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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 computationSun, 21 Oct 2007 13:21:45 -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/21/xtih440fx354m8o1192997841.htm/, Retrieved Thu, 09 May 2024 17:55:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1315, Retrieved Thu, 09 May 2024 17:55:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Investigating Ass...] [2007-10-21 20:21:45] [640491d00f3c9cca22cbf779aa38ac16] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101.50
126.60
93.90
89.80
93.40
101.50
110.40
105.90
108.40
113.90
86.10
69.40
101.20
100.50
98.00
106.60
90.10
96.90
125.90
112.00
100.00
123.90
79.80
83.40
113.60
112.90
104.00
109.90
99.00
106.30
128.90
111.10
102.90
130.00
87.00
87.50
117.60
103.40
110.80
112.60
102.50
112.40
135.60
105.10
127.70
137.00
91.00
90.50
122.40
123.30
124.30
120.00
118.10
119.00
142.70
123.60
129.60
146.90
108.70
99.40
Dataseries Y:
Download CSV
Histogram 
112,70
118,40
108,10
105,40
114,60
106,90
115,90
109,80
101,80
114,20
110,80
108,40
127,50
128,60
116,60
127,40
105,00
108,30
125,00
111,60
106,50
130,30
115,00
116,10
134,00
126,50
125,80
136,40
114,90
110,90
125,50
116,80
116,80
125,50
104,20
115,10
132,80
123,30
124,80
122,00
117,40
117,90
137,40
114,60
124,70
129,60
109,40
120,90
134,90
136,30
133,20
127,20
122,70
120,50
137,80
119,10
124,30
134,30
121,70
125,00

Tables (Output of Computation)





Summary of compuational 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 compuational 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=1315&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]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=1315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1315&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean108.94120.151666666667
Biased Variance252.93106666666789.3981638888889
Biased Standard Deviation15.90380667219859.45506022661352
Covariance103.851457627119
Correlation0.679122267263171
Determination0.46120705389267
T-Test7.04613592232611
p-value (2 sided)2.45216469352272e-09
p-value (1 sided)1.22608234676136e-09
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 108.94 & 120.151666666667 \tabularnewline
Biased Variance & 252.931066666667 & 89.3981638888889 \tabularnewline
Biased Standard Deviation & 15.9038066721985 & 9.45506022661352 \tabularnewline
Covariance & 103.851457627119 \tabularnewline
Correlation & 0.679122267263171 \tabularnewline
Determination & 0.46120705389267 \tabularnewline
T-Test & 7.04613592232611 \tabularnewline
p-value (2 sided) & 2.45216469352272e-09 \tabularnewline
p-value (1 sided) & 1.22608234676136e-09 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1315&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]108.94[/C][C]120.151666666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]252.931066666667[/C][C]89.3981638888889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]15.9038066721985[/C][C]9.45506022661352[/C][/ROW]
[ROW][C]Covariance[/C][C]103.851457627119[/C][/ROW]
[ROW][C]Correlation[/C][C]0.679122267263171[/C][/ROW]
[ROW][C]Determination[/C][C]0.46120705389267[/C][/ROW]
[ROW][C]T-Test[/C][C]7.04613592232611[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.45216469352272e-09[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.22608234676136e-09[/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=1315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1315&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
Mean108.94120.151666666667
Biased Variance252.93106666666789.3981638888889
Biased Standard Deviation15.90380667219859.45506022661352
Covariance103.851457627119
Correlation0.679122267263171
Determination0.46120705389267
T-Test7.04613592232611
p-value (2 sided)2.45216469352272e-09
p-value (1 sided)1.22608234676136e-09
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')