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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, 02 Nov 2009 03:05:54 -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/2009/Nov/02/t1257156464flwv8g69nhpjksu.htm/, Retrieved Fri, 03 May 2024 16:32:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=52467, Retrieved Fri, 03 May 2024 16:32:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
- RMPD  [Bivariate Explorative Data Analysis] [run sequence plot] [2009-10-27 18:21:30] [134dc66689e3d457a82860db6471d419]
-    D    [Bivariate Explorative Data Analysis] [eigen creatie] [2009-10-28 20:41:39] [134dc66689e3d457a82860db6471d419]
- RMPD        [Pearson Correlation] [] [2009-11-02 10:05:54] [244731fa3e7e6c85774b8c0902c58f85] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100.80
101.33
101.88
101.85
102.04
102.22
102.63
102.65
102.54
102.37
102.68
102.76
102.82
103.31
103.23
103.60
103.95
103.93
104.25
104.38
104.36
104.32
104.58
104.68
104.92
105.46
105.23
105.58
105.34
105.28
105.70
105.67
105.71
106.19
106.93
107.44
107.85
108.71
109.32
109.49
110.20
110.62
111.22
110.88
111.15
111.29
111.09
111.24
111.45
111.75
111.07
111.17
110.96
110.50
110.48
110.66
110.46
Dataseries Y:
Download CSV
Histogram 
97
98
95
89
89
89
90
86
92
91
95
99
98
95
96
94
98
98
98
98
102
101
92
99
101
99
102
102
101
99
98
98
99
92
96
94
97
97
93
91
89
87
89
91
83
78
75
80
76
76
78
81
82
83
89
89
88

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' @ 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52467&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=52467&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52467&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' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean106.38894736842192.140350877193
Biased Variance12.068819944598354.1206525084641
Biased Standard Deviation3.474020717353077.35667401129506
Covariance-16.8955639097744
Correlation-0.64948921929189
Determination0.421836245976389
T-Test-6.33472637729602
p-value (2 sided)4.61013130317777e-08
p-value (1 sided)2.30506565158889e-08
Degrees of Freedom55
Number of Observations57

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 106.388947368421 & 92.140350877193 \tabularnewline
Biased Variance & 12.0688199445983 & 54.1206525084641 \tabularnewline
Biased Standard Deviation & 3.47402071735307 & 7.35667401129506 \tabularnewline
Covariance & -16.8955639097744 \tabularnewline
Correlation & -0.64948921929189 \tabularnewline
Determination & 0.421836245976389 \tabularnewline
T-Test & -6.33472637729602 \tabularnewline
p-value (2 sided) & 4.61013130317777e-08 \tabularnewline
p-value (1 sided) & 2.30506565158889e-08 \tabularnewline
Degrees of Freedom & 55 \tabularnewline
Number of Observations & 57 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52467&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]106.388947368421[/C][C]92.140350877193[/C][/ROW]
[ROW][C]Biased Variance[/C][C]12.0688199445983[/C][C]54.1206525084641[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.47402071735307[/C][C]7.35667401129506[/C][/ROW]
[ROW][C]Covariance[/C][C]-16.8955639097744[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.64948921929189[/C][/ROW]
[ROW][C]Determination[/C][C]0.421836245976389[/C][/ROW]
[ROW][C]T-Test[/C][C]-6.33472637729602[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.61013130317777e-08[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.30506565158889e-08[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]55[/C][/ROW]
[ROW][C]Number of Observations[/C][C]57[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=52467&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52467&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
Mean106.38894736842192.140350877193
Biased Variance12.068819944598354.1206525084641
Biased Standard Deviation3.474020717353077.35667401129506
Covariance-16.8955639097744
Correlation-0.64948921929189
Determination0.421836245976389
T-Test-6.33472637729602
p-value (2 sided)4.61013130317777e-08
p-value (1 sided)2.30506565158889e-08
Degrees of Freedom55
Number of Observations57


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')