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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 computationSat, 23 Jul 2016 13:55:26 +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/23/t1469313445guphpwz7ciy5z8p.htm/, Retrieved Tue, 07 May 2024 19:34:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295938, Retrieved Tue, 07 May 2024 19:34:49 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20038
13212
166839
3249
138357
1221
548055
11644
1339539
374056
75198
8511
33851
172887
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454039
1699
9575
32996
18521
15813
1774725
56717
12542
16778
32051
1550537
240216
29208
49553
57113
23226
181811
34254
295164
64138
100917
330799
25164
26485
4532
272217
2421682
1818
3355772
38617
235574
2441
58827
1209
8713
19385
309929
138347
17036
2073543
861934
23802
296075
1814763
13891
4123258
35827
184361
60937
163612
7404
11997
31287
45731
48354
64874
11324
296218
12037
9643
1263
1144331
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110009
15938
12995
1977
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19997
11806
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81797
243632
46213
16929
30881
192084
284777
474783
230117
103135
166908
199044
1326015
789
646002
15658
43866
292739
100249
49491
5707
312798
1377873
1199057
78824
492618
664738
523581
9242
48057
395282
4518
28883
48613
718221
47932
26998
131805
370293
2848755
17946996
57471
62644
371337
186205
35955
27066
14197
Dataseries Y:
Download CSV
Histogram 
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14
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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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295938&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295938&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295938&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'Sir Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean445481.4452554743.21167883211679
Biased Variance2663484586863.25290.196067984442
Biased Standard Deviation1632018.5620461717.0351421474681
Covariance27253891.5594676
Correlation0.973141534451188
Determination0.947004446074012
T-Test49.1160208761826
p-value (2 sided)5.41723440687669e-88
p-value (1 sided)2.70861720343835e-88
95% CI of Correlation[0.962519771748754, 0.980782603772405]
Degrees of Freedom135
Number of Observations137

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 445481.445255474 & 3.21167883211679 \tabularnewline
Biased Variance & 2663484586863.25 & 290.196067984442 \tabularnewline
Biased Standard Deviation & 1632018.56204617 & 17.0351421474681 \tabularnewline
Covariance & 27253891.5594676 \tabularnewline
Correlation & 0.973141534451188 \tabularnewline
Determination & 0.947004446074012 \tabularnewline
T-Test & 49.1160208761826 \tabularnewline
p-value (2 sided) & 5.41723440687669e-88 \tabularnewline
p-value (1 sided) & 2.70861720343835e-88 \tabularnewline
95% CI of Correlation & [0.962519771748754, 0.980782603772405] \tabularnewline
Degrees of Freedom & 135 \tabularnewline
Number of Observations & 137 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295938&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]445481.445255474[/C][C]3.21167883211679[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2663484586863.25[/C][C]290.196067984442[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1632018.56204617[/C][C]17.0351421474681[/C][/ROW]
[ROW][C]Covariance[/C][C]27253891.5594676[/C][/ROW]
[ROW][C]Correlation[/C][C]0.973141534451188[/C][/ROW]
[ROW][C]Determination[/C][C]0.947004446074012[/C][/ROW]
[ROW][C]T-Test[/C][C]49.1160208761826[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]5.41723440687669e-88[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.70861720343835e-88[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.962519771748754, 0.980782603772405][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]135[/C][/ROW]
[ROW][C]Number of Observations[/C][C]137[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295938&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295938&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
Mean445481.4452554743.21167883211679
Biased Variance2663484586863.25290.196067984442
Biased Standard Deviation1632018.5620461717.0351421474681
Covariance27253891.5594676
Correlation0.973141534451188
Determination0.947004446074012
T-Test49.1160208761826
p-value (2 sided)5.41723440687669e-88
p-value (1 sided)2.70861720343835e-88
95% CI of Correlation[0.962519771748754, 0.980782603772405]
Degrees of Freedom135
Number of Observations137






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 52219, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 65421, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 32.199, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 39.281, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 52219, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 65421, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 32.199, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 39.281, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295938&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 52219, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 65421, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 32.199, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 39.281, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295938&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295938&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 = 52219, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 65421, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 32.199, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 39.281, 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()