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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 computationThu, 17 Nov 2011 03:23:35 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/17/t1321518223qta86umfpk1r7ft.htm/, Retrieved Fri, 19 Apr 2024 09:47:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=144276, Retrieved Fri, 19 Apr 2024 09:47:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2011-11-17 08:23:35] [3eda06f9e914bde86f40a764ca976328] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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35
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31
27
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Dataseries Y:
Download CSV
Histogram 
41
39
30
31
34
35
39
34
36
37
38
36
38
39
33
32
36
38
39
32
32
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39
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39
41
36
33
33
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31
27
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34
32
29
36
29
35
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38
35
38
37
38
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38
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32
37
39
29
37
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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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=144276&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=144276&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=144276&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' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean34.092592592592634.6234567901235
Biased Variance12.540809327846411.3211781740588
Biased Standard Deviation3.541300513631453.36469585164229
Covariance4.41396365309409
Correlation0.368155267777861
Determination0.135538301192589
T-Test5.00862056456748
p-value (2 sided)1.43595671975305e-06
p-value (1 sided)7.17978359876525e-07
Degrees of Freedom160
Number of Observations162

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 34.0925925925926 & 34.6234567901235 \tabularnewline
Biased Variance & 12.5408093278464 & 11.3211781740588 \tabularnewline
Biased Standard Deviation & 3.54130051363145 & 3.36469585164229 \tabularnewline
Covariance & 4.41396365309409 \tabularnewline
Correlation & 0.368155267777861 \tabularnewline
Determination & 0.135538301192589 \tabularnewline
T-Test & 5.00862056456748 \tabularnewline
p-value (2 sided) & 1.43595671975305e-06 \tabularnewline
p-value (1 sided) & 7.17978359876525e-07 \tabularnewline
Degrees of Freedom & 160 \tabularnewline
Number of Observations & 162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=144276&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]34.0925925925926[/C][C]34.6234567901235[/C][/ROW]
[ROW][C]Biased Variance[/C][C]12.5408093278464[/C][C]11.3211781740588[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.54130051363145[/C][C]3.36469585164229[/C][/ROW]
[ROW][C]Covariance[/C][C]4.41396365309409[/C][/ROW]
[ROW][C]Correlation[/C][C]0.368155267777861[/C][/ROW]
[ROW][C]Determination[/C][C]0.135538301192589[/C][/ROW]
[ROW][C]T-Test[/C][C]5.00862056456748[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.43595671975305e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]7.17978359876525e-07[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]160[/C][/ROW]
[ROW][C]Number of Observations[/C][C]162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=144276&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=144276&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
Mean34.092592592592634.6234567901235
Biased Variance12.540809327846411.3211781740588
Biased Standard Deviation3.541300513631453.36469585164229
Covariance4.41396365309409
Correlation0.368155267777861
Determination0.135538301192589
T-Test5.00862056456748
p-value (2 sided)1.43595671975305e-06
p-value (1 sided)7.17978359876525e-07
Degrees of Freedom160
Number of Observations162


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')