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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationMon, 25 Jul 2011 17:18:17 -0400
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/Jul/26/t13116294687ax9fe9g7td5liu.htm/, Retrieved Thu, 16 May 2024 18:14:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123120, Retrieved Thu, 16 May 2024 18:14:37 +0000
QR Codes:

Original text written by user:Economic Freedom index for 21 1st world countries vs. Gini UN Income Inequality 2011
IsPrivate?No (this computation is public)
User-defined keywordsUS,EU,UK,Japan, Australia, New Zealand
Estimated Impact233

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Economic Freedom ...] [2011-07-25 21:18:17] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
82.5
82.3
81.9
80.8
78.7
78.6
77.8
74.7
74.5
74
72.8
71.9
71.9
71.8
70.3
70.2
70.2
64.6
64
60.3
60.3
Dataseries Y:
Download CSV
Histogram 
35.2
36.2
33.7
32.6
34.3
24.7
40.8
30.9
36
26.9
24.9
29.1
25
28.3
25.8
34.7
33
32.7
38.5
34.3
36

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123120&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123120&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123120&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean73.05238095238132.0761904761905
Biased Variance43.370113378684821.0722902494331
Biased Standard Deviation6.585598938493364.59045643149275
Covariance-0.928690476190474
Correlation-0.0292570506939854
Determination0.000855975015310431
T-Test-0.127583143042455
p-value (2 sided)0.899819520056714
p-value (1 sided)0.449909760028357
Degrees of Freedom19
Number of Observations21

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 73.052380952381 & 32.0761904761905 \tabularnewline
Biased Variance & 43.3701133786848 & 21.0722902494331 \tabularnewline
Biased Standard Deviation & 6.58559893849336 & 4.59045643149275 \tabularnewline
Covariance & -0.928690476190474 \tabularnewline
Correlation & -0.0292570506939854 \tabularnewline
Determination & 0.000855975015310431 \tabularnewline
T-Test & -0.127583143042455 \tabularnewline
p-value (2 sided) & 0.899819520056714 \tabularnewline
p-value (1 sided) & 0.449909760028357 \tabularnewline
Degrees of Freedom & 19 \tabularnewline
Number of Observations & 21 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123120&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]73.052380952381[/C][C]32.0761904761905[/C][/ROW]
[ROW][C]Biased Variance[/C][C]43.3701133786848[/C][C]21.0722902494331[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]6.58559893849336[/C][C]4.59045643149275[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.928690476190474[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0292570506939854[/C][/ROW]
[ROW][C]Determination[/C][C]0.000855975015310431[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.127583143042455[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.899819520056714[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.449909760028357[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]19[/C][/ROW]
[ROW][C]Number of Observations[/C][C]21[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123120&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123120&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
Mean73.05238095238132.0761904761905
Biased Variance43.370113378684821.0722902494331
Biased Standard Deviation6.585598938493364.59045643149275
Covariance-0.928690476190474
Correlation-0.0292570506939854
Determination0.000855975015310431
T-Test-0.127583143042455
p-value (2 sided)0.899819520056714
p-value (1 sided)0.449909760028357
Degrees of Freedom19
Number of Observations21


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')