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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 computationSat, 20 Oct 2007 07:30:46 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/20/5pmnqjmbuh4xelk1192890439.htm/, Retrieved Fri, 03 May 2024 03:04:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1102, Retrieved Fri, 03 May 2024 03:04:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact238

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [WS2Q10 G6 werkloo...] [2007-10-20 14:30:46] [68cb8c72d4101523a7ee439633ed352d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,8
7,7
7,7
7,7
7,7
7,6
7,5
7,4
7,4
7,5
7,6
7,6
8,1
7,8
8
7,9
7,9
7,8
6,7
6,6
6,6
7,7
7,9
8
7,7
7,5
7,6
7,8
7,8
7,7
7,4
7,5
7,2
7,5
7,6
7,6
7,8
7,7
7,7
8,2
8,2
8,1
7,8
7,8
7,7
6,7
6,7
6,7
7,2
6,9
6,8
7,2
7,1
6,9
6,9
6,7
6,5
6,6
6,6
6,5
Dataseries Y:
Download CSV
Histogram 
8,6
8,5
8,5
9
9
8,8
8
7,9
8,1
9,3
9,4
9,4
9,3
9
9,1
9,7
9,7
9,6
8,3
8,2
8,4
10,6
10,9
10,9
9,6
9,3
9,3
9,6
9,5
9,5
9
8,9
9
10,1
10,2
10,2
9,5
9,3
9,3
9,4
9,3
9,1
9
8,9
9
9,8
10
9,8
9,4
9
8,9
9,3
9,1
8,8
8,9
8,7
8,6
9,1
9,3
8,9

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1102&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1102&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1102&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean7.4359.21333333333333
Biased Variance0.2346083333333330.387822222222222
Biased Standard Deviation0.4843638439575490.622753741235026
Covariance0.0932542372881356
Correlation0.304005382695977
Determination0.0924192727081275
T-Test2.43025943330400
p-value (2 sided)0.0182026895502614
p-value (1 sided)0.00910134477513069
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 7.435 & 9.21333333333333 \tabularnewline
Biased Variance & 0.234608333333333 & 0.387822222222222 \tabularnewline
Biased Standard Deviation & 0.484363843957549 & 0.622753741235026 \tabularnewline
Covariance & 0.0932542372881356 \tabularnewline
Correlation & 0.304005382695977 \tabularnewline
Determination & 0.0924192727081275 \tabularnewline
T-Test & 2.43025943330400 \tabularnewline
p-value (2 sided) & 0.0182026895502614 \tabularnewline
p-value (1 sided) & 0.00910134477513069 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1102&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]7.435[/C][C]9.21333333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.234608333333333[/C][C]0.387822222222222[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.484363843957549[/C][C]0.622753741235026[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0932542372881356[/C][/ROW]
[ROW][C]Correlation[/C][C]0.304005382695977[/C][/ROW]
[ROW][C]Determination[/C][C]0.0924192727081275[/C][/ROW]
[ROW][C]T-Test[/C][C]2.43025943330400[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0182026895502614[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00910134477513069[/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=1102&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1102&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
Mean7.4359.21333333333333
Biased Variance0.2346083333333330.387822222222222
Biased Standard Deviation0.4843638439575490.622753741235026
Covariance0.0932542372881356
Correlation0.304005382695977
Determination0.0924192727081275
T-Test2.43025943330400
p-value (2 sided)0.0182026895502614
p-value (1 sided)0.00910134477513069
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')