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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 computationFri, 12 Nov 2010 09:39:22 +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/Nov/12/t128955470809d2f4rwhhwo1lw.htm/, Retrieved Tue, 30 Apr 2024 13:01:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=94061, Retrieved Tue, 30 Apr 2024 13:01:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [mini-tutorial cor...] [2010-11-12 09:39:22] [dcc54e7e6e8c80b7c45e040080afe6ab] [Current]
-    D    [Pearson Correlation] [] [2010-11-12 17:37:29] [b1e5ec7263cdefe98ec76e1a1363de05]
-    D      [Pearson Correlation] [] [2010-11-12 18:50:27] [b1e5ec7263cdefe98ec76e1a1363de05]
-             [Pearson Correlation] [mini turtorial : ...] [2010-11-17 09:52:04] [2c786c21adba4dd4c8af44dce5258f06]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
11
7
17
10
12
12
11
11
12
13
14
16
11
10
11
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9
11
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9
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17
9
9
12
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10
11
14
9
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17
5
12
12
6
24
12
12
14
7
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14
8
11
9
11
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11
12
9
15
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15
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10
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8
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11
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8
9
15
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21
14
18
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13
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12
19
15
11
11
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12
16
9
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8
13
17
9
15
8
7
12
14
6
8
17
10
11
14
11
13
12
11
9
12
20
12
13
12
12
9
15
24
7
17
11
17
11
12
14
11
16
21
14
20
13
11
15
19
Dataseries Y:
Download CSV
Histogram 
24
25
30
19
22
22
25
23
17
21
19
19
15
16
23
27
22
14
22
23
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24
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25
26
29
32
25
29
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17
28
29
26
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14
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26
20
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32
25
25
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15
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14
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31
22
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23
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17
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27
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17
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32
21
21
18
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20
17
18
19
22
15
14
18
24
35
29
21
25
20
22
13
26
17
25
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24
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26
24
16
23
18
16
26
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29
21
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27
25
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10
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26
24
29
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24
22
17

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94061&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94061&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean12.855345911949722.1446540880503
Biased Variance11.796685257703417.6708990941814
Biased Standard Deviation3.434630294180644.20367685415773
Covariance3.5400445824377
Correlation0.243646049703442
Determination0.0593633975360922
T-Test3.14773572842313
p-value (2 sided)0.00196949201538432
p-value (1 sided)0.00098474600769216
Degrees of Freedom157
Number of Observations159

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 12.8553459119497 & 22.1446540880503 \tabularnewline
Biased Variance & 11.7966852577034 & 17.6708990941814 \tabularnewline
Biased Standard Deviation & 3.43463029418064 & 4.20367685415773 \tabularnewline
Covariance & 3.5400445824377 \tabularnewline
Correlation & 0.243646049703442 \tabularnewline
Determination & 0.0593633975360922 \tabularnewline
T-Test & 3.14773572842313 \tabularnewline
p-value (2 sided) & 0.00196949201538432 \tabularnewline
p-value (1 sided) & 0.00098474600769216 \tabularnewline
Degrees of Freedom & 157 \tabularnewline
Number of Observations & 159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94061&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]12.8553459119497[/C][C]22.1446540880503[/C][/ROW]
[ROW][C]Biased Variance[/C][C]11.7966852577034[/C][C]17.6708990941814[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.43463029418064[/C][C]4.20367685415773[/C][/ROW]
[ROW][C]Covariance[/C][C]3.5400445824377[/C][/ROW]
[ROW][C]Correlation[/C][C]0.243646049703442[/C][/ROW]
[ROW][C]Determination[/C][C]0.0593633975360922[/C][/ROW]
[ROW][C]T-Test[/C][C]3.14773572842313[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00196949201538432[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00098474600769216[/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=94061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94061&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
Mean12.855345911949722.1446540880503
Biased Variance11.796685257703417.6708990941814
Biased Standard Deviation3.434630294180644.20367685415773
Covariance3.5400445824377
Correlation0.243646049703442
Determination0.0593633975360922
T-Test3.14773572842313
p-value (2 sided)0.00196949201538432
p-value (1 sided)0.00098474600769216
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')