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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, 20 Dec 2017 11:51:23 +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/2017/Dec/20/t1513768425xysg1eh6r3lrps8.htm/, Retrieved Tue, 14 May 2024 20:27:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310479, Retrieved Tue, 14 May 2024 20:27:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsTotal population vs. GDP total
Estimated Impact94

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson correlation] [2017-12-20 10:51:23] [97ca58e32232a99e44a6c848c7facc09] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2913021
36117637
2877311
8363404
9054332
1240862
9490583
10895586
3722084
7395599
34005274
4417781
1112607
10474410
5547683
84107606
1331475
5363352
65027512
3926000
81776930
11121341
10000023
318041
74567511
30762701
4560155
7623600
59277417
7182390
16321581
2998083
5447900
2097555
4337141
3097282
506953
2070739
3562045
619428
32409639
16615394
4889252
38042794
10573100
1779676
20246871
142849449
27425676
7291436
5391428
2048583
46576897
9378126
7824909
7641630
10639931
72326914
45870700
8270684
62766365
309348193
23606779
Dataseries Y:
Download CSV
Histogram 
11926953259
1,61207E+11
9260284938
3,90212E+11
52902703376
25713271277
57231904543
4,83549E+11
17164279813
50610031136
1,61346E+12
59665427465
25562251656
2,07016E+11
3,21995E+11
2,18888E+11
19490936349
2,478E+11
2,64684E+12
11638536834
3,41709E+12
2,99362E+11
1,30256E+11
13254818331
4,6779E+11
1,38517E+11
2,21343E+11
2,33755E+11
2,12506E+12
26425379437
1,48047E+11
1,15419E+11
4794357795
23757368290
38009950249
37120517694
53212476812
9407168702
5811604052
4139192053
93216746662
8,3639E+11
4,28527E+11
4,79321E+11
2,38303E+11
1,25122E+11
1,67998E+11
1,52492E+12
5,28207E+11
39460357731
89501012916
48013606745
1,43159E+12
4,88378E+11
5,81209E+11
5642178580
44050929160
7,71877E+11
1,36013E+11
2,8988E+11
2,42968E+12
1,49644E+13
30906749533

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310479&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310479&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310479&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean24594402.5555556633608126910.921
Biased Variance20378160678232623.78864830658927e+24
Biased Standard Deviation45142176.15294221946445043300.55
Covariance79683349611838554112
Correlation0.892470941928219
Determination0.796504382186242
T-Test15.4518851544979
p-value (2 sided)9.24881918741228e-23
p-value (1 sided)4.62440959370614e-23
95% CI of Correlation[0.827737865460179, 0.933760062370229]
Degrees of Freedom61
Number of Observations63

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 24594402.5555556 & 633608126910.921 \tabularnewline
Biased Variance & 2037816067823262 & 3.78864830658927e+24 \tabularnewline
Biased Standard Deviation & 45142176.1529422 & 1946445043300.55 \tabularnewline
Covariance & 79683349611838554112 \tabularnewline
Correlation & 0.892470941928219 \tabularnewline
Determination & 0.796504382186242 \tabularnewline
T-Test & 15.4518851544979 \tabularnewline
p-value (2 sided) & 9.24881918741228e-23 \tabularnewline
p-value (1 sided) & 4.62440959370614e-23 \tabularnewline
95% CI of Correlation & [0.827737865460179, 0.933760062370229] \tabularnewline
Degrees of Freedom & 61 \tabularnewline
Number of Observations & 63 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310479&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]24594402.5555556[/C][C]633608126910.921[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2037816067823262[/C][C]3.78864830658927e+24[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]45142176.1529422[/C][C]1946445043300.55[/C][/ROW]
[ROW][C]Covariance[/C][C]79683349611838554112[/C][/ROW]
[ROW][C]Correlation[/C][C]0.892470941928219[/C][/ROW]
[ROW][C]Determination[/C][C]0.796504382186242[/C][/ROW]
[ROW][C]T-Test[/C][C]15.4518851544979[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]9.24881918741228e-23[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.62440959370614e-23[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.827737865460179, 0.933760062370229][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]61[/C][/ROW]
[ROW][C]Number of Observations[/C][C]63[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310479&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310479&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
Mean24594402.5555556633608126910.921
Biased Variance20378160678232623.78864830658927e+24
Biased Standard Deviation45142176.15294221946445043300.55
Covariance79683349611838554112
Correlation0.892470941928219
Determination0.796504382186242
T-Test15.4518851544979
p-value (2 sided)9.24881918741228e-23
p-value (1 sided)4.62440959370614e-23
95% CI of Correlation[0.827737865460179, 0.933760062370229]
Degrees of Freedom61
Number of Observations63






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1595.3, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5455.4, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.9932, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 14.154, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1595.3, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5455.4, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.9932, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 14.154, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310479&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1595.3, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5455.4, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 8.9932, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 14.154, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310479&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310479&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 = 1595.3, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5455.4, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.9932, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 14.154, 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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Variance',header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Standard Deviation',header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Covariance',header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation',header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Determination',header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-Test',header=TRUE)
a<-table.element(a,as.matrix(corxy$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')
qqPlot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qqPlot(y,main='QQplot of variable y')
dev.off()