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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 computationThu, 23 Nov 2017 13:33:53 +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/Nov/23/t1511441862juyigqcgas41zod.htm/, Retrieved Sat, 18 May 2024 14:38:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308187, Retrieved Sat, 18 May 2024 14:38:55 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [pearsoncorrelation] [2017-11-23 12:33:53] [c3f6c042221bc0560258fcac410d8eeb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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36 000
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11 242
90 215
326
228
14 034
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18 491
12 913
100 000
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17 859
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52 000
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52 000
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27 368
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46 500
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80 000
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70 745
20 516
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24 000
20 000
1 025
70 000
0
3 084 506
9 206
10 882
29 828
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18 269
710
32 031
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10 659
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10 393
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2 662
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9 964
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68 120
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10 000
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41 214
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10 000
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5 000
2 188
25 000
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18 127
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37 000
18 013
17 504
2 803
28 074
637 957
12 804
10 000
27 607
18 736
337
15 869
0
4 123
85 291
16 340
9 133
2 676
0
14 634
0
10 000
3 030
9 695
4 000
2 960
54 938
634 746
7 164
100
1 451 529
55 000
23 747
4 200
127 800
53 779
3 000
9 573
16 897
500
15 463
13 650
20 833
0
22 376
26 253
107 441
16 725
0
66 711
517
13 986
0
18 352
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70 000
1 100
59 343
14 548
7 214
78 780
20 400
0
11 492
2 998
37 240
8 240
11 322
716 360
26 059
9 666
10 000
33 100
24 573
4 700
50 400
0
25 217
22 692
1 921
33 000
0
5 000
80 000
0
2 000
0
46 297
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4 435
104 600
9 950
30 000
5 000
15 000
179 895
14 164
6 620
15 000
25 150
8 537
50
14 768
9 187
176
21 507
3 643
68 350
13 671
26 771
30 540
3 811
111 680
22 465
0
59 450
10 760
19 739
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15 626
30 000
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19 082
10 339
149 066
206 278
14 879
23 609
0
99 014
20 000
57 675
9 517
275 000
20 000
91 500
40 810
12 150
4 489
13 067
0
2 375 691
800
6 743
6 200
11 332
14 795
220 000
13 000
5 000
19 940
10 000
78 320
350
13 618
0
60 000
7 000
2 000
8 510
839 804
24 000
18 782
0
5 590
206 514
9 862
14 051
Dataseries Y:
Download CSV
Histogram 
24
0
10
4
45
2
4
9
3
10
7
40
5
4
8
6
1
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3
44
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0
14
37
3
4
0
8
11
6
4
26
0
37
5
0
4
39
8
0
3
5
5
45
2
0
15
5
4
7
0
7
0
19
1
3
4
57
4
47
8
42
0
52
5
5
29
5
10
10
7
79
38
5
0
43
3
60
7
79
0
8
3
4
9
4
9
2
0
2
26
40
35
79
0
5
0
10
10
2
4
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44
41
43
0
6
5
55
11
3
0
5
76
0
0
2
20
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15
5
18
20
6
23
0
0
14
12
3
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6
17
47
32
0
0
0
3
0
4
2
0
6
1
8
0
5
5
3
9
45
8
5
4
47
10
32
46
5
5
9
34
0
3
38
0
2
30
3
70
0
5
4
22
54
0
3
3
50
0
50
0
15
9
5
40
5
7
5
0
6
24
0
3
45
45
6
5
44
4
50
30
30
0
10
3
7
50
0
7
7
0
79
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55
45
2
14
17
3
0
7
30
10
11
7
5
5
4
0
0
15
0
4
6
7
3
3
6
4
3
0
19
7
6
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10
3
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9
60
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30
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30
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2
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0
0
15
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20
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22
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10
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9
9
0
4
10
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8
3
0
8
48
11
9
0
27
10
9
30

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=308187&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=308187&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308187&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
Mean70742.177257525113.5418060200669
Biased Variance84579047542.3131314.422165300164
Biased Standard Deviation290824.77119790417.7319532285692
Covariance1267822.17545061
Correlation0.245027848863699
Determination0.0600386467187717
T-Test4.35550656855925
p-value (2 sided)1.83007126999879e-05
p-value (1 sided)9.15035634999395e-06
95% CI of Correlation[0.135359658583427, 0.348764746169138]
Degrees of Freedom297
Number of Observations299

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 70742.1772575251 & 13.5418060200669 \tabularnewline
Biased Variance & 84579047542.3131 & 314.422165300164 \tabularnewline
Biased Standard Deviation & 290824.771197904 & 17.7319532285692 \tabularnewline
Covariance & 1267822.17545061 \tabularnewline
Correlation & 0.245027848863699 \tabularnewline
Determination & 0.0600386467187717 \tabularnewline
T-Test & 4.35550656855925 \tabularnewline
p-value (2 sided) & 1.83007126999879e-05 \tabularnewline
p-value (1 sided) & 9.15035634999395e-06 \tabularnewline
95% CI of Correlation & [0.135359658583427, 0.348764746169138] \tabularnewline
Degrees of Freedom & 297 \tabularnewline
Number of Observations & 299 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308187&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]70742.1772575251[/C][C]13.5418060200669[/C][/ROW]
[ROW][C]Biased Variance[/C][C]84579047542.3131[/C][C]314.422165300164[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]290824.771197904[/C][C]17.7319532285692[/C][/ROW]
[ROW][C]Covariance[/C][C]1267822.17545061[/C][/ROW]
[ROW][C]Correlation[/C][C]0.245027848863699[/C][/ROW]
[ROW][C]Determination[/C][C]0.0600386467187717[/C][/ROW]
[ROW][C]T-Test[/C][C]4.35550656855925[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.83007126999879e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]9.15035634999395e-06[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.135359658583427, 0.348764746169138][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]297[/C][/ROW]
[ROW][C]Number of Observations[/C][C]299[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308187&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308187&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
Mean70742.177257525113.5418060200669
Biased Variance84579047542.3131314.422165300164
Biased Standard Deviation290824.77119790417.7319532285692
Covariance1267822.17545061
Correlation0.245027848863699
Determination0.0600386467187717
T-Test4.35550656855925
p-value (2 sided)1.83007126999879e-05
p-value (1 sided)9.15035634999395e-06
95% CI of Correlation[0.135359658583427, 0.348764746169138]
Degrees of Freedom297
Number of Observations299






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 47647, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 231.19, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 85.44, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 30.617, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 47647, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 231.19, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 85.44, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 30.617, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308187&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 47647, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 231.19, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 85.44, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 30.617, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308187&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308187&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 = 47647, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 231.19, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 85.44, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 30.617, 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()