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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 computationWed, 01 Apr 2009 02:26:40 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Apr/01/t1238574691z6fy8kzyd0ezr59.htm/, Retrieved Mon, 13 May 2024 02:04:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39233, Retrieved Mon, 13 May 2024 02:04:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact279

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [correlation betwe...] [2009-04-01 08:26:40] [1984061bf22bf08f21378a4ab826d2a6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.51
0.53
0.505
0.535
0.575
0.53
0.595
0.505
0.81
0.58
0.575
0.715
0.615
0.54
0.675
0.725
0.695
0.83
0.61
0.7
0.78
0.75
0.83
0.985
0.83
0.63
0.74
0.87
1
0.86
Dataseries Y:
Download CSV
Histogram 
0.01
0.005
0.005
0.108
0.063
0.043
0.065
0.013
0.145
0.13
0.283
0.348
0.355
0.293
0.47
0.138
0.485
0.483
0.36
0.405
0.588
0.628
0.59
0.863
0.58
0.523
0.773
0.558
0.955
0.653

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39233&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39233&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39233&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 time6 seconds
R Server'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean0.6876666666666670.363933333333333
Biased Variance0.01985455555555560.0730643288888889
Biased Standard Deviation0.1409061941702900.270304141457154
Covariance0.0330350114942529
Correlation0.83843311063904
Determination0.702970081015858
T-Test8.14042984808558
p-value (2 sided)7.31627181060901e-09
p-value (1 sided)3.65813590530450e-09
Degrees of Freedom28
Number of Observations30

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.687666666666667 & 0.363933333333333 \tabularnewline
Biased Variance & 0.0198545555555556 & 0.0730643288888889 \tabularnewline
Biased Standard Deviation & 0.140906194170290 & 0.270304141457154 \tabularnewline
Covariance & 0.0330350114942529 \tabularnewline
Correlation & 0.83843311063904 \tabularnewline
Determination & 0.702970081015858 \tabularnewline
T-Test & 8.14042984808558 \tabularnewline
p-value (2 sided) & 7.31627181060901e-09 \tabularnewline
p-value (1 sided) & 3.65813590530450e-09 \tabularnewline
Degrees of Freedom & 28 \tabularnewline
Number of Observations & 30 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39233&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]0.687666666666667[/C][C]0.363933333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0198545555555556[/C][C]0.0730643288888889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.140906194170290[/C][C]0.270304141457154[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0330350114942529[/C][/ROW]
[ROW][C]Correlation[/C][C]0.83843311063904[/C][/ROW]
[ROW][C]Determination[/C][C]0.702970081015858[/C][/ROW]
[ROW][C]T-Test[/C][C]8.14042984808558[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]7.31627181060901e-09[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]3.65813590530450e-09[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]28[/C][/ROW]
[ROW][C]Number of Observations[/C][C]30[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39233&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39233&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
Mean0.6876666666666670.363933333333333
Biased Variance0.01985455555555560.0730643288888889
Biased Standard Deviation0.1409061941702900.270304141457154
Covariance0.0330350114942529
Correlation0.83843311063904
Determination0.702970081015858
T-Test8.14042984808558
p-value (2 sided)7.31627181060901e-09
p-value (1 sided)3.65813590530450e-09
Degrees of Freedom28
Number of Observations30


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')