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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, 05 Dec 2010 15:33:01 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/05/t12915631024vhd52o2satukhl.htm/, Retrieved Wed, 01 May 2024 22:38:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105422, Retrieved Wed, 01 May 2024 22:38:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Paper: Pearson co...] [2010-12-05 15:33:01] [380f6bceef280be3d93cc6fafd18141e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
24
25
30
19
22
22
25
23
17
21
19
19
15
16
23
27
22
14
22
23
23
21
19
18
20
23
25
19
24
22
25
26
29
32
25
29
28
17
28
29
26
25
14
25
26
20
18
32
25
25
23
21
20
15
30
24
26
24
22
14
24
24
24
24
19
31
22
27
19
25
20
21
27
23
25
20
21
22
23
25
25
17
19
25
19
20
26
23
27
17
17
19
17
22
21
32
21
21
18
18
23
19
20
21
20
17
18
19
22
15
14
18
24
35
29
21
25
20
22
13
26
17
25
20
19
21
22
24
21
26
24
16
23
18
16
26
19
21
21
22
23
29
21
21
23
27
25
21
10
20
26
24
29
19
24
19
24
22
17
Dataseries Y:
Download CSV
Histogram 
24
25
17
18
18
16
20
16
18
17
23
30
23
18
15
12
21
15
20
31
27
34
21
31
19
16
20
21
22
17
24
25
26
25
17
32
33
13
32
25
29
22
18
17
20
15
20
33
29
23
26
18
20
11
28
26
22
17
12
14
17
21
19
18
10
29
31
19
9
20
28
19
30
29
26
23
13
21
19
28
23
18
21
20
23
21
21
15
28
19
26
10
16
22
19
31
31
29
19
22
23
15
20
18
23
25
21
24
25
17
13
28
21
25
9
16
19
17
25
20
29
14
22
15
19
20
15
20
18
33
22
16
17
16
21
26
18
18
17
22
30
30
24
21
21
29
31
20
16
22
20
28
38
22
20
17
28
22
31

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105422&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105422&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105422&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean22.144654088050321.5849056603774
Biased Variance17.670899094181432.5446778212887
Biased Standard Deviation4.203676854157735.70479428387113
Covariance10.2566276570337
Correlation0.425006175572502
Determination0.180630249274764
T-Test5.88308473256788
p-value (2 sided)2.352110550774e-08
p-value (1 sided)1.176055275387e-08
Degrees of Freedom157
Number of Observations159

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 22.1446540880503 & 21.5849056603774 \tabularnewline
Biased Variance & 17.6708990941814 & 32.5446778212887 \tabularnewline
Biased Standard Deviation & 4.20367685415773 & 5.70479428387113 \tabularnewline
Covariance & 10.2566276570337 \tabularnewline
Correlation & 0.425006175572502 \tabularnewline
Determination & 0.180630249274764 \tabularnewline
T-Test & 5.88308473256788 \tabularnewline
p-value (2 sided) & 2.352110550774e-08 \tabularnewline
p-value (1 sided) & 1.176055275387e-08 \tabularnewline
Degrees of Freedom & 157 \tabularnewline
Number of Observations & 159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105422&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]22.1446540880503[/C][C]21.5849056603774[/C][/ROW]
[ROW][C]Biased Variance[/C][C]17.6708990941814[/C][C]32.5446778212887[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.20367685415773[/C][C]5.70479428387113[/C][/ROW]
[ROW][C]Covariance[/C][C]10.2566276570337[/C][/ROW]
[ROW][C]Correlation[/C][C]0.425006175572502[/C][/ROW]
[ROW][C]Determination[/C][C]0.180630249274764[/C][/ROW]
[ROW][C]T-Test[/C][C]5.88308473256788[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.352110550774e-08[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.176055275387e-08[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]157[/C][/ROW]
[ROW][C]Number of Observations[/C][C]159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105422&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105422&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
Mean22.144654088050321.5849056603774
Biased Variance17.670899094181432.5446778212887
Biased Standard Deviation4.203676854157735.70479428387113
Covariance10.2566276570337
Correlation0.425006175572502
Determination0.180630249274764
T-Test5.88308473256788
p-value (2 sided)2.352110550774e-08
p-value (1 sided)1.176055275387e-08
Degrees of Freedom157
Number of Observations159


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')