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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, 19 Dec 2010 16:30:48 +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/19/t1292776280ajiv0g0rzkkdpvq.htm/, Retrieved Sun, 05 May 2024 06:08:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112594, Retrieved Sun, 05 May 2024 06:08:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2010-12-18 12:49:04] [f72e5115d7374b3b3f29ba3966e5379d]
- RM D  [Pearson Correlation] [] [2010-12-18 14:06:21] [f72e5115d7374b3b3f29ba3966e5379d]
-   PD      [Pearson Correlation] [] [2010-12-19 16:30:48] [303f3b5c313268114bcf87589378f503] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12
8
8
8
9
7
4
11
7
7
12
10
10
8
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Dataseries Y:
Download CSV
Histogram 
26
23
25
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29
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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' @ 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=112594&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=112594&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112594&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
Mean8.2264150943396222.3333333333333
Biased Variance7.2820695383885115.1530398322851
Biased Standard Deviation2.698530996373493.89269056467183
Covariance-2.14556962025316
Correlation-0.202966928951268
Determination0.0411955742479089
T-Test-2.59722809274516
p-value (2 sided)0.0102912443361978
p-value (1 sided)0.00514562216809888
Degrees of Freedom157
Number of Observations159

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8.22641509433962 & 22.3333333333333 \tabularnewline
Biased Variance & 7.28206953838851 & 15.1530398322851 \tabularnewline
Biased Standard Deviation & 2.69853099637349 & 3.89269056467183 \tabularnewline
Covariance & -2.14556962025316 \tabularnewline
Correlation & -0.202966928951268 \tabularnewline
Determination & 0.0411955742479089 \tabularnewline
T-Test & -2.59722809274516 \tabularnewline
p-value (2 sided) & 0.0102912443361978 \tabularnewline
p-value (1 sided) & 0.00514562216809888 \tabularnewline
Degrees of Freedom & 157 \tabularnewline
Number of Observations & 159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112594&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]8.22641509433962[/C][C]22.3333333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]7.28206953838851[/C][C]15.1530398322851[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.69853099637349[/C][C]3.89269056467183[/C][/ROW]
[ROW][C]Covariance[/C][C]-2.14556962025316[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.202966928951268[/C][/ROW]
[ROW][C]Determination[/C][C]0.0411955742479089[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.59722809274516[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0102912443361978[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00514562216809888[/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=112594&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112594&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
Mean8.2264150943396222.3333333333333
Biased Variance7.2820695383885115.1530398322851
Biased Standard Deviation2.698530996373493.89269056467183
Covariance-2.14556962025316
Correlation-0.202966928951268
Determination0.0411955742479089
T-Test-2.59722809274516
p-value (2 sided)0.0102912443361978
p-value (1 sided)0.00514562216809888
Degrees of Freedom157
Number of Observations159


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
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')