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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 computationWed, 20 Jul 2016 22:21:58 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jul/20/t1469049824ypklv7lbcbly2lo.htm/, Retrieved Sat, 04 May 2024 04:05:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295905, Retrieved Sat, 04 May 2024 04:05:09 +0000
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Original text written by user:PIB en millones según la estimación para el año 2016 del Fondo Monetario Internacional
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Correlación núm v...] [2016-07-20 21:21:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7
14
3
15
5
4
1
3
49
4
1
1
20
2
13
21
4
13
14
8
1
1
1
7
4
3
3
12
1
6
1
2
2
2
191
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Dataseries Y:
Download CSV
Histogram 
404293
1138085
494121
3101247
1631943
482347
422422
332477
3934664
258702
149692
1092634
1615074
224999
2703378
2756748
8642758
2170909
4901102
1848518
17793
815646
1091700
832623
356209
168187
1005449
3684643
1720027
473413
160998
1665332
1099030
339481
18558129
552298
3010746
2227176
1108111
982380
971967
741031
723518
667443
647823
578651
576547
515745
471877
429120
414566
413846
389149
319818
289791
288382
285976
281939
287533
258444
257417
223024
187947
184438
183358
171363
169445
167692
141861
138461
136855
126968
125862
114701
97502
91096
88600
87196
83057
82725
82355
79884
78621
75535
74888
74391
73463
72644
70091
64799
63964
62709
60977
55730
54205
52947
49081
44306
41057
40532
37549
37322
36687
35832
34844
34575
33187
32650
31333
30878
29037
28102
28058
25341
25323
24647
24566
23306
22948
20095
19053
18901
18745
18595
15382
15154
10849
9166
2680
2097

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295905&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295905&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295905&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean3.38461538461538712209.992307692
Biased Variance305.2366863905333700970998399.47
Biased Standard Deviation17.47102419409161923790.78862528
Covariance29805884.8479428
Correlation0.879978722415062
Determination0.774362551903245
T-Test20.9590486792466
p-value (2 sided)3.31407262476996e-43
p-value (1 sided)1.65703631238498e-43
95% CI of Correlation[0.834189033788071, 0.913718151370211]
Degrees of Freedom128
Number of Observations130

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3.38461538461538 & 712209.992307692 \tabularnewline
Biased Variance & 305.236686390533 & 3700970998399.47 \tabularnewline
Biased Standard Deviation & 17.4710241940916 & 1923790.78862528 \tabularnewline
Covariance & 29805884.8479428 \tabularnewline
Correlation & 0.879978722415062 \tabularnewline
Determination & 0.774362551903245 \tabularnewline
T-Test & 20.9590486792466 \tabularnewline
p-value (2 sided) & 3.31407262476996e-43 \tabularnewline
p-value (1 sided) & 1.65703631238498e-43 \tabularnewline
95% CI of Correlation & [0.834189033788071, 0.913718151370211] \tabularnewline
Degrees of Freedom & 128 \tabularnewline
Number of Observations & 130 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295905&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]3.38461538461538[/C][C]712209.992307692[/C][/ROW]
[ROW][C]Biased Variance[/C][C]305.236686390533[/C][C]3700970998399.47[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]17.4710241940916[/C][C]1923790.78862528[/C][/ROW]
[ROW][C]Covariance[/C][C]29805884.8479428[/C][/ROW]
[ROW][C]Correlation[/C][C]0.879978722415062[/C][/ROW]
[ROW][C]Determination[/C][C]0.774362551903245[/C][/ROW]
[ROW][C]T-Test[/C][C]20.9590486792466[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.31407262476996e-43[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.65703631238498e-43[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.834189033788071, 0.913718151370211][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]128[/C][/ROW]
[ROW][C]Number of Observations[/C][C]130[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295905&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295905&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
Mean3.38461538461538712209.992307692
Biased Variance305.2366863905333700970998399.47
Biased Standard Deviation17.47102419409161923790.78862528
Covariance29805884.8479428
Correlation0.879978722415062
Determination0.774362551903245
T-Test20.9590486792466
p-value (2 sided)3.31407262476996e-43
p-value (1 sided)1.65703631238498e-43
95% CI of Correlation[0.834189033788071, 0.913718151370211]
Degrees of Freedom128
Number of Observations130






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 55845, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 18328, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 36.893, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 25.463, p-value < 2.2e-16


\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 55845, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 18328, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 36.893, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 25.463, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295905&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 55845, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 18328, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 36.893, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 25.463, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295905&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295905&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 55845, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 18328, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 36.893, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 25.463, p-value < 2.2e-16


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
library(psychometric)
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
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, sub=main)
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', na.rm = T)
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,'95% CI of Correlation',header=TRUE)
a<-table.element(a,paste('[',CIr(r=cxy, n = lx, level = .95)[1],', ', CIr(r=cxy, n = lx, level = .95)[2],']',sep=''),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')
library(moments)
library(nortest)
jarque.x <- jarque.test(x)
jarque.y <- jarque.test(y)
if(lx>7) {
ad.x <- ad.test(x)
ad.y <- ad.test(y)
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Normality Tests',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.y'),'
',sep=''))
a<-table.row.end(a)
if(lx>7) {
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.y'),'
',sep=''))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
library(car)
bitmap(file='test2.png')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()