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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 computationFri, 09 Nov 2007 04:33:47 -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/Nov/09/t11946078357qmwb33iroqmkfk.htm/, Retrieved Mon, 06 May 2024 13:29:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=736, Retrieved Mon, 06 May 2024 13:29:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact240

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson Correlati...] [2007-11-09 11:33:47] [be05d2a6ec818ae782d70be836232bb4] [Current]
-    D    [Pearson Correlation] [Correlation manne...] [2008-12-11 23:43:11] [4ddbf81f78ea7c738951638c7e93f6ee]
-    D      [Pearson Correlation] [Correlation manne...] [2008-12-11 23:46:52] [4ddbf81f78ea7c738951638c7e93f6ee]
-    D        [Pearson Correlation] [Correlation vrouw...] [2008-12-11 23:49:12] [4ddbf81f78ea7c738951638c7e93f6ee]
- R PD    [Pearson Correlation] [Paper: pearson co...] [2008-12-13 22:17:07] [005293453b571dbccb80b45226e44173]
-    D    [Pearson Correlation] [] [2008-12-21 23:01:34] [82d1081ec88d38a0607f8d504e46982e]
-    D    [Pearson Correlation] [] [2008-12-21 23:05:38] [82d1081ec88d38a0607f8d504e46982e]
-    D    [Pearson Correlation] [] [2008-12-21 23:08:56] [82d1081ec88d38a0607f8d504e46982e]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
112,6
113,8
107,8
103,2
103,3
101,2
107,7
110,4
101,9
115,9
89,9
88,6
117,2
123,9
100
103,6
94,1
98,7
119,5
112,7
104,4
124,7
89,1
97
121,6
118,8
114
111,5
97,2
102,5
113,4
109,8
104,9
126,1
80
96,8
117,2
112,3
117,3
111,1
102,2
104,3
122,9
107,6
121,3
131,5
89
104,4
128,9
135,9
133,3
121,3
120,5
120,4
137,9
126,1
133,2
146,6
103,4
117,2
Dataseries Y:
Download CSV
Histogram 
105,1
113,3
99,1
100,3
93,5
98,8
106,2
98,3
102,1
117,1
101,5
80,5
105,9
109,5
97,2
114,5
93,5
100,9
121,1
116,5
109,3
118,1
108,3
105,4
116,2
111,2
105,8
122,7
99,5
107,9
124,6
115
110,3
132,7
99,7
96,5
118,7
112,9
130,5
137,9
115
116,8
140,9
120,7
134,2
147,3
112,4
107,1
128,4
137,7
135
151
137,4
132,4
161,3
139,8
146
154,6
142,1
120,5

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=736&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=736&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=736&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
Mean111.726666666667117.311666666667
Biased Variance181.492288888889297.600030555556
Biased Standard Deviation13.471907396092417.2510878078907
Covariance183.34595480226
Correlation0.775758457594566
Determination0.6018011845295
T-Test9.36247204571827
p-value (2 sided)3.36397576461422e-13
p-value (1 sided)1.68198788230711e-13
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 111.726666666667 & 117.311666666667 \tabularnewline
Biased Variance & 181.492288888889 & 297.600030555556 \tabularnewline
Biased Standard Deviation & 13.4719073960924 & 17.2510878078907 \tabularnewline
Covariance & 183.34595480226 \tabularnewline
Correlation & 0.775758457594566 \tabularnewline
Determination & 0.6018011845295 \tabularnewline
T-Test & 9.36247204571827 \tabularnewline
p-value (2 sided) & 3.36397576461422e-13 \tabularnewline
p-value (1 sided) & 1.68198788230711e-13 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=736&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]111.726666666667[/C][C]117.311666666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]181.492288888889[/C][C]297.600030555556[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]13.4719073960924[/C][C]17.2510878078907[/C][/ROW]
[ROW][C]Covariance[/C][C]183.34595480226[/C][/ROW]
[ROW][C]Correlation[/C][C]0.775758457594566[/C][/ROW]
[ROW][C]Determination[/C][C]0.6018011845295[/C][/ROW]
[ROW][C]T-Test[/C][C]9.36247204571827[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.36397576461422e-13[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.68198788230711e-13[/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=736&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=736&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
Mean111.726666666667117.311666666667
Biased Variance181.492288888889297.600030555556
Biased Standard Deviation13.471907396092417.2510878078907
Covariance183.34595480226
Correlation0.775758457594566
Determination0.6018011845295
T-Test9.36247204571827
p-value (2 sided)3.36397576461422e-13
p-value (1 sided)1.68198788230711e-13
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')