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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 computationMon, 20 Dec 2010 11:32:40 +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/20/t1292844620vsjc31f9q6bwu5q.htm/, Retrieved Fri, 03 May 2024 21:48:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112853, Retrieved Fri, 03 May 2024 21:48:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [] [2010-12-20 11:28:40] [1908ef7bb1a3d37a854f5aaad1a1c348]
-    D    [Pearson Correlation] [] [2010-12-20 11:32:40] [23ca1b0f6f6de1e008a90be3f55e3db8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19,6000
16,0000
17,7000
19,8000
17,0000
17,4000
18,9000
15,7000
15,2000
15,8000
16,0000
16,1000
16,2000
12,5000
14,8000
15,4000
13,6000
14,2000
15,0000
14,1000
13,7000
14,4000
15,6000
19,7000
20,4000
16,1000
20,1000
20,6000
19,3000
20,5000
19,2000
19,0000
18,7000
16,5000
19,0000
20,5000
18,4000
16,2000
18,1000
19,3000
18,3000
17,2000
19,6000
17,2000
17,4000
16,0000
18,5000
18,4000
18,2000
14,9000
16,3000
18,3000
18,0000
15,9000
19,6000
16,6000
16,2000
16,6000
17,5000
16,2000
17,5000
13,8000
14,9000
17,2000
15,6000
16,2000
17,4000
15,1000
14,5000
15,1000
15,5000
15,9000
15,9000
12,3000
14,4000
16,0000
13,9000
14,7000
16,2000
13,8000
13,2000
13,5000
13,5000
15,0000
14,5000
10,5000
13,7000
13,9000
13,4000
14,0000
14,3000
13,3000
13,2000
12,6000
13,7000
15,6000
14,4000
11,0000
13,7000
13,8000
14,3000
14,0000
14,6000
13,1000
13,2000
11,6000
13,3000
14,4000
13,3000
11,3000
13,2000
14,1000
14,0000
12,9000
15,2000
13,6000
13,7000
Dataseries Y:
Download CSV
Histogram 
18,9000
16,6000
17,2000
19,2000
17,1000
17,7000
18,7000
15,9000
16,0000
16,8000
16,0000
16,8000
16,3000
13,6000
14,3000
15,5000
13,9000
14,3000
15,8000
14,5000
15,1000
15,8000
17,2000
20,4000
21,3000
18,2000
20,2000
21,1000
19,7000
21,5000
20,2000
19,0000
20,2000
18,0000
19,5000
20,3000
18,0000
16,4000
17,8000
18,5000
18,2000
16,7000
19,1000
16,8000
17,5000
16,2000
17,9000
17,7000
17,2000
15,7000
15,2000
17,7000
17,4000
15,9000
19,7000
16,7000
16,9000
18,0000
17,6000
15,2000
16,5000
14,7000
14,1000
16,9000
15,2000
15,4000
16,8000
14,8000
14,1000
15,0000
14,8000
15,0000
15,1000
12,8000
13,0000
15,7000
12,8000
13,9000
15,4000
13,2000
12,7000
13,5000
12,8000
13,9000
13,3000
10,7000
12,3000
12,9000
12,5000
13,0000
13,9000
13,1000
13,1000
13,0000
12,8000
14,2000
13,0000
11,2000
12,1000
12,9000
13,2000
13,2000
13,5000
12,4000
12,4000
11,6000
12,6000
13,1000
12,3000
11,4000
11,8000
13,4000
13,6000
12,9000
14,5000
13,3000
13,5000

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112853&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]3 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=112853&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112853&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean15.723931623931615.5350427350427
Biased Variance5.34882898677776.5316779896267
Biased Standard Deviation2.312753550808582.55571477078854
Covariance5.69277483053345
Correlation0.954892306670436
Determination0.911819317338385
T-Test34.4839166105132
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom115
Number of Observations117

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 15.7239316239316 & 15.5350427350427 \tabularnewline
Biased Variance & 5.3488289867777 & 6.5316779896267 \tabularnewline
Biased Standard Deviation & 2.31275355080858 & 2.55571477078854 \tabularnewline
Covariance & 5.69277483053345 \tabularnewline
Correlation & 0.954892306670436 \tabularnewline
Determination & 0.911819317338385 \tabularnewline
T-Test & 34.4839166105132 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 115 \tabularnewline
Number of Observations & 117 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112853&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]15.7239316239316[/C][C]15.5350427350427[/C][/ROW]
[ROW][C]Biased Variance[/C][C]5.3488289867777[/C][C]6.5316779896267[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.31275355080858[/C][C]2.55571477078854[/C][/ROW]
[ROW][C]Covariance[/C][C]5.69277483053345[/C][/ROW]
[ROW][C]Correlation[/C][C]0.954892306670436[/C][/ROW]
[ROW][C]Determination[/C][C]0.911819317338385[/C][/ROW]
[ROW][C]T-Test[/C][C]34.4839166105132[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]115[/C][/ROW]
[ROW][C]Number of Observations[/C][C]117[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112853&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112853&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
Mean15.723931623931615.5350427350427
Biased Variance5.34882898677776.5316779896267
Biased Standard Deviation2.312753550808582.55571477078854
Covariance5.69277483053345
Correlation0.954892306670436
Determination0.911819317338385
T-Test34.4839166105132
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom115
Number of Observations117


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')