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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 15:54:46 +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/t1291564358y1i9c6onml05po5.htm/, Retrieved Wed, 01 May 2024 18:55:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105433, Retrieved Wed, 01 May 2024 18:55:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Forecasting] [WS9 fout] [2010-12-03 12:26:23] [1fd136673b2a4fecb5c545b9b4a05d64]
- R P   [ARIMA Forecasting] [] [2010-12-03 14:12:57] [b98453cac15ba1066b407e146608df68]
F   P     [ARIMA Forecasting] [WS9: ARIMA foreca...] [2010-12-03 14:39:04] [1fd136673b2a4fecb5c545b9b4a05d64]
- RMPD        [Pearson Correlation] [Paper: Pearson co...] [2010-12-05 15:54:46] [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
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27
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14
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32
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17
28
29
26
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14
25
26
20
18
32
25
25
23
21
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15
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24
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14
24
24
24
24
19
31
22
27
19
25
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21
27
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25
20
21
22
23
25
25
17
19
25
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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
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24
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Dataseries Y:
Download CSV
Histogram 
26
23
25
23
19
29
25
21
22
25
24
18
22
15
22
28
20
12
24
20
21
20
21
23
28
24
24
24
23
23
29
24
18
25
21
26
22
22
22
23
30
23
17
23
23
25
24
24
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21
24
24
28
16
20
29
27
22
28
16
25
24
28
24
23
30
24
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25
25
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23
26
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25
24
29
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27
26
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24
27
24
24
29
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24
24
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20
27
26
25
21
21
19
21
21
16
22
29
15
17
15
21
21
19
24
20
17
23
24
14
19
24
13
22
16
19
25
25
23
24
26
26
25
18
21
26
23
23
22
20
13
24
15
14
22
10
24
22
24
19
20
13
20
22
24
29
12
20
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24
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20

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105433&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105433&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105433&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean22.144654088050322.3333333333333
Biased Variance17.670899094181415.1530398322851
Biased Standard Deviation4.203676854157733.89269056467183
Covariance5.79957805907173
Correlation0.352190108955845
Determination0.124037872846330
T-Test4.71502843665285
p-value (2 sided)5.29774482638246e-06
p-value (1 sided)2.64887241319123e-06
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 & 22.3333333333333 \tabularnewline
Biased Variance & 17.6708990941814 & 15.1530398322851 \tabularnewline
Biased Standard Deviation & 4.20367685415773 & 3.89269056467183 \tabularnewline
Covariance & 5.79957805907173 \tabularnewline
Correlation & 0.352190108955845 \tabularnewline
Determination & 0.124037872846330 \tabularnewline
T-Test & 4.71502843665285 \tabularnewline
p-value (2 sided) & 5.29774482638246e-06 \tabularnewline
p-value (1 sided) & 2.64887241319123e-06 \tabularnewline
Degrees of Freedom & 157 \tabularnewline
Number of Observations & 159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105433&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]22.3333333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]17.6708990941814[/C][C]15.1530398322851[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.20367685415773[/C][C]3.89269056467183[/C][/ROW]
[ROW][C]Covariance[/C][C]5.79957805907173[/C][/ROW]
[ROW][C]Correlation[/C][C]0.352190108955845[/C][/ROW]
[ROW][C]Determination[/C][C]0.124037872846330[/C][/ROW]
[ROW][C]T-Test[/C][C]4.71502843665285[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]5.29774482638246e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.64887241319123e-06[/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=105433&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105433&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
Mean22.144654088050322.3333333333333
Biased Variance17.670899094181415.1530398322851
Biased Standard Deviation4.203676854157733.89269056467183
Covariance5.79957805907173
Correlation0.352190108955845
Determination0.124037872846330
T-Test4.71502843665285
p-value (2 sided)5.29774482638246e-06
p-value (1 sided)2.64887241319123e-06
Degrees of Freedom157
Number of Observations159


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1.4 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
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')