09:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111

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] [Screen dimensions] [2010-09-25 10:10:17] [b98453cac15ba1066b407e146608df68]
- R       [Pearson Correlation] [Scatterplot] [2011-10-02 19:13:11] [7a9891c1925ad1e8ddfe52b8c5887b5b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1280
1024
1120
1024
1280
1280
1280
1024
1280
1280
1280
1280
1280
1688
1440
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1280
1280
1280
1176
1280
1503
1440
1366
1280
1024
1280
2560
1280
1024
1280
1280
1440
1280
1440
1024
1440
1143
1280
1440
1280
1366
1024
1408
1366
1176
1920
1257
1280
1280
1440
1680
1440
1024
1140
1280
1280
1280
1280
1280
1440
1280
1152
1280
1280
1440
1280
1280
1440
1280
1280
1440
1280
1280
1600
1024
1366
1280
1280
1440
1366
1280
1024
1280
1440
1280
1280
1408
1280
1600
1600
1680
1440
1440
917
1280
1760
1280
1280
1280
1024
1366
1440
1280
1280
1920
1024
1024
1600
1117
1440
983
1024
1024
1280
1440
1280
1280
1280
1440
1280
1024
1024
1152
1280
1024
1366
1680
1680
1280
1366
1024
1440
1024
1280
1280
1280
1024
1280
Dataseries Y:
Download CSV
Histogram 
1024
768
700
768
800
1024
800
768
800
1024
800
800
1024
949
900
1200
800
800
768
735
800
845
900
768
768
768
800
1440
768
768
1024
800
900
800
900
768
900
857
800
900
800
768
768
880
768
735
1200
785
800
800
900
1050
900
768
641
1024
800
800
800
800
900
800
864
1024
800
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1024
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1024
900
768
768
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768
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768
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880
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1050
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1024
1080
768
768
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698
900
737
768
640
800
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800
800
800
900
800
768
768
864
768
768
768
1050
1050
800
768
768
900
768
800
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800
768
800

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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=125143&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=125143&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=125143&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' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1309.15107913669844.503597122302
Biased Variance45390.718182288712936.8686920967
Biased Standard Deviation213.050975548784113.740356479557
Covariance18734.6480033365
Correlation0.767558899807277
Determination0.589146664673358
T-Test14.0161451635828
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom137
Number of Observations139

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1309.15107913669 & 844.503597122302 \tabularnewline
Biased Variance & 45390.7181822887 & 12936.8686920967 \tabularnewline
Biased Standard Deviation & 213.050975548784 & 113.740356479557 \tabularnewline
Covariance & 18734.6480033365 \tabularnewline
Correlation & 0.767558899807277 \tabularnewline
Determination & 0.589146664673358 \tabularnewline
T-Test & 14.0161451635828 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 137 \tabularnewline
Number of Observations & 139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=125143&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]1309.15107913669[/C][C]844.503597122302[/C][/ROW]
[ROW][C]Biased Variance[/C][C]45390.7181822887[/C][C]12936.8686920967[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]213.050975548784[/C][C]113.740356479557[/C][/ROW]
[ROW][C]Covariance[/C][C]18734.6480033365[/C][/ROW]
[ROW][C]Correlation[/C][C]0.767558899807277[/C][/ROW]
[ROW][C]Determination[/C][C]0.589146664673358[/C][/ROW]
[ROW][C]T-Test[/C][C]14.0161451635828[/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]137[/C][/ROW]
[ROW][C]Number of Observations[/C][C]139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=125143&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=125143&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
Mean1309.15107913669844.503597122302
Biased Variance45390.718182288712936.8686920967
Biased Standard Deviation213.050975548784113.740356479557
Covariance18734.6480033365
Correlation0.767558899807277
Determination0.589146664673358
T-Test14.0161451635828
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom137
Number of Observations139


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')